designing dynamic delivery parking spots in urban areas to

Research ArticleDesigning Dynamic Delivery Parking Spots in Urban Areas toReduce Traffic Disruptions

Mireia Roca-Riu1 Jin Cao2 Igor Dakic2 and Monica Menendez3

1 Institute for Transport Planning and Systems ETH Zurich HIL F 342 Stefano-Franscini-Platz 5 8093 Zurich Switzerland2Institute for Transport Planning and Systems ETH Zurich HIL F 412 Stefano-Franscini-Platz 5 8093 Zurich Switzerland3Institute for Transport Planning and Systems ETH Zurich HIL F 372 Stefano-Franscini-Platz 5 8093 Zurich Switzerland

Correspondence should be addressed to Mireia Roca-Riu mireiaroca-riuivtbaugethzch

Received 10 February 2017 Revised 16 May 2017 Accepted 12 June 2017 Published 29 August 2017

Academic Editor Jose L Moura

Copyright copy 2017 Mireia Roca-Riu et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Pick-up and delivery services are essential for businesses in urban areas However due to the limited space in city centers it mightbe unfeasible to provide sufficient loadingunloading spots As a result this type of operations often interferes with traffic byoccupying road space (eg illegal parking) In this study a potential solution is investigated Dynamic Delivery Parking Spots(DDPS) With this concept based on the time-varying traffic demand the area allowed for delivery parking changes over timein order to maximize delivery opportunities while reducing traffic disruptions Using the hydrodynamic theory of traffic flow weanalyze the traffic discharging rate on an urban link with DDPS In comparison to the situation without delivery parking theresults show that although DDPS occupy some space on a driving lane it is possible to keep the delay at a local level that is withoutspreading to the network In this paper we provide amethodology for theDDPS design so that the delivery requests can be satisfiedwhile their negative impacts on traffic are reduced A simulation study is used to validate themodel and to estimate delay comparedto real situations with illegal parking showing that DDPS can reduce systemrsquos delay

1 Introduction

Urban logistic facilities devoted to the loading and unload-ing operations from transport companies are essential forefficient urban deliveries [1] Thus urban logistic facilitiesare widely used and typically placed in city centers with ahigh level of commercial activities [2] The existence andthe proper management of these facilities are crucial toserve citiesrsquo needs To minimize their negative effects on thesurroundings loading and unloading facilities are normallyplaced outside driving lanes However this is not alwaysfeasible due to the limited public space in downtown areasIn some areas illegal parking is highly used in freightoperations For example in Paris illegal double parking isused for up to 50 of the freight movements [3] Localauthorities often face a dilemma on how to allocate publicspace among loadingunloading activities traffic parkingpublic transport and so on To address that multiuse lanes

have become an innovative yet pragmatic solution At differ-ent times of the day these lanes can be devoted to differentusages such as general traffic buses only loadingunloadingactivities or residential parking In Spain for example ithas been successfully implemented in Barcelona [4] andBilbao [5] The multiple uses of the lane can accommodatedifferent activities in a day However they block the wholelane (within a given link or potentially across links) evenwhen there is not enough demand of the specific activity touse the entire space In the case of loading and unloadingactivities the demand is rarely high enough to occupy awholelane throughout a link not to mention across multiple linksAdditionally on the traffic side the blockage of the wholelane is simply unwise since the capacity of the street dropsdrastically To address that in this paper we investigate theprovision of DynamicDelivery Parking Spots (DDPS) DDPSoccupy only a portion of the driving lane and the allowedarea changes dynamically over the day to guarantee proper

HindawiJournal of Advanced TransportationVolume 2017 Article ID 6296720 15 pageshttpsdoiorg10115520176296720

2 Journal of Advanced Transportation

traffic performance according to different levels of trafficdemand

DDPS can providemany benefits in practiceThe numberof dedicated (ie fixed) loadingunloading spots can bereduced since some of the operations might happen inDDPS Additionally the city can make a better use of theexisting space for example by devoting part of the trafficlanes to freight activities when the traffic demand is lowAdditionally DDPS could be regulated with a prebookingparking system [6 7] that guarantees the optimal use of thedevoted space

Moreover DDPS can be easily implemented only few andinexpensive infrastructure changes are required technolog-ical equipment is available and the existing trafficparkingmanagement and control strategies can be used For infras-tructure in-pavement lights in the shoulder lane can clearlyindicate the area where delivery is allowed similar to the useof Bus Lane Intermittent Priority (BLIP) [8] Apart from theuse of in-pavement lights vehicle detectors can be placed atthe different spots of the DDPS for detecting the presenceof vehicles Such detectors can also be used to control thecorrect use of DDPS For example when a vehicle is usingincorrectly DDPS a signal could be automatically sent to thecontrol authorities

This paper aims to provide basic guidelines for DDPS onurban areas so that the deliveries can be carried out whiletraffic disruptions are kept to a minimum DDPS providespace for loadingunloading activities on the shoulder laneof the street but they are only allowed if the traffic delayis kept local (ie traffic delay is kept on the link and doesnot spread over the network) In other words traffic mustpass smoothly the upstream intersection the lane drop atthe delivery spot and the downstream intersection withno queue spillover to other links in the network Using thehydrodynamic theory of traffic flow we analyze the trafficdischarge rate at both the upstream and the downstreamintersections taking into consideration that a portion ofthe shoulder lane is blocked In particular we model therelation between the delivery location within the link thetraffic demand arriving from upstream and the disruptionsto traffic Based on such relation the location of the DDPScan be regulated as a function of the traffic demand toreduce the traffic disruptions as much as possible In order tovalidate the developedmodel show its applicability in amorerealistic situation and analyze the effect of stochastic arrivalsa simulation study is performed The simulation is also usedto evaluate the performance of DDPS in comparison to illegaldelivery parking

The rest of this paper is organized as follows Section 2lists and describes the existing literature highlighting thedifferences to this paper Section 3 shows the analyticalmodelwhere generalized suggestions concerning the location ofDDPS are made Section 4 shows a numerical example toillustrate how the model is applied to a particular caseSection 5 validates the model with simulation in a set ofscenarios Then it compares the overall delay between thesystem with DDPS and the current situation with illegalparking Section 6 summarizes the findings of this study

2 Literature Review

On-street parking highly influences urban traffic perfor-mance mostly from three different perspectives First theparking lanes occupy road space leading to reduced trafficcapacity on the road and the neighboring network [9 10]Second the parkingunparking maneuver itself generates atemporary traffic bottleneck which blocks vehicles arrivingfrom upstream and causes extra travel time [11ndash15] Thirdspecial parking behaviors such as illegal (eg double) parkingor loadingunloading trucksbuses take space from drivinglanes reducing the road capacity unreasonably and causinginconvenience and confusion to other travelers [16 17]

As a special case delivery vehicles can cover all thesethree negative aspects and more importantly their load-ingunloading processes and the ensued traffic issues occurrecurrently It is therefore of great importance to improveand optimize the loading and unloading operations to reducetheir effects on the traffic performance To that end multipleresearchers have developed different control schemes [18 19]Recent work [20] evaluated the effects of pick-up maneuverson traffic flows near maximal capacity which were proved tohave amajor impact on traffic conditions In order to evaluatethe effects on travel times a potential tool was developedin [21] and some additional investigations can be found in[22] Very recently the macroscopic impacts of deliveries indouble lane parking in an arterial corridor were assessed witha simulation study [23] Our paper with a different approachis focused on providing guidelines on the location and thenumber of spots avoiding the negative effects at the networklevel

Other researchers have evaluated the traffic effects ofparking maneuvers [24 25] They have proposed a model toanalyze the impact of parking maneuvers on a road segmentand their influence on the capacity of nearby intersectionsand the overall network It is shown that under certainconditions such as low traffic demand or optimum parkinglocation parking maneuvers do not affect traffic throughputeven in caseswhen one-lane road is analyzed Similar patternsare observed for curbside bus stops [26] Evidently load-ingunloading operations last normally much longer [2 27]than the time needed for parking maneuvers and bus stopsbut they happen less frequently and a prebooked schedule asstudied in [6] can be implemented

From the network perspective [28 29] have shown thatat a network level it is possible to remove lanes or even linksto a certain extent without reducing much of the networkcapacity Such findings are encouraging as they indicate thattemporarily removing some portions of a lane might not bevery disruptive if the effects are kept local

Implementation of various Information and TechnologySystems (ITS) strategies such as parking guidance or trafficsignal control has proven to be very beneficial for traffic oper-ations at the network level [30] For example [31] presenteda model for determining the optimal display of parkingguidance and information sign configuration that minimizesqueue lengths and distance traveled while searching forparking Similarly in the fuzzy logic-based model developedby [32] each delivery vehicle can receive information on

Journal of Advanced Transportation 3

whether to park or not based upon the current given stateof the parking (eg space availability)

On the other hand as an important element of ITStraffic signal systems have been one of the most cost effectiveinvestments [33] For example an Adaptive Traffic ControlSystem (ATCS) has been developed as the most advancedtraffic signal system technology for coordinated network con-trol ATCSs systems continuously make small adjustmentsto signal timing parameters in response to changing trafficdemand and patterns [34]These adjustments aim to improvenetwork-wide efficiency by dealing with fluctuations in trafficdemand These systems could also improve the performanceof DDPS in case of nonrecurring traffic conditions [35]

The study of urban freight transport and city logisticpolicies requires specific site-oriented studies to collect dataFor example [2] compared the cities of Rome Barcelona andSantander regarding the current distribution patterns andregulations In different cities policies to reduce the numberof commercial vehicles have been studied and implementedsuch as urban consolidation centers or off-hour deliveriesFreight flows are determined by the interactions among dif-ferent actors shippers carriers and receivers Some of thesepolicies have failed to reduce the demand as they targetedcarriers which do not usually have enough decision powerto change the delivery performance (delivery time locationetc) The problems of parking in urban areas considering thespecific challenges for freight have been studied in [36] Thework analyzed the balance between the demand for parkingand the available on-street supply in a case study on the cityof New York In New York City off-hour delivery programshave been fostered with money incentives for receivers in apilot test providing significant benefits and demonstrating ahigh potential for full implementation [37]This paper on theother hand focuses on the provision of more parking spaceswhen some capacity of the traffic lane is available but thedemand for delivery parking operations remains unchanged

Recently [38] developed a simulation framework forplanningmanaging and controlling urban delivery schemesLast-minute reservations were proved to significantly im-prove the system in terms of the total service time com-pared to a scenario without booking To the best of theauthorsrsquo knowledge there is no study modelling the specificson dynamic usage of a driving lane for loadingunloadingpurposes Hence this paper aims to fill this gap by pro-viding preliminary understanding on how the DDPS couldbe arranged without significantly affecting the performanceof traffic and by validating the systemrsquos parameters in amicrosimulation environment This is considered a firststep towards the implementation of DDPS Further researchmight be needed to address some more practical issuesregarding such implementation

3 Analytical Model

This section is divided into four subsections assumptionsand definitions formulations relaxation of assumptionssummary of the formulations and guidance In the firstsubsection we introduce the scope of the model and the

Delivery(DI)(UI)

L

L1 L2

Figure 1 General situation of the DDPS on a given link between theupstream intersection (UI) and the downstream intersection (DI)Notice that in this example a 2-lane street is presented but themethodology is generalized to any number of lanes 119899 (119899 ge 2)

main tools used for the analysis In the second subsectionwe analyze the discharging rate of both the upstream andthe downstream intersections taking into consideration thelane drop at the location of the delivery area In the thirdsubsection we discuss the relaxation of some assumptionsFinally in the fourth subsection we summarize the formula-tions and provide a roadmap to guide readers to the correctexpression depending on the local conditions including thetraffic demand

31 Assumptions and Definitions Our analysis focuses on astreet with a number of 119899 (119899 ge 2) lanes per direction Onthis street a dynamic delivery area (an area can consist ofseveral spots) is placed on the link between two consecutiveintersections The total length of the link is 119871 the distancebetween the delivery area and the upstream intersection(UI) is 1198711 and the distance between the delivery area andthe downstream intersection (DI) is 1198712 Figure 1 depicts thesituation with an example of a 2-lane street Notice that theloadingunloading vehicles would temporarily occupy thedynamic delivery area (gridded) and block a part of the lanereducing the road capacity All the notation used within thepaper can be found in Table 2 in the Appendix

We assume that the geometry of the street is the samethroughout the link We also assume for simplicity thatthe intersections are coordinated with a green wave signalcontrol Due to the green wave when no delivery operationis conducted (ie there is no blockage) the traffic dischargedfrom the UI should be able to cross the DI without anystop or delay Naturally the conditions change when aloadingunloading operation takes place on the dynamicdelivery area Some vehicles arriving on the shoulder lanewill have to stop upstream of the dynamic delivery areawhile some other vehicles might merge into the other lanesand cross the DI Depending on how large 1198711 is the queuemight (or not) spill over into the UI and affect traffic on theupstream links Therefore to limit the impacts of DDPS ontraffic we aim to find the conditions such that there is noqueue spillback toUI To analyze these potential effects underthe different traffic states we define several variables below

We denote 119888 as the length of the signal cycle and 119892 as thelength of the green signal For the analysis we assume thatthese parameters are the same for both intersections Laterin this section we will discuss how the relaxation of theseassumptions would affect the model


State 2

State 4

State 1

State 3

Flow

(n minus 1)S

nKJ Density

nS

nq

0

(a)

nS

nq nq

Arrival

Virtual departure

Time

Cum

ulat

ive n

umbe

r of v

ehic

les

ts tq

(b)

Figure 2 (a) Triangular fundamental diagram for the street with a number of 119899 lanes (b) Illustrative queuing diagram for undersaturatedconditions

For the purpose of modelling traffic conditions a tri-angular fundamental diagram (FD) is assumed based onthe hydrodynamic theory of traffic flow Such assumptionhas been previously validated with empirical studies [39ndash42]Figure 2(a) depicts an illustrative FD with the different trafficstates that might be observed on a link State 1 represents thetraffic flow arriving from upstream (119902) state 2 represents thestopping traffic in front of the red light state 3 representsthe traffic discharging from the queue at the intersections(assuming there is no queue spillback from downstream)state 4 represents the capacity of the street at the deliveryarea where only a number of 119899 minus 1 lanes can be used Thesaturation flow rate per lane is S thus 119899119878 is the total saturationflow rate of the street and (119899 minus 1)119878 is the link capacity at thelocation of DDPSThe jam density per lane is119870119869 (119899119870119869 for theentire road) Notice that we define the arrival flow rate (ietraffic demand volume) for the whole street as 119902 such that119902 isin [0 119899119878]

The queuing diagram in Figure 2(b) is given as anillustrative example It shows the cumulative number ofarrivals and departures at the UI without the interruption ofloadingunloading vehicles One can notice that the arrivalhas a constant flow of 119902 and the virtual departure rate can beat the maximum of 119899119878 (ie saturation flow) during the greensignal the shaded area is the delay generated by the red signalwithin a cycle The queuing diagram can help in visualizingthe delay generated by potential delivery operations and willbe used in the following subsection to show different cases

We also assume that most of the flow is arriving fromupstream In other words only a rather small number ofturning vehicles enter the link during the red signal (119902119905)compared to the flow arriving from upstream (ie 119902119905 ≪ 119902)For this reason their effects on the overall traffic operationscan be neglected

Note that the DDPS concept is developed for load-ingunloading operations as they have shown to be crucialin an urban context However the facility could serve similarparking operations for other purposes such as service trips

or on-demand passenger transport services In cases whenother operations are allowed in the area it is importantto ensure that the features of such operations are alignedwith the DDPS concept and the model presented here Forinstance the parking duration cannot be unlimited Longservice trips (ie more than 2 h) might not be suitable forDDPS locations where the traffic demand changes rapidlygiven that the allowed parking area will change accordingly

32 Formulations In this subsection we investigate thelocation of the delivery area such that no traffic spillover isgenerated The location is defined by the distance betweenthe delivery area and the neighboring intersections We willfind theminimumdistance values (1198711 and1198712) that guaranteethat no traffic spillover is caused to other links (ieminimumvalues for 1198711 and 1198712) Denote such minimum distances as 1198891and 1198892 To find their formulations we first define some newvariables

In the absence of DDPS the maximum number ofvehicles (119873) that can be discharged during a cycle in a streetwith 119899 lanes can be calculated using (1) If the intersection isundersaturated (119902 le 119899(119878119892119888)) 119873 is the total traffic demandarriving at the intersection in one cycle (119902119888) given ourassumption that the number of turning vehicles is negligibleIf the intersection is oversaturated (119902 gt 119899(119878119892119888)) 119873 isthe maximum number of vehicles that can discharge (at thesaturation flow rate) during the green signal (119899119878119892)

119873 = 119902119888 if 119902 le 119899119878119892

119888 119899119878119892 if 119902 gt 119899119878119892

119888 (1)

In the presence of DDPS the maximum number ofvehicles which can be discharged at the intersection duringa cycle by the 119899 minus 1 lanes that are not blocked 119873119889 can becalculated using (2) Note that due to the merging effectsthe number of discharged vehicles will be reduced by a factorof 120573 isin [0 1] A factor equal to 1 represents a perfect merge


of the vehicles on the shoulder lane to the immediate nextlane causing no decrease in the lane capacityThis factor alsodepends on the number of remaining free lanes the higherthe number of lanes the smaller the overall effect (ie thehigher the 120573) Merging effects and the impact of lane changeshave been studied in freeway environments either with anendogenous model [43ndash45] simulation [46 47] or empiricaldata [48 49] In this paper as it will be later shown the 120573parameter can be easily calibrated with a simple simulationexperiment performed in a controlled manner

119873119889 =

119902119888 if 119902 le (119899 minus 1) 119878119892119888 120573

(119899 minus 1) 119878119892120573 if 119902 gt (119899 minus 1) 119878119892119888 120573 (2)

Denote119873119894 119894 isin 1 2 as themaximumnumber of vehiclesthat could be accommodated in the distance of 119889119894 in the lanewith the delivery area Its expression is written in

119873119894 = 119889119894119870119869 forall119894 isin 1 2 (3)

1198731 and 1198732 are the number of queued (jammed) vehicles thatcould fit into the space before or after the dynamic deliveryarea on a single lane Intuitively the larger1198731 and1198732 are theless traffic delay the loadingunloading operation causes Inthe case of1198731 a larger space can guarantee that the queuewillnot spill over to the UI In the case of1198732 a larger space wouldallow storing enough vehicles in front of the DI to guaranteethat it does not starve fromvehiclersquos flowonce the green signalstarts

In other words to avoid a service rate reduction at theUI independently of the duration of the operation 1198731 mustbe equal to or larger than the difference between 119873 and 119873119889By formulating 1198731 ge 119873 minus 119873119889 we can obtain 1198891 = 1198731119870119869it is written as (4a) (4b) and (4c) where 120573 = (119899 minus (119899 minus 1)120573)represents the overall percentage of capacity lost at theDDPS

1198891 = 0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573] (4a)

1198891 = 119902119888 minus (119899 minus 1) 119878119892120573119870119869 if 119902 isin [(119899 minus 1) 119878119892

119888 120573 119899119878119892119888 ] (4b)

1198891 = 119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (4c)

In other words when 1198711 is larger than 1198891 the servicerate at the UI is not affected and the delivery area doesnot generate lingering delays affecting the upstream trafficperformance Note that for long links 119871 gt 119878119892120573119870119869 it willbe possible to allow DDPS without affecting the UI

Figure 3 shows the three pieces of linear curves resultingfrom the plot of the three subequations above ((4a)ndash(4c))Each of the three pieces corresponds to a different scenarioaccording to the traffic demand The traffic demand isanalyzed between 0 and the total capacity of the link (119899119878)Thetwo relevant traffic demand levels where scenarios change are119899(119878119892119888) representing the traffic capacity at the intersectionwhen using all lanes and (119899 minus 1)(119878119892119888)120573 representing the

nSg

c

d1

cKJ

(n minus 1)Sg

c

Sg

KJ

0 nS q

Figure 3 Value of 1198891 in relation to the traffic demand volume 119902

capacity at the intersection when using one less lane (includ-ing the merging effects) Recall that 119892 and 119888 are the durationof green time and the length of signal cycle respectivelyThisleads to the three different scenarios described below

Scenario 1 The UI is very undersaturated 119902 isin [0 (119899 minus1)(119878119892119888)120573] (4a) as the demand is very low Recall that (119899 minus1)(119878119892119888) represents the capacity of an intersectionwhen using119899minus1 lanes and 120573 accounts for the merging effects With suchlow demand the site remains undersaturated even if one laneis completely blocked byDDPS In otherwords the other 119899minus1available lanes can serve all the traffic demand given that thearrival flow is small enough (119873 minus 119873119889 = 0) As a result 1198891 isalso zero (ie the delivery area can occupy all the way backto the UI and the UI would still be able to fully discharge thearriving traffic within every cycle)

Scenario 2 The UI is undersaturated in the absence of adelivery area 119902 isin [(119899 minus 1)(119878119892119888)120573 119899(119878119892119888)] (4b) Howeverthe intersection would become oversaturated if the right lanewas to be completely occupied In other words the demandis lower than the capacity of the intersection using all lanes119899(119878119892119888) but higher than the capacity of the intersection withone lane blocked (119899 minus 1)(119878119892119888)120573 Hence to ensure thatthe intersection remains undersaturated we need to providesome storage space that is 1198711 gt 0The storage space requiredis equivalent to 119873 minus 119873119889 = 119902119888 minus (119899 minus 1)119878119892120573 The distanceevidently increases as the traffic demand (119902) growsScenario 3 The intersection is oversaturated in any case withor without the delivery area 119902 isin [119899(119878119892119888) 119899119878] (4c) Thedemand exceeds the capacity of the intersection even withall available lanes 119899(119878119892119888) In others words all the lanesdischarge traffic at the saturation flow rate (S) during thewhole green signal DDPS can only be allowed if the spaceremaining on the same lane is able to accommodate thevehicles blocked that is the vehicles arriving from upstreamthat cannot be accommodated in the (119899 minus 1) lanes 119873 minus 119873119889 =119878119892(119899 minus (119899 minus 1)120573) To guarantee this we need a minimumdistance 1198891 = 119878119892120573119870119869 with 120573 = (119899 minus (119899 minus 1)120573) Notice thatthis is independent of the value of 119902 as the amount of vehiclesentering the intersection is limited by the traffic signal not bythe traffic demand

With 1198891 already defined we can now formulate 1198892 (iethe minimum length of 1198712 distance between the deliveryarea and the DI such that the DI does not starve for traffic)


Cum

Time

Virtual departure at the DI

Real departure at the DI due to the delivery blockage Vehicles blocked

by delivery operation (B)

Vehicles cannot pass the DI (B)

(n minus 1)S

(n minus 1)S

ＧＣＨ N1

SN2

S

ＧＣＨ nN1 nN2

nS

nS

nS

q

q

N

N

Figure 4 Virtual departure and real departure curves at the DI for the cases where the service rate at DI is not affected

One should note that the computation of the 1198892 distance atthe DI is different from the case of the UI for two reasonsFirst the arrival pattern has changed sincewe need to accountfor vehicles affected by the delivery operations which can bestored before or after the dynamic delivery area Second thesignal control is correlated between these two intersectionsthat is green wave Therefore the vehicles that successfullydeparted theUI and are not blocked by the delivery operationcan also directly depart the DI However the vehicles whichare held behind the dynamic delivery area can only arrive atthe DI later than they were supposed to (in the worst case allvehicles will arrive during the following red signal and will beforced to discharge during the next cycle) In any case evenwhen some vehicles are forced to wait for the next cycle theright value for 1198892 can limit the disruptions to traffic so thatthe service rate is not reduced We will find 1198892 that satisfiesthis condition

The queuing diagram of Figure 4 depicts the virtualdeparture at the DI and the real departure at the DI dueto the delivery blockage The virtual departure refers to thepotential departure at the DI in the absence of DDPS (iethe same as the departure from the UI assuming no platoondispersion and perfect coordination) Due to the traffic signalcoordination (ie green wave) during the first cycle ofblockage the discharging rate at the DI is (119899 minus 1)119878120573 sincethe blockage makes the full shoulder lane useless and therest of the lanes will be affected by the merging maneuversSome of the vehicles from the first cycle cannot cross the DIin time and are stored in front of the red signal using all lanesavailable downstream of the parking area During the secondcycle of the blockage at the beginning the DI can dischargeat the saturation flow 119899119878 given that vehicles stored in the1198712 area discharge using all available lanes This lasts for aperiod equivalent to themin11987311198781198732119878 as themin1198731 1198732

is the number of vehicles that will be stored within the linkAfterwards the discharging rate drops again to the saturationflowof 119899minus1 lanes that is (119899minus1)119878120573 until either the queue clearsup or the green signal ends

Note that for the departure curve we assume that oncethe green signal is activated vehicles start discharging atthe maximum flow It is true that the effects of perception-reaction time and acceleration time will make the timedischarging at the maximum flow slightly longer Howeverthis will happen at both intersections (UI andDI)when trafficflows are critical (Scenarios 2 and 3 of Figure 3) With thepresence of DDPS there will be vehicles waiting in front ofthe traffic light not only for the UI but also for the DI

The queue left at the end of the second cycle depends onthe value of 1198712 and its relation to 1198711 When 1198712 le 1198711 thenumber of vehicles that can discharge DI is limited by thesmallest distance that is 1198712 When 1198712 ge 1198711 the numberof vehicles that can discharge DI is fixed by 1198711 that is 1198731vehicles can discharge We compare the queue at the DI atthe end of the first and second green signal to see if thequeue diminishes We aim to find the critical length of 1198712for which the queue gets smaller over cycles independentlyof the duration of the blockage Geometrically based onFigure 4 we can obtain the number of vehicles that cannotpass the DI at the end of both the first and the second cycle ofblockage Let us denote119861 as the number of vehicles queuing attheDI at the end of the first green signal and1198611015840 as the numberof vehicles after the second green signalTheir expressions arewritten as

119861 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]

119873 minus (119899 minus 1) 119878119892120573 if 119902 isin [(119899 minus 1) 119878119892119888 120573 119899119878]

(5)


1198611015840 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]

2119873 minus 2 (119899 minus 1) 119878119892120573 minus 1198732 if 119902 isin [(119899 minus 1) 119878119892119888 120573 119899119878]

(6)

Eq (5) calculates the number of vehicles queuing at theDI at the end of the first green signal When 119902 is below thethreshold no vehicles queue as even with the blockage theDI is able to serve all the vehicles within its green signalAbove this threshold the number of vehicles queuing isgiven by the difference between119873 (the maximum number ofvehicles that can be discharged during a cycle) and (119899minus1)119878119892120573(the number of vehicles that can be discharged with one laneblocked)

In a similar way we calculate in (6) 1198611015840 the number ofvehicles queuing at the DI after the second green signalOnce again when the demand is below the given thresh-old no vehicles queue Above this threshold the queuingvehicles are calculated as the sum of the three followingcomponents +2119873 the maximum number of vehicles thatcan be discharged during the two cycles (first and second)minus2(119899 minus 1)119878119892120573 the number of vehicles that can be dischargedwith one lane blocked during the two cycles and minus1198732 thenumber of vehicles that could not pass the DI during thefirst cycle and were stored in front of the delivery area readyto be discharged in the second cycle In both equationsthe threshold represents the maximum flow for which novehicles are delayed during one cycle Below this thresholdno vehicles queue at the DI at the end of the cycle

In the case when the number of blocked vehiclesdecreases after the second cycle the delay decreases overtime Otherwise the delay increases over time From thisaspect if 1198611015840 lt 119861 the delivery operation is acceptable in theopposite case the delivery operation should be avoided sincethe delay will linger over time and sooner or later will spreadover the network Denote 1198892 as the minimum distance of 1198712that would allow this to happen it is written as (7) where120573 = (119899 minus (119899 minus 1)120573)

1198892 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]

119902119888 minus (119899 minus 1) 119878119892120573119870119869 if 119902 isin [(119899 minus 1) 119878119892

119888 120573 119899119878119892119888 ]

119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (7)

In other words if 1198712 ge 1198892 then the service rate at theDI can recover over time DDPS could also be consideredwhen the lingering delay for the duration of the blockageis not significant and can be cleared some cycles after theblockage ends However this is not considered here and willbe developed in future work Although 1198891 and 1198892 are derivedwith different approaches interestingly they lead to the sameexpression In other words for any given traffic demand(119902) the minimum distance to the upstream intersection andthe minimum distance to the downstream intersection areequivalent to each other In the end both intersections havea similar performance with the blockage after the first cycleBoth intersections have exactly the same traffic demand thathas to be served within one cycle The traffic demand is

served with the nonblocked lanes plus the storage capacityConsidering that the capacity of the nonblocked lanes is thesame the storage space in front of or after the blockage areais also equivalent

Figure 5 shows the necessary area to allow the provisionof DDPS in relation to the traffic demand (119902) As can be seenin Figure 5 there are two possible situations when dynamicdelivery areas can be provided

(i) In Figure 5(a) as the link length is larger than2119878119892120573119870119869 the dynamic delivery area is always possiblebetween 119878119892120573119870119869 and 119871 minus 119878119892120573119870119869 However if 119902 issmaller than 119899(119878119892119888) the allowed area can be evenlarger In the extreme case where the demand israther low lt(119899 minus 1)(119878119892119888)120573 the whole lane betweenthe UI and DI can be used for DDPS

(ii) In Figure 5(b) when the link length is smallerthan 2119878119892120573119870119869 but the traffic demand is also smalldynamic delivery areas are still possible Denote 119902maxas the maximum traffic demand volume with whichDDPS are possible it can be found based on 1198891 =119871 minus 1198892 Its expression is written in

119902max = 119871119870119869 + 2 (119899 minus 1) 1198781198921205732119888 (8)

If the link is seen as between location 0 (the start of thelink in the considered traveling direction) and 119871 (the end ofthe link) the parking area can be provided within [1198891 119871minus1198891]33 Relaxation of Assumptions Some of the model assump-tions will be relaxed and discussed here Regarding the signalcontrol the model assumes equality of signal cycle lengthsand equality of green signal lengths for both intersectionsThe case for different signal cycle lengths requires a newmodel formulation which would need to particularly studythe traffic behavior within different combinations of signalcycle length For example if the UI signal cycle length istwice as long as the DI signal cycle length the model wouldneed to be adapted to account for the behavior of the trafficflow until the same pattern is repeated Notice however thatit is very common for cities to have the same signal cyclelength at nearby intersections In such cases theDDPSmodelpresented here will be valid

On the other hand the same signal cycle length at nearbyintersections does not guarantee the same green signal lengthHowever unless there are specific reasons to define it differ-ently many consecutive intersections have similar values forthe green signal length Otherwise bottlenecks or capacitylosswould occur leading to an inefficient signal coordinationIn case when the green signal lengths of the UI and the DIare not exactly equal the results of the model would slightlychange We denote 1198921 and 1198922 as the green time for the UIand the DI respectively In this case the levels of demandthat determine the different possible scenarios of Figure 3will be computed as in (4a) (4b) and (4c) but substituting119892 = min1198921 1198922 In other words different demand thresholdswill be determined by theminimumof the green signal length


0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)

Dynamic parking area

0

Allow dynamicparking space Not allow

q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)

Figure 5 Values of 1198891 and 1198892 in relation to the traffic demand volume 119902 (a) If 119871 ge 2119878119892120573119870119869 (b) If 119871 lt 2119878119892120573119870119869

between the two intersectionsThen we can still use the threescenarios described before for the DDPS design In Scenario1 of Figure 3 for undersaturated states DDPS can still beprovided In scenario 2 for undersaturated traffic states thatcould become oversaturated with DDPS DDPS could beprovided but only under some conditions When 1198921 gt 1198922it is not advisable to provide DDPS as the traffic signalsalready create a bottleneck which could only be worsenedwith DDPS When 1198921 lt 1198922 it would be possible to slightlyreduce 1198892 as the longer green signal at the DI requires lessstorage space after the DDPS blockage Finally in scenario3 for oversaturated states DDPS can only be provided whenthe length of the link is long enough to guarantee sufficientstorage space

Last but not least we now discuss the possible relaxationof the assumption of a uniform arrival pattern The arrivalpattern has been assumed to be uniform at the UI (ievehiclesrsquo arrival is uniformly distributed throughout thelength of the signal cycle)However when the demand arrivesin platoons the model can still be used For instance let usassume that the first vehicle of the platoon arrives at the UIin the middle of the green signal In such case the first halfof the green time is not used but during the second halfvehicles discharge at the saturation flow rate until the end ofthe green or the end of the platoon It could happen that a partof the platoon could not cross theUI in the same green signalIn that case this portion of the platoon remains queuing atthe UI At the next green signal this queue discharges at thesaturation rate until either all incoming vehicles are served orthe green signal ends This behavior is similar to the uniformarrival pattern for our modelling purposes Another examplecould be the case when the first vehicle of the platoon arrivesduring the red signal leaving one green signal completelyunused During the red signal vehicles arrive and queue infront of the UI As in the previous case at the beginning ofthe next green signal the queue discharges at the saturationrate Hence even if vehicles arrive in platoons at the UI the

signal pattern will shape how the vehicles arrive at the DDPSand our model can still be used in these situations

34 Summary of Formulations Assuming that each deliveryspace needs a distance of 119909 meters the number of possiblespaces is (119871 minus 21198891)119909 which depends on 119902 and 119871 Table 1summarizes the generalized formulations for the area whereto provide DDPS and the number of available spaces basedon 119902 and 119871 This table provides a simplified diagram for theproposedmethodologyThe description of all the parametersused can be found inTable 2Under the column scenarios thespecific conditions can be identified and for each of themwe specify if DDPS can be provided (column provision) inwhich space it should be placed (column area to provide) andthe number of delivery spaces (last column)

As shown inTable 1 several steps need to be taken in orderto define a specific case First the length of the link needs to bechecked If 119871 ge 2119878119892120573119870119869 there is always an area available toprovide delivery parking spots When the link length is longthe central area of the link can always be used by the deliveryvehiclesThe exact length of the available area depends on thetraffic demand (119902) If 119871 lt 2119878119892120573119870119869 DDPS can be providedonly if 119902 le 119902max and the length of the area also depends on 119902Finally in the case where 119871 is comparatively short that is 119871 lt2119878119892120573119870119869 and traffic demand is higher than 119902max no deliveryparking spot should be allowed

The applicability of the methodology is illustrated in thenext sectionHowever in order to implementDDPS in realitythe following two conditions are required First a reliable toolfor traffic flow forecasting is essential in order to estimatetraffic flows in the given street Most medium-sized or bigcities already have loop detectors installed which provideinformation that can be used to accurately estimate the flowSecond it should be noted that in periods with saturation oftraffic or in areas with saturated traffic flow within the dayDDPS should not be provided


Table 1 Provision suggestions on the dynamic delivery areas under various conditions

Scenarios Provision Area to provide Number of delivery spaces toprovide

If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573

119870119869 119871 minus 119902119888 minus (119899 minus 1)119878119892120573119870119869 ] 119871 minus 2[119902119888 minus (119899 minus 1)119878119892120573]119870119869119909

If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869

If 119902 le 119902max YesIf 119902 isin [0 (119899 minus 1) 119878119892

119888 120573] [0 119871] 119871119909

If 119902 isin [(119899 minus 1) 119878119892119888 120573 119902max] [119902119888 minus (119899 minus 1)119878119892120573

119870119869 119871 minus 119902119888 minus (119899 minus 1)119878119892120573119870119869 ] 119871 minus 2 [119902119888 minus (119899 minus 1)119878119892120573] 119870119869119909

If 119902 gt 119902max No mdash mdash mdash

Table 2 Parameters acronyms and scenarios

Parameters119861 Number of vehicles queuing at the DI at the end of the first green signal1198611015840 Number of vehicles queuing at the DI at the end of the second green signal119870119869 Jam density per lane119871 Total length of the link1198711 Distance between the delivery area and the upstream intersection1198712 Distance between the delivery area and the downstream intersectionN Maximum number of vehicles that can be discharged during a cycle119873119889 Maximum number of vehicles that can be discharged at the intersection during a cycle by the 119899 minus 1 lanes that are not blocked119873119894119894 isin 1 2 Maximum number of vehicles that could be accommodated in the distance of 119889119894 in the lane with the delivery area

S Saturation flow rate per lane119888 Length of the signal cycle1198891 Minimum distance value of 1198711 that guarantees that no traffic spillover is caused to other links1198892 Minimum distance value of 1198712 that guarantees that no traffic spillover is caused to other links119892 Length of the green signal1198921 1198922 Green time for the UI and the DI119899 Number of lanes per direction119902 Traffic flow arriving from upstream119902max Maximum traffic demand volume with which DDPS are possible119909 Distance needed for each delivery space120573 Factor that represents the merge effect of the vehicles on the shoulder lane to the immediate next lane120573 (119899 minus (119899 minus 1)120573)Transformation of the 120573 parameter to simplify the notation

AcronymsACTS Adaptive Traffic Control SystemDDPS Dynamic Delivery Parking SpotsDI Downstream intersectionFD Fundamental DiagramITS Information and Technology SystemsUI Upstream intersection

ScenariosS0 Illegal parking with random arrival and locationS1 DDPSS2 DDPS with prebooking systemV1 DDPSV2 One lane blocked


4 Illustration of the Model

In this section we use a numerical example (divided into twoparts) to illustrate the application of the proposed method-ology Given the data for a particular link we exemplifyhow the results from the analytical formulation could aid thedesign of a DDPS The results show how the model can beused in a two-lane (119899 = 2) link under realistic conditionsThe following values are assumed saturation flow rate 119878= 1800 vehhrlane jam density is 119870119869 = 150 vehkmlanedistance needed for each delivery space is 119909 = 85 meters [50]and link length 119871 = 120 meters The green signal (119892) lasts 35seconds and the cycle length (119888) is 70 seconds

In the first part we analyze the traffic demands for whichwe can allowDDPSon a given link the location of the parkingspots and the number of spots allowed to be placed In thesecond part we assume a given daily traffic demand patternand provide an overview of how the DDPS should changeover the length of the day

Asmentioned before the calibration of the120573 parameter isperformedwith a simple simulation experimentWe comparethe total number of served vehicles on the one-lane link(without a blockage) and the two-lane link (with a blockage)In case of the one-lane link we simply calculate the totalnumber of vehicles served during the simulation periodGiven that the used traffic demand is large enough to saturatethe intersection this is the maximum number of vehiclesthat the link can handle due to the signalized intersectionThen under the same traffic conditions a two-lane link issimulated with a blockage on the right (shoulder) lane Inthis case we calculate the effect of the merging vehicles Dueto the blockage the vehicles circulating on the shoulder laneneed to merge to the left lane causing less vehicles (originallyarriving at the left lane) to be served compared to the one-lane link scenarioThis reduction was calculated for differentsimulation settings considering diverse lengths of mergingareas and the average value found was 120573 = 09241 Location of DDPS We will first analyze whether it ispossible to provide a dynamic delivery area and the locationsof such provision Following Table 1 we detect which are thepossible scenarios

Step 1 2119878119892120573119870119869 = (2 sdot 1800(353600)108150) sdot 1000 = 252meters

Step 2 Is 119871 ge 2119878119892120573119870119869 No therefore we can only providedynamic delivery when 119902 le 119902max

Step 3 Based on (8) 119902max = (119871119870119869 + 2(119899 minus 1)119878119892120573)2119888 =1290 vehhrStep 4 Area to provide provision

(i) if 119902 isin [0 (119899minus1)(119892119888)119878120573] that is if 119902 isin [0 828] vehhrthe area to provide dynamic delivery is within [0 119871]that is [0 120] meters

(ii) if 119902 isin [(119899 minus 1)(119892119888)119878120573 119902max] that is if 119902 isin [8281290] vehhr the area to provide dynamic delivery is

within [(119902119888minus(119899minus1)119878119892120573)119870119869 119871minus(119902119888minus(119899minus1)119878119892120573)119870119869]that is [013119902 minus 10733 22733 minus 013119902] meters

Step 5 Number of delivery spaces to be provided

(i) if 119902 isin [0 (119899minus1)(119892119888)119878120573] that is if 119902 isin [0 828] vehhrwe can provide 119871119909 that is 14 spaces

(ii) if 119902 isin [(119899 minus 1)(119892119888)119878120573 119902119898119886119909] that is if 119902 isin[828 1290] vehhr we can provide (119871 minus 2(119902119888 minus (119899 minus1)119878119892120573)119870119869)119909 that is 3937 minus 003119902 spaces

The results of the case study are presented in Figure 6(a)

42 Temporal Variations across the Day In this examplewe analyze the link during the entire day and show howthe dynamic delivery area changes according to the trafficdemand The graph on the top of Figure 6(b) shows trafficdemand variations during a given day (an input to themodel)with the two peak hours (morning and afternoon)The graphat the bottom shows the time-space diagram for the dynamicdelivery area

During the times of the day when traffic demand islower than (119899 minus 1)(119892119888)119878120573 we can allow DDPS on thefull link given that the traffic demand is low enough Inother words the other free lane can accommodate all thedemand Furthermore when traffic demand is between (119899 minus1)(119892119888)119878120573 and 119902max the dynamic delivery area is reducedlinearly in relation to the demand until no space can beprovided Finally during the decrease of the traffic demandafter midday we can provide a delivery area for some hoursusing the lane capacity that the decrease of traffic demandleaves unoccupied

5 Validation and Evaluation of the Model

In this section the results of a simulation study based onthe numerical example described above are presented Theobjectives of the simulation are twofold (1) to validate theresults of the analyticalmodel inmore realistic scenarios (egstochastic vehiclersquos arrival) and (2) to evaluate the perfor-mance of the proposed DDPS concept through a comparisonwith the current situation of illegal delivery parking Thissection is divided into two subsections one for the modelvalidation and one for the DDPS performance evaluation

Simulation experiments are conducted using a VISSIMmicrosimulation platform [51] To account for the stochasticnature of vehiclesrsquo arrival in the simulation model multipleVISSIM simulation runs with various random seeds wereexecuted for all scenarios Each simulation was one hour and15 minutes long with a 15-minute warm-up time and onehour of evaluation time

51 Model Validation For the validation of the analyticalmodel two different scenarios representing different man-agement strategies of the delivery parking operations areanalyzed The first scenario (V1) considers the provision ofDDPS in the central part of the link with the length (numberof spots) determined according to the analytical formulationThe length for DDPS is determined in each case according to


q0

=120

m

828 1290

Provision No provisionL=

120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)

Figure 6 (a) Values of 1198891 and 1198892 in relation to the traffic demand volume 119902 (b) Dynamic delivery area variations across the day

the traffic demand and signal timing parameters (see Table 1)In this scenario we also assume that the spots are occupied allthe time due to a prebooking system Secondly we evaluatea hypothetical scenario (V2) in which one lane is completelydevoted to the delivery parking In total three levels of trafficdemand (988 1090 and 1190 vehh) are used as an input in thesimulation platform for each scenario The levels of demandare chosen such that they correspond to the provision of 9 6and 3 DDPS spots of 85 meters respectively in the case ofV1

For comparison purposes we analyze two performancemeasures the average queue length in the UI and the latentdemand The latter represents the number of vehicles thatcannot be served during the simulation (ie due to thespillback at the UI)

Results reveal that no latent demand is generated inscenario V1 suggesting that the presence of DDPS does notcause spillbacks However when the portion of the road spacedevoted to DDPS is larger than what is recommended by theproposed analytical model (the case of V2 scenario) there isa latent demand at the end of the simulation (2 15 and24 for the traffic demand of 988 1090 and 1190 vehh resp)causing spillbacks In addition one can observe fromFigure 7the average queue length in each scenario and for each trafficdemand In the V2 scenario the queue length nearly reachesthe length of the upstream link which is another sign of thespillback effect

In reality when parking is not available delivery vehiclesmight park illegally to perform loading and unloading oper-ations affecting the overall network performance Thereforewe conduct another set of simulation experiments in order toinvestigate the benefits of DDPS compared to the potentiallyillegal parking maneuvers Tested scenarios and the results ofthese experiments are provided in the next subsection

998 1090 1190Traffic demand (vehh)

V1 - DDPSV2 - one lane blocked

Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)

Length of the upstream link is 200 m

Figure 7 Average queue length (m) in the validation scenarios V1and V2

52 DDPS Performance Compared to Illegal Parking In thissubsection the performance of DDPS is analyzed with thethree following scenarios

(1) S0 scenario representing the current situation wheresome delivery vehicles perform random illegal park-ing in the shoulder lane (see Figure 8(a)) In realitythe delivery parking location is usually chosen basedon the proximity to the destination In our simulationwe assume that delivery vehicles choose a randomlocation within the link arriving with a randompattern during the simulation period From that


S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)

Figure 8 (a) S0 illegal parking with random arrival and location (b) S1-DDPS (c) S2-DDPS with prebooking system

perspective five different random arrival patterns aretested

(2) S1 scenario representing the dynamic operations ofDDPS where the shoulder lane is blocked only whenthere are delivery vehicles operating (see Figure 8(b))Vehicles operate only in the DDPS area determinedaccording to the given traffic demand and signaltiming parameters In other words delivery vehiclesdo not park at a random location but within thearea assigned according to the DDPS formulation(Table 1) The same random arrival patterns of deliv-ery vehicles from the previous scenario are used

(3) S2 scenario representing the operation of a DDPScombined with a prebooking system When a pre-booking system is used delivery vehicles are assigneda given parking time in advance according to theirpreferences which respects the capacity of the facilityat all times [6] Given the provision of DDPS spotswith a prebooking systemwe assume that the deliveryparking demand can be higher and uses the facilityduring most of the time (at the maximum capacity)For that reason in this scenario other vehicles cannotuse this part of the lane at all (see Figure 8(c)) Inthis case delivery vehicles have a preassigned timetherefore the arrival pattern is not random

In scenarios S0 and S1 we assume that there will be ademand of 9 delivery vehicles per hour which will performdelivery operations at the studied link In the S0 scenariodelivery vehicles decide to park illegally as no facility isavailable at all in the S1 scenario delivery vehicles use oneof the available parking spots provided In contrast S2 canserve an increased number of delivery vehicles per hour asthe DDPS is used with a prebooked assignment and parkingspots can be used all the time

The average duration of loadingunloading operationsvaries depending on the type of goods and also acrossdifferent cities For example in the city of Barcelona theaverage delivery time is around 18 minutes [25] and vehiclesare allowed to park in dedicated areas for a maximum of30 minutes Other cities such as Valencia Lyon Romeor Westminster have similar time restrictions for deliveryparking [2 3 52] In the city of NewYork the average parkingtime can reach 18 h [37] as multiple customers are served

from the same parking location Also some cities allowother activities such as service vehicles to use these parkingfacilities In general DDPS is a solution for parking times upto a maximum of 30 minutes given that for longer parkingperiods traffic conditionsmight change andDDPSmight notbe available anymore In cases where parking time is muchlonger other alternatives should be considered for parkingIn this simulation study we consider three different parkingtimes (10 20 and 30 minutes) and analyze their impact onthe traffic performance Note that the variation of parkingtimeswould not affect the provision ofDDPS but the numberof vehicles that could be served that is the capacity of theparking facility

To investigate the impact of each scenario (S0 S1 andS2) on the traffic performance the average delay per vehicleis used as shown in Figure 9 Note that the average vehicledelay of scenario S0 (illegal parking) is significant A systemwithout delivery parking (enforced regulation) was alsosimulated and the average delay registered ranged from 16to 17 secvehMoreover the average delay increases with boththe length of the loadingunloading operations and the trafficdemand

With DDPS in S1 scenario we show that this delay can besignificantly reduced if the same delivery demand uses thefacility located in the center of the link (defined according tothe analytical method in Table 1)

Nevertheless when the traffic demand is high andorloadingunloading operations last long DDPS might nothave enough capacity to serve the randomly arriving deliveryvehicles (ie it might not be possible to position all deliveryvehicles withinDDPS spots at a given time)These cases for S1have not been simulated and are represented with symbolInstead the S2 scenario where DDPS is combined with aprebooking system is a much better option as it allows us tooptimally assign the delivery demand to parking spots andincrease the capacity of DDPS In this case we assumed thatthe DDPS area will be blocked for the total simulation periodso that other vehicles cannot use it The delay caused in thesystem with a prebooking DDPS (in dashed lines in Figure 9)is lower than illegal parking except for only one case whentraffic demand is low and parking time is only 10 minutes Inall other cases DDPS with a prebooking system causes lowerdelay in the system and in exchange it offers much moredelivery parking capacity for the DDPS users


10 20 30

S2

S0 - illegal parkingS1 - DDPS wo prebookingS2 - DDPS w prebooking

Parking duration (min)

0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty

S0 - illegal parkingS1 - DDPS wo

S2 - DDPS w prebookingempty not simulated data for S1

prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)

Figure 9 Average delay (secveh) in scenarios S0 S1 and S2 in case of traffic demand (a) 988 vehh (b) 1090 vehh (c) 1190 vehh

6 Conclusions

In this paper we have introduced the concept of DynamicDelivery Parking Spots (DDPS) a novel solution for loadingand unloading operations in urban areas DDPS are delivery

facilities located on the shoulder lane of a link that are acti-vated dynamically keeping the traffic delay to a minimum

Current loading and unloading operations happen eitherin dedicated areas outside traffic lanes or when these lanesare full or nonexisting in curbside parking or illegally as


in-lane parking DDPS can be a solution to provide deliveryoperations reducing the negative effects on traffic at the sametime

DDPS temporarily block the shoulder lane creatingtraffic disruptions However within certain conditions it ispossible to keep these disruptions at the local level that iswithout generating network effectsThanks to this DDPS canmake a more efficient use of the scarce urban space that istaking traffic lane capacity for loadingunloading activitieswhen possible

In this paper we develop the detailed analytical formu-lations to quantify the traffic effects of DDPS and find theconditions required to keep the delay at the local level Somesimplifications are needed but with this clear guidelines onwhere and when to allow DDPS are provided

Simulation experiments are carried out to validate theresults of the formulation and to further show the applicabil-ity of the proposed concept in realistic scenarios Moreoverwe are able to compare the delay caused by the DDPS to thereal situation where theremight be illegal delivery parking inthe shoulder lane

In summary DDPS can be located on a link if even withthe blocked lane the remaining capacity of the link plus thestorage capacity of the blocked lane is able to cope with thetraffic demand If this criterion is met then DDPS should belocated at the center of the link that is far from intersectionsand leaving some capacity of the blocked lane for traffic thatwill later merge or diverge to other lanes of the link Asshown with the simulation experiments DDPS can reducethe vehicle delay compared to the case when delivery vehiclespark illegally

Future research steps could extend the analytical modelto incorporate different assumptions For example the effectsof turning vehicles or pedestrian crossings could be incor-porated Additionally small lingering delays could also beaccepted to allow DDPS The accumulated delays can bequantified to allow a number of DDPS that minimize or limitthe delay given the number of cycles of the blockage

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was partially supported by ETH Research GrantETH-40 14-1 and the Project CALog funded by the HaslerFoundation The authors thank Dr Qiao Ge for providingsupport with the simulation used in this manuscript

References

[1] L Ma ldquoAnalysis of unloading goods in urban streets andrequired datardquo City Logistics II pp 367ndash379 2001

[2] A Nuzzolo A Comi A Ibeas and J L Moura ldquoUrban freighttransport and city logistics policies indications from RomeBarcelona and Santanderrdquo International Journal of SustainableTransportation vol 10 no 6 pp 552ndash566 2016

[3] A Beziat ldquoParking for FreightVehicles inDenseUrbanCentersThe Issue of Delivery Areas in Parisrdquo in Proceeding of the TRB94th Annual Meeting Compendium of Papers Washington DCUSA 2015

[4] European Union INTERREG IVC ldquoSustainable urban goodslogistics city logistics best practices a handbook for authoritiesBarcelona Spain 2011rdquo

[5] JPIsla Logıstica ldquoCriteria to determine the usage of multi-lanesindividual loadingunloading areas and night deliveriesrdquo 2010

[6] M Roca-Riu E Fernandez and M Estrada ldquoParking slotassignment for urban distribution models and formulationsrdquoOmega vol 57 pp 157ndash175 2015

[7] K YangM Roca-Riu andMMenendez ldquoAn auction approachto prebook urban logistics faciliesrdquoWorking Paper 2017

[8] M Eichler and C F Daganzo ldquoBus lanes with intermittentpriority strategy formulae and an evaluationrdquo TransportationResearch Part B Methodological vol 40 no 9 pp 731ndash7442006

[9] C Chick On-Street Parking A Guide to Practice LandorPublishing London United Kingdom 1996

[10] M Valleley Parking Perspectives A Source Book for The Devel-opment of Parking Policy Landor Publishing London UK 1997

[11] S Yousif and Purnawan ldquoOn-street parking effects on trafficcongestionrdquo Traffic Engineering and Control vol 40 no 9 1999

[12] S Yousif and Purnawan ldquoTraffic operations at on-street park-ing facilitiesrdquo in Proceedings of the Institution of Civil Engineers -Transport vol 157 pp 189ndash194 2004

[13] A I Portilla B Alonso Orena J L Moura Berodia and F JR Dıaz ldquoUsing MMInf queueing model in on-street parkingmaneuversrdquo Journal of Transportation Engineering vol 135 no8 pp 527ndash535 2009

[14] X Ye and J Chen ldquoTraffic delay caused by curb parking set inthe influenced area of signalized intersectionrdquo in Proceedings ofthe 11th International Conference of Chinese Transportation Pro-fessionals Towards Sustainable Transportation Systems ICCTP2011 pp 566ndash578 Nanjing China August 2011

[15] H Guo Z Gao X Yang X Zhao and W Wang ldquoModelingtravel time under the influence of on-street parkingrdquo Journalof Transportation Engineering vol 138 no 2 pp 229ndash235 2011

[16] L D Han S-M Chin O Franzese and H Hwang ldquoEstimatingthe impact of pickup- and delivery-related illegal parkingactivities on trafficrdquo Journal of the Transportation ResearchBoard vol 1906 pp 49ndash55 2005

[17] M Kladeftiras and C Antoniou ldquoSimulation-based assessmentof double-parking impacts on traffic and environmental condi-tionsrdquo Journal of the Transportation Research Board no 2390pp 121ndash130 2013

[18] AWenneman KM N Habib andM J Roorda ldquoDisaggregateanalysis of relationships between commercial vehicle parkingcitations parking supply and parking demandrdquo Journal of theTransportation Research Board vol 2478 pp 28ndash34 2015

[19] S V Ukkusuri K Ozbay W F Yushimito S Iyer E F Morguland J Holguın-Veras ldquoAssessing the impact of urban off-hourdelivery program using city scale simulation modelsrdquo EUROJournal on Transportation and Logistics vol 5 no 2 pp 205ndash230 2016

[20] N Chiabaut ldquoInvestigating impacts of pickup-delivery maneu-vers on trafficflowdynamicsrdquoTransportationResearch Procediavol 6 pp 351ndash364 2015

[21] E Hans N Chiabaut and L Leclercq ldquoClustering approach forassessing the travel time variability of arterialsrdquo Journal of theTransportation Research Board vol 2422 pp 42ndash49 2014


[22] N Chiabaut ldquoImpacts of urban logistics on traffic flow dynam-icsanalytical investigationsrdquo in Proceedings of the The 94thmeeting of the Transportation Research Board WashingtonUSA

[23] C Lopez J Gonzalez-Feliu N Chiabaut and L LeclercqldquoAssessing the impacts of goods deliveriesrsquo double line parkingon the overall traffic under realistic conditionsrdquo in Proceedingsof the 6th International Conference on Information SystemsLogistics and Supply Chain (ILS rsquo16) June 2016

[24] J Cao M Menendez and V Nikias ldquoThe effects of on-streetparking on the service rate of nearby intersectionsrdquo Journal ofAdvanced Transportation vol 50 no 4 pp 406ndash420 2016

[25] J Cao and M Menendez ldquoGeneralized effects of on-streetparking maneuvers on the performance of nearby signalizedintersectionsrdquo Journal of the Transportation Research Board vol2483 pp 30ndash38 2015

[26] N Luthy S I Guler and M Menendez ldquoSystemwide effects ofbus stops bus bays vs curbside bus stopsrdquo in Proceedings of theTRB 95th Annual Meeting Compendium of Papers 2016

[27] PROINTEC ldquoMethodological study and development ofprojects about improvements in urban distribution and load-ingunloading operationsrdquo Barcelona Municipality 1997

[28] J Ortigosa and M Menendez ldquoTraffic performance on quasi-grid urban structuresrdquo Cities vol 36 pp 18ndash27 2014

[29] J Ortigosa andMMenendez ldquoTraffic dynamics of lane removalon grid networksrdquoWorking Paper 2015

[30] J Cao and M Menendez ldquoQuantification of potential cruisingtime savings through intelligent parking servicesrdquo WorkingPaper 2017

[31] R GThompson K Takada and S Kobayakawa ldquoOptimisationof parking guidance and information systems display configu-rationsrdquoTransportation Research Part C Emerging Technologiesvol 9 no 1 pp 69ndash85 2001

[32] D Teodorovic and P Lucic ldquoIntelligent parking systemsrdquoEuropean Journal of Operational Research vol 175 no 3 pp1666ndash1681 2006

[33] S Sunkari ldquoThe benefits of retiming traffic signalsrdquo ITE Journal(Institute of Transportation Engineers) vol 74 no 4 pp 26ndash292004

[34] M Papageorgiou Ed Concise Encyclopedia of Traffic amp Trans-portation Systems 1991

[35] A Stevanovic I Dakic and M Zlatkovic ldquoComparison ofadaptive traffic control benefits for recurring and non-recurringtraffic conditionsrdquo IET Intelligent Transport Systems vol 11 no3 pp 142ndash151 2016

[36] M Jaller J Holguın-Veras and S Hodge ldquoParking in the cityrdquoJournal of the Transportation Research Record vol 2379 pp 46ndash56 2013

[37] J Holguın-Veras K Ozbay A Kornhauser et al ldquoOverallimpacts of off-hour delivery programs in New York city met-ropolitan areardquo Journal of the Transportation Research Recordvol 2238 pp 68ndash76 2011

[38] A Comi B Buttarazzi M M Schiraldi R Innarella MVarisco and L Rosati ldquoDynaLOAD a simulation frameworkfor planning managing and controlling urban delivery baysrdquoTransportation Research Procedia vol 22 pp 335ndash344 2017

[39] J H Banks ldquoFreeway speed-flow-concentration relationshipsmore evidence and interpretationsrdquo Journal of the Transporta-tion Research Board vol 1225 pp 53ndash60 1989

[40] M J Cassidy ldquoBivariate relations in nearly stationary highwaytrafficrdquo Transportation Research Part B Methodological vol 32no 1 pp 49ndash59 1998

[41] F L Hall B L Allen and M A Gunter ldquoEmpirical analysisof freeway flow-density relationshipsrdquo Transportation ResearchPart A General vol 20 no 3 pp 197ndash210 1986

[42] J R Windover and M J Cassidy ldquoSome observed details offreeway traffic evolutionrdquoTransportationResearch Part A Policyand Practice vol 35 no 10 pp 881ndash894 2001

[43] L Leclercq J A Laval and N Chiabaut ldquoCapacity drops atmerges An endogenous modelrdquo Transportation Research PartB Methodological vol 45 no 9 pp 1302ndash1313 2011

[44] M Menendez and C F Daganzo ldquoEffects of HOV lanes onfreeway bottlenecksrdquo Transportation Research Part B Method-ological vol 41 no 8 pp 809ndash822 2007

[45] M Menendez An Analysis of HOV Lanes Their Impact onTraffic [PhD thesis] Department of Civil and EnvironmentalEngineeringUniversity of California Berkeley CAUSA 2006

[46] Q Ge and M Menendez ldquoA simulation study for the staticearly merge and late merge controls at freeway work zonesrdquoin Proceedings of the 13th Swiss Transport Research Conference2013

[47] I Chatterjee P Edara S Menneni and C Sun ldquoReplication ofwork zone capacity values in a simulation modelrdquo Journal of theTransportation Research Board vol 2130 pp 138ndash148 2009

[48] F Soriguera I Martınez M Sala and M Menendez ldquoEffectsof low speed limits on freeway traffic flowrdquo TransportationResearch Part C Emerging Technologies vol 77 pp 257ndash2742017

[49] M J Cassidy K Jang and C F Daganzo ldquoThe smoothingeffect of carpool lanes on freeway bottlenecksrdquo TransportationResearch Part A Policy and Practice vol 44 no 2 pp 65ndash752010

[50] K W Ogden Urban goods movement a guide to policy andplanning Aldershot Hants England 1992

[51] P AG Ptv Vissim 7 User Manual Kahlsruhe Germany 2014[52] M A Figliozzi ldquoAnalysis of the efficiency of urban commercial

vehicle tours data collection methodology and policy implica-tionsrdquo Transportation Research Part B Methodological vol 41no 9 pp 1014ndash1032 2007

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



traffic performance according to different levels of trafficdemand

DDPS can providemany benefits in practiceThe numberof dedicated (ie fixed) loadingunloading spots can bereduced since some of the operations might happen inDDPS Additionally the city can make a better use of theexisting space for example by devoting part of the trafficlanes to freight activities when the traffic demand is lowAdditionally DDPS could be regulated with a prebookingparking system [6 7] that guarantees the optimal use of thedevoted space

Moreover DDPS can be easily implemented only few andinexpensive infrastructure changes are required technolog-ical equipment is available and the existing trafficparkingmanagement and control strategies can be used For infras-tructure in-pavement lights in the shoulder lane can clearlyindicate the area where delivery is allowed similar to the useof Bus Lane Intermittent Priority (BLIP) [8] Apart from theuse of in-pavement lights vehicle detectors can be placed atthe different spots of the DDPS for detecting the presenceof vehicles Such detectors can also be used to control thecorrect use of DDPS For example when a vehicle is usingincorrectly DDPS a signal could be automatically sent to thecontrol authorities

This paper aims to provide basic guidelines for DDPS onurban areas so that the deliveries can be carried out whiletraffic disruptions are kept to a minimum DDPS providespace for loadingunloading activities on the shoulder laneof the street but they are only allowed if the traffic delayis kept local (ie traffic delay is kept on the link and doesnot spread over the network) In other words traffic mustpass smoothly the upstream intersection the lane drop atthe delivery spot and the downstream intersection withno queue spillover to other links in the network Using thehydrodynamic theory of traffic flow we analyze the trafficdischarge rate at both the upstream and the downstreamintersections taking into consideration that a portion ofthe shoulder lane is blocked In particular we model therelation between the delivery location within the link thetraffic demand arriving from upstream and the disruptionsto traffic Based on such relation the location of the DDPScan be regulated as a function of the traffic demand toreduce the traffic disruptions as much as possible In order tovalidate the developedmodel show its applicability in amorerealistic situation and analyze the effect of stochastic arrivalsa simulation study is performed The simulation is also usedto evaluate the performance of DDPS in comparison to illegaldelivery parking

The rest of this paper is organized as follows Section 2lists and describes the existing literature highlighting thedifferences to this paper Section 3 shows the analyticalmodelwhere generalized suggestions concerning the location ofDDPS are made Section 4 shows a numerical example toillustrate how the model is applied to a particular caseSection 5 validates the model with simulation in a set ofscenarios Then it compares the overall delay between thesystem with DDPS and the current situation with illegalparking Section 6 summarizes the findings of this study

2 Literature Review

On-street parking highly influences urban traffic perfor-mance mostly from three different perspectives First theparking lanes occupy road space leading to reduced trafficcapacity on the road and the neighboring network [9 10]Second the parkingunparking maneuver itself generates atemporary traffic bottleneck which blocks vehicles arrivingfrom upstream and causes extra travel time [11ndash15] Thirdspecial parking behaviors such as illegal (eg double) parkingor loadingunloading trucksbuses take space from drivinglanes reducing the road capacity unreasonably and causinginconvenience and confusion to other travelers [16 17]

As a special case delivery vehicles can cover all thesethree negative aspects and more importantly their load-ingunloading processes and the ensued traffic issues occurrecurrently It is therefore of great importance to improveand optimize the loading and unloading operations to reducetheir effects on the traffic performance To that end multipleresearchers have developed different control schemes [18 19]Recent work [20] evaluated the effects of pick-up maneuverson traffic flows near maximal capacity which were proved tohave amajor impact on traffic conditions In order to evaluatethe effects on travel times a potential tool was developedin [21] and some additional investigations can be found in[22] Very recently the macroscopic impacts of deliveries indouble lane parking in an arterial corridor were assessed witha simulation study [23] Our paper with a different approachis focused on providing guidelines on the location and thenumber of spots avoiding the negative effects at the networklevel

Other researchers have evaluated the traffic effects ofparking maneuvers [24 25] They have proposed a model toanalyze the impact of parking maneuvers on a road segmentand their influence on the capacity of nearby intersectionsand the overall network It is shown that under certainconditions such as low traffic demand or optimum parkinglocation parking maneuvers do not affect traffic throughputeven in caseswhen one-lane road is analyzed Similar patternsare observed for curbside bus stops [26] Evidently load-ingunloading operations last normally much longer [2 27]than the time needed for parking maneuvers and bus stopsbut they happen less frequently and a prebooked schedule asstudied in [6] can be implemented

From the network perspective [28 29] have shown thatat a network level it is possible to remove lanes or even linksto a certain extent without reducing much of the networkcapacity Such findings are encouraging as they indicate thattemporarily removing some portions of a lane might not bevery disruptive if the effects are kept local

Implementation of various Information and TechnologySystems (ITS) strategies such as parking guidance or trafficsignal control has proven to be very beneficial for traffic oper-ations at the network level [30] For example [31] presenteda model for determining the optimal display of parkingguidance and information sign configuration that minimizesqueue lengths and distance traveled while searching forparking Similarly in the fuzzy logic-based model developedby [32] each delivery vehicle can receive information on






3 Analytical Model


Delivery(DI)(UI)

L

L1 L2







State 2

State 4

State 1

State 3

Flow

(n minus 1)S

nKJ Density

nS

nq

0

(a)

nS

nq nq

Arrival

Virtual departure

Time

Cum

ulat

ive n

umbe

r of v

ehic

les

ts tq

(b)









119873 = 119902119888 if 119902 le 119899119878119892

119888 119899119878119892 if 119902 gt 119899119878119892

119888 (1)




119873119889 =

119902119888 if 119902 le (119899 minus 1) 119878119892119888 120573

(119899 minus 1) 119878119892120573 if 119902 gt (119899 minus 1) 119878119892119888 120573 (2)


119873119894 = 119889119894119870119869 forall119894 isin 1 2 (3)



1198891 = 0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573] (4a)


119888 120573 119899119878119892119888 ] (4b)

1198891 = 119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (4c)



nSg

c

d1

cKJ

(n minus 1)Sg

c

Sg

KJ

0 nS q







Cum

Time





(n minus 1)S

(n minus 1)S

ＧＣＨ N1

SN2

S

ＧＣＨ nN1 nN2

nS

nS

nS

q

q

N

N







119861 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(5)


1198611015840 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(6)




1198892 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


119888 120573 119899119878119892119888 ]

119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (7)






119902max = 119871119870119869 + 2 (119899 minus 1) 1198781198921205732119888 (8)




0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)


0


q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)











If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














3 Analytical Model


Delivery(DI)(UI)

L

L1 L2







State 2

State 4

State 1

State 3

Flow

(n minus 1)S

nKJ Density

nS

nq

0

(a)

nS

nq nq

Arrival

Virtual departure

Time

Cum

ulat

ive n

umbe

r of v

ehic

les

ts tq

(b)









119873 = 119902119888 if 119902 le 119899119878119892

119888 119899119878119892 if 119902 gt 119899119878119892

119888 (1)




119873119889 =

119902119888 if 119902 le (119899 minus 1) 119878119892119888 120573

(119899 minus 1) 119878119892120573 if 119902 gt (119899 minus 1) 119878119892119888 120573 (2)


119873119894 = 119889119894119870119869 forall119894 isin 1 2 (3)



1198891 = 0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573] (4a)


119888 120573 119899119878119892119888 ] (4b)

1198891 = 119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (4c)



nSg

c

d1

cKJ

(n minus 1)Sg

c

Sg

KJ

0 nS q







Cum

Time





(n minus 1)S

(n minus 1)S

ＧＣＨ N1

SN2

S

ＧＣＨ nN1 nN2

nS

nS

nS

q

q

N

N







119861 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(5)


1198611015840 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(6)




1198892 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


119888 120573 119899119878119892119888 ]

119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (7)






119902max = 119871119870119869 + 2 (119899 minus 1) 1198781198921205732119888 (8)




0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)


0


q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)











If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










State 2

State 4

State 1

State 3

Flow

(n minus 1)S

nKJ Density

nS

nq

0

(a)

nS

nq nq

Arrival

Virtual departure

Time

Cum

ulat

ive n

umbe

r of v

ehic

les

ts tq

(b)









119873 = 119902119888 if 119902 le 119899119878119892

119888 119899119878119892 if 119902 gt 119899119878119892

119888 (1)




119873119889 =

119902119888 if 119902 le (119899 minus 1) 119878119892119888 120573

(119899 minus 1) 119878119892120573 if 119902 gt (119899 minus 1) 119878119892119888 120573 (2)


119873119894 = 119889119894119870119869 forall119894 isin 1 2 (3)



1198891 = 0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573] (4a)


119888 120573 119899119878119892119888 ] (4b)

1198891 = 119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (4c)



nSg

c

d1

cKJ

(n minus 1)Sg

c

Sg

KJ

0 nS q







Cum

Time





(n minus 1)S

(n minus 1)S

ＧＣＨ N1

SN2

S

ＧＣＨ nN1 nN2

nS

nS

nS

q

q

N

N







119861 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(5)


1198611015840 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(6)




1198892 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


119888 120573 119899119878119892119888 ]

119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (7)






119902max = 119871119870119869 + 2 (119899 minus 1) 1198781198921205732119888 (8)




0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)


0


q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)











If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119873119889 =

119902119888 if 119902 le (119899 minus 1) 119878119892119888 120573

(119899 minus 1) 119878119892120573 if 119902 gt (119899 minus 1) 119878119892119888 120573 (2)


119873119894 = 119889119894119870119869 forall119894 isin 1 2 (3)



1198891 = 0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573] (4a)


119888 120573 119899119878119892119888 ] (4b)

1198891 = 119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (4c)



nSg

c

d1

cKJ

(n minus 1)Sg

c

Sg

KJ

0 nS q







Cum

Time





(n minus 1)S

(n minus 1)S

ＧＣＨ N1

SN2

S

ＧＣＨ nN1 nN2

nS

nS

nS

q

q

N

N







119861 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(5)


1198611015840 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(6)




1198892 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


119888 120573 119899119878119892119888 ]

119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (7)






119902max = 119871119870119869 + 2 (119899 minus 1) 1198781198921205732119888 (8)




0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)


0


q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)











If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Cum

Time





(n minus 1)S

(n minus 1)S

ＧＣＨ N1

SN2

S

ＧＣＨ nN1 nN2

nS

nS

nS

q

q

N

N







119861 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(5)


1198611015840 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(6)




1198892 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


119888 120573 119899119878119892119888 ]

119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (7)






119902max = 119871119870119869 + 2 (119899 minus 1) 1198781198921205732119888 (8)




0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)


0


q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)











If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1198611015840 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


(6)




1198892 =

0 if 119902 isin [0 (119899 minus 1) 119878119892119888 120573]


119888 120573 119899119878119892119888 ]

119878119892120573119870119869 if 119902 isin [119899119878119892

119888 119899119878] (7)






119902max = 119871119870119869 + 2 (119899 minus 1) 1198781198921205732119888 (8)




0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)


0


q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)











If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 q

q (example)

Space

LDynamic

parking area

d1

d2

Sg KJ

Sg KJ

nSnSg

c(n minus 1)

Sg

c

(a)


0


q

q (example)

Space

L

d1

d2

Sg KJ

Sg KJ

nSg

c(n minus 1)

Sg

c

nS

qＧＲ

(b)











If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












If 119871 ge 2119878119892120573119870119869 Yes

If 119902 isin [0 (119899 minus 1) 119878119892120573119888 ] [0 119871] 119871

119909If 119902 isin [(119899 minus 1) 119878119892120573

119888 119899119878119892119888 ] [119902119888 minus (119899 minus 1)119878119892120573


If 119902 isin [119899119878119892119888 119899119878] [119878119892120573

119870119869 119871 minus 119878119892120573119870119869 ] 119871 minus 2119878119892120573119870119869119909

If 119871 lt 2119878119892120573119870119869


119888 120573] [0 119871] 119871119909































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































q0

=120

m

828 1290


120Ｇ

60m

60m

Space

(vehh)

(a)

Time (h)

Time (h)

24126 18

ordm

24126 18

(n minus 1)gS

c

qＧＲ

L

q

(b)








Parking strategies

0

20

40

60

80

100

120

140

160

180

200

Aver

age q

ueue

leng

th (m

)






S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










S0

Illegal

(a)

S1

DDPS

(b)

S2

DDPS prebooking

(c)












10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10 20 30

S2



0

10

20

30

40

50

60

70

80

90

100

110

120Av

erag

e del

ay (s

ecv

eh)

(a)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty



prebooking

(b)

10 20 30

S2


0

10

20

30

40

50

60

70

80

90

100

110

120

Aver

age d

elay

(sec

veh

)

empty empty empty



prebooking

(c)


6 Conclusions













Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Acknowledgments


References






















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









designing dynamic delivery parking spots in urban areas to

Documents