traffic engineering analysis

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P A R T II

TRAFFIC, STREETS, ANDHIGHWAYS

Source: HANDBOOK OF TRANSPORTATION ENGINEERING


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TRAFFIC, STREETS, AND HIGHWAYS


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6.3

CHAPTER 6

TRAFFIC ENGINEERING ANALYSIS

Baher AbdulhaiDepartment of Civil Engineering,

University of Toronto, Toronto, Ontario, Canada

Lina KattanDepartment of Civil Engineering,

University of Toronto, Toronto, Ontario, Canada

6.1 TRAFFIC ENGINEERING PRIMER

6.1.1 Traffic Engineering

Traffic engineering, or, in more modern terms, traffic control and management, concernsitself with the provision of efficient mobility of people and goods while preserving safetyand minimizing all harmful impacts on the environment. A broader look at traffic engineeringmight include a variety of engineering skills, including design, construction, operations,maintenance, and optimization of transportation systems. Practically speaking, however, traf-fic engineering focuses more on systems operations than on construction and maintenanceactivities.

6.1.2 Evolution of Current Transportation Systems and Problems

Automobile ownership and hence dependence and truck usage have been on the rise sincethe Second World War. In the United States, the Federal Aid Highway Act of 1956 authorizedthe National System of Interstate and Defense Highways. For a couple of decades thereafter,the prime focus was on the creation of this immense mesh of freeways, considered to be thelargest public works project in the history of the planet. Very quickly, transportation profes-sionals realized that the growth in automobile use and dependence is outpacing the growthin capacity building, not to mention other problems, such as lack of funds to maintain thegiant infrastructure. Ever-rising congestion levels testify to this, and hence the sustainabilityof continued capacity creation came under the limelight, with fierce criticism by planners,and environmentalists alike. Recognition quickly crystallized that we need to move smarterand make intelligent use of existing capacity before any attempt to add more. The Inter-

modal Surface Transportation Efficiency Act (ISTEA, pronounced ice tea) of 1991,

Source: HANDBOOK OF TRANSPORTATION ENGINEERING


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6.4 CHAPTER SIX

marked the formal birth of intelligent transportation systems (ITS). Heavy emphasis wasplaced on the use of technology to utilize existing capacity efficiently instead of continuednew construction, in addition to emphasizing intermodalism and modernization of publictransport to curb automobile dependence. ISTEA dedicated $659 million dollars to researchand development and experimental projects geared towards the intelligent use of the national

transportation infrastructure. In 1998, the U.S. Congress passed the Transportation EquityAct for the 21st Century (TEA-21), which earmarked $1.2 billion dollars for mainstreamingITS with emphasis on deployment. For the most part, similar initiatives took place all overthe modern world, including Canada, Europe, Australia, and Japan. Hence, the modern trans-portation engineering field focused on, in addition to the basics, a number of key directions,such as intermodalism, using technology to improve transportation provisions under ITS,managing ever-rising congestion through supply control and demand management, and pro-tecting the environment.

6.1.3 Transportation Systems: Mobility and Accessibility

Land transportation systems include all roadway and parking facilities dedicated to movingand storing private, public, and commercial vehicles. Those facilities serve two principal butcontradicting functions: mobility and accessibility. Mobility is the common-sense objectiveof transportation, aiming at the fastest but safe movement of people or goods. Access toterminal points (homes, businesses) is also essential at trip ends. Mobility requires leastfriction with terminal points, while accessibility requires slow speeds and hence contradictsmobility. Fortunately, roads systems evolved in a hierarchical manner to serve both withoutconflict. For urban areas, for instance, the American Association for State Highway andTransportation Officials (AASHTO) defines the hierarchy of roads as follows:

1. Urban principal arterial system, including interstate highways, freeways, and other urbanarterials, all have some level of access control to promote mobility; typified by high

volumes and speeds.2. Urban minor arterial street system, which augments the freeway system, emphasizes rel-

atively high mobility while connecting freeways to collectors.

3. Urban collector street system, collecting traffic from local streets and streaming it ontoarterials, with somewhat balanced emphasis on both mobility and accessibility.

4. Urban local street system, primarily provides access to terminal points, and hence delib-erately discourages high mobility and emphasizes low volumes and speeds.

AASHTO has a somewhat similar classification for rural roads, defining the level ofmobility versus accessibility provided by each class.

With the above hierarchical classification in mind, traffic control and management strat-egies must recognize and preserve the functional classification of the road at hand. Forinstance, improper provision of mobility on freeways and arterials might result in neighbor-hood infiltration by traffic, an undesirable and spreading phenomenon in todays congestedurban areas.

6.1.4 Emerging Trends

Intelligent Transportation Systems (ITS). Intelligent transportation systems, an emergingglobal phenomenon, are a broad range of diverse technologies applied to transportation inan attempt to save lives, money and time. The range of technologies involved includesmicroelectronics, communications, and computer informatics, and cuts across disciplines



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TRAFFIC ENGINEERING ANALYSIS 6.5

such as transportation engineering, telecommunications, computer science, financing, elec-tronics, commerce, and automobile manufacturing. ITS and the underlying technologies willsoon put a computer (which has the potential to eliminate human error) in each car to guideus to our destinations, away from congestion, interact with the road, and even drive itself.Although ITS sounds futuristic, it is becoming reality at a very fast pace. Already, real

systems, products, and services are at work all the over the world. Alot remains to be done,but the future of ITS is promising. Many aspects of our lives have been more pleasant andproductive through the use of advanced technologies, and it is time for the transportationindustry to catch up and benefit from technology. ITS can go beyond a transportation systemwhose primary controlling technology is the four-way traffic signal.

Some scattered computer-based solutions to transportation problems date back to the late1950s and early 1960s. The first large-scale application of a computerized signal controlsystem in the world took place in Metropolitan Toronto, Canada, during the early 1960s.However, the ITS field as we know it today started to mature only in the early 1990s, whenit was known as intelligent vehicle and highway systems (IVHS). The name change tointelligent transportation systems reflects broadening to include all aspects of transportation.Several forces have driven the ITS field. As mentioned earlier, transportation practitioners

and researchers alike realized that road building can never keep pace with the increasingdemand for travel. Some countries, like the United States, invested billions of dollars inbuilding road networks and infrastructure and are now faced with the challenge of revitalizingthis huge network and making the best use of its already existing capacity before expandingfurther. Another set of driving forces is environment-related. Damage to the environmentfrom traffic emissions rose to unprecedented alarming levels. In Canada for instance, trans-portation represents the single largest source of greenhouse gas emissions, accounting for 27percent of the total emissions, which is estimated to increase to 42 percent by the year 2020.The problem is even greater in more car-dependent societies like the United States. Roadsafety, or the lack of, and escalating death tolls and injuries in traffic accidents each yearare yet a third set of forces. For all these reasons, more road building is not always viableor desirable. High-tech computer, electronic, and communication technologies offer one at-

tractive and promising approach, and hence the current appeal of ITS. A healthy ITS industrywould also have other non-traffic-related societal benefits, including stimulation of new in-formation technology-based industries and creation of new markets and jobs. Therefore, ITSis more than just intelligent solutions on the road. It is a new strategic direction for nationaland international economies. The market share of ITS is projected to expand over the nextdecade from an annual world market of $25 billion in 2001 to $90 billion in 2011. Aprojected $209 billion will be invested in ITS between now and 2011 (ITS-America). Accessto this sizable market is vital to the transportation and related technology sectors.

One important attribute of this emerging new face of the transportation industryshapedby ITSis that it is no longer restricted to civil engineers or to a single department oragency. Given the broad range of technologies involved, the ITS field is multidepartmental,multiagency, and multijurisdictional, cutting across the public, private, and academic sectors.

This broadness will certainly enhance potential, widen scope, and revolutionize the way wehandle our transportation systems, but it will also pose institutional challenges that we mustbe aware of and prepared for.

ITS Subsystems. Collectively, ITS aims to enhance the utilization of existing roadwaycapacity, as well as increase capacity itself. Enhancing the use of existing capacity is achiev-able through improved distribution of traffic, dynamically sending traffic away from con-gested hotspots to underutilized segments of the network, and the elimination of bottleneck-causing controls such as conventional toll plazas. Increasing the physical capacity itself ispossible through automation of driving and elimination of the human behavior element al-together. This is the promise of automated highway systems that could potentially double ortriple the number of vehicles a single lane can handle. From this perspective, ITS can bedivided into two main categories of systems:



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6.6 CHAPTER SIX

1. Advanced traffic management and traveler information systems (ATMS and ATIS, orcombined as ATMIS)

2. Advanced vehicle control and automated highway systems (AVCS and AHS)

ATMIS provide extensive traffic surveillance, assessment of recurring congestion due torepetitive high demands, and detection of nonrecurring congestion due to incidents, trafficinformation and route guidance dissemination to drivers, and adaptive optimization of controlsystems such as traffic signals and ramp meters. Current and near-future trends in ATMIStend to rely on centralized management in traffic management centers (TMCs). TMCs gaugetraffic conditions by receiving information from vehicle detectors throughout the network aswell as the vehicles themselves, as probes formulate control measures in the center anddisseminate control to field devices as well as information and guidance to drivers. Newertrends of distributed control are emerging but have not crystallized yet. The main distin-guishing characteristics of ATMIS are real-time operation and network-wide multijurisdic-tional implementation.

AVCS provides better control of the vehicle itself, either by assisting the driver or byautomating the driving process in an auto-pilot-like fashion in order to increase capacity andenhance safety. Full automation (AHS) can result in higher speeds at lesser headways, andhence higher lane capacity. Automation can be applied to individual vehicles as free agentsin a nonautomated mix of traffic or as fully automated lanes carrying platoons of electron-ically linked vehicles. Although AHS is technically promising, an array of unsettled issuesremains, including legal liabilities in the event of incident due to any potential automaticcontroller failure, technical reliability issues, and social issues. Therefore, AHS is still fu-turistic at the current stage of ITS. The feasible alternative, however, is to use the technologyto assist the driver, who remains in control of the vehiclethat is, to make the vehiclesmarter. Such intelligent vehicles will detect obstacles on the road and in the blind spotsand warn the driver accordingly, maintain constant distance from the vehicle ahead, and alerta sleepy driver who is going off the road. As technology improves further, the role of the

intelligent vehicle can move from a simple warning to full intervention and accident pre-vention by applying the brakes or overriding faulty steering decisions.The prime distinction between ATMIS and AVCS is that ATMIS focus on smoothing out

traffic flow in the network by helping the driver make best route-choice decisions and op-timizing the control systems in the network, while AVCS focus on the driver, the operationof the vehicle, and traffic maneuvers in the immediate vehicle vicinity. AVCS focus onenhancing the drivers awareness and perception, aiding decision-making by providing earlywarning and potentially initiating action, and eventually using sensory inputs and computercontrol in place of human sensory reactions and control.

ITS User Services. Another way to look at the constituents of ITS is from the end-userperspective. In the United States, for instance, a collection of interrelated user services isdefined and grouped into user-service bundles. As reported by the Intelligent Transportation

Society of America (ITS-America), 29 user services have been defined to date as summarizedin Table 6.1. These services and their definitions/descriptions are expected to evolve andundergo further refinements in time. User services are composed of multiple technologicalelements or functions, which may be in common with other services. For example, a singleuser service will usually require several technologies, such as advanced communications,mapping, and surveillance, which may be shared with other user services. This commonalityof technological functions is one basis for the suggested bundling of services. In some othercases, the institutional perspectives of organizations that will deploy the services providedthe rationale for the formation of a specific bundle. The users of this service or the ITSstakeholders include travelers using all modes of transportation, transportation managementcenter operators, transit operators, metropolitan planning organizations (MPOs), commercialvehicle owners and operators, state and local governments, and many others who will benefit

from deployment of ITS.



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TABLE 6.1 ITS User Services

Bundle User Services

1. Travel and Traffic Management 1. Pretrip Travel Information

2. En route Driver Information3. Route Guidance4. Ride Matching and Reservation5. Traveler Services Information6. Traffic Control7. Incident Management8. Travel Demand Management9. Emissions Testing and Mitigation

10. Highway Rail Intersection

2. Public Transportation Management 1. Public Transportation Management2. En-Route Transit Information3. Personalized Public Transit

4. Public Travel Security3. Electronic Payment 1. Electronic Payment Services

4. Commercial Vehicle Operations 1. Commercial Vehicle Electronic Clearance2. Automated Roadside Safety Inspection3. On-Board Safety Monitoring4. Commercial Vehicle Administrative Processes5. Hazardous Materials Incident Response6. Commercial Fleet Management

5. Emergency Management 1. Emergency Notification and Personal Security2. Emergency Vehicle Management

6. Advanced Vehicle Control and SafetySystems

1. Longitudinal Collision Avoidance2. Lateral Collision Avoidance

3. Intersection Collision Avoidance4. Vision Enhancement for Crash Avoidance5. Safety Readiness6. Pre-Crash Restraint Deployment7. Automated Vehicle Operation

7. Information Management 1. Archived Data Function

8. Maintenance and Construction Management 1. Maintenance and Construction Operation

ITS Architecture. We deal with and benefit from systems architectures almost every day,

although we might not know what an architecture is or what it is for. For instance, one dayyou purchase a television set, and later you purchase a videocassette recorder from a differentretailer and by a different manufacturer, but you never worry about whether they will worktogether. Similarly, you might buy a low-end radio receiver and a high-end compact diskplayer and again assume they will work together just fine. You travel with your FM radioreceiver and it works everywhere. This seamless operation of different systems or compo-nents of a system has not come about by chance, thanks to a mature industry and widelyadopted architectures and related standards that ensure such interoperability. The ITS indus-try, however, is still in its infancy. It is rapidly evolving in different places all over the world,and different groups are pursuing its development. Users are at risk of investing or adoptingcertain ITS equipment that works only locally. Similarly, if left without adequate guidance,stakeholders could easily develop systems solutions to their needs, which might be incom-

patible with those of regional neighbors. For instance, an in-vehicle navigation system pur-



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chased in California might not work in Nevada, or a system purchased in Ontario might notwork once the user crosses the border to New York. Therefore, to ensure seamless ITSoperation, some sort of global or at least national system architecture and related standardsare needed. To maximize fully the potential of ITS technologies, system design solutionsmust be compatible at the system interface level in order to share data, provide coordinated,

area-wide integrated operations, and support interoperable equipment and services whereappropriate. An ITS architecture provides this overall guidance to ensure system, product,and service compatibility/interoperability without limiting the design options of the stake-holder. In this chapter we use the U.S. ITS National System architecture only as an example.We are confident that similar efforts are underway in almost every ITS-active country, pro-ducing architectures that are more or less similar to the American architecture.

In the United States, Congress directed the U.S. Department of Transportation (DOT) topromote nationwide compatibility of ITS. Spearheaded by the U.S. DOT and the IntelligentTransportation Society of America (ITS-America), four major teams were formed in 1993.The four teams proposed four different architectures. The two most promising architectureswere selected, integrated, and refined in the form of the final architecture. A rich set ofdocuments describing every detail of the final architecture can be found on the ITS-America

website (www.itsa.org), which we summarize in the following section.It is important to understand that the architecture is neither a system design nor a designconcept. It is a framework around which multiple design approaches can be developed tomeet the individual needs of the user while maintaining the benefits of a common architecturenoted above. The architecture defines the functions(e.g., gather traffic information or requesta route) that must be performed to implement a given user service; the physical subsystemswhere these functions reside (e.g., the roadside or the vehicle); the interfaces/ informationflows between the physical subsystems; and the communicationrequirements for the infor-mation flows (e.g., wireline or wireless). In addition, it identifies and specifies the require-ments for the standards needed to support national and regional interoperability, as well asproduct standards needed to support economy of scale considerations in deployment. Thefunction view of ITS is referred to as the logical architecture as shown in Figure 6.1. Func-

tions such as manage traffic, for instance, can be further divided into finer processes suchas detect pollution levels and process pollution data. The systems view is referred toas the physical architecture as shown in Figure 6.1. Figure 6.1 also shows communicationsrequirements and information flows. The physical architecture partitions the functions definedby the logical architecture into systems and, at a lower level, subsystems, based on thefunctional similarity of the process specifications and the location where the functions arebeing performed. The physical architecture defines four systems, traveler, center, roadside,and vehicle, and nineteen subsystems. Subsystems are composed of equipment packageswith specific functional attributes. Equipment packages are defined to support analyses anddeployment. They represent the smallest units within a subsystem that might be purchased.In deployments, the character of a subsystem deployment is determined by the specificequipment packages chosen. For example, one municipal deployment of a traffic management

subsystem may select collect traffic surveillance and basic signal control equipment pack-ages, while a state traffic management center may select collect traffic surveillance andfreeway control packages. In addition, subsystems may be deployed individually or in ag-gregations or combinations that will vary by geography and time based on local deploymentchoices. A traffic management center may include a traffic management subsystem, infor-mation provider subsystem, and emergency management subsystem, all within one building,while another traffic management center may concentrate only on the management of trafficwith the traffic management subsystem.

The architecture has identified four communication media types to support the commu-nication requirements between the nineteen subsystems: They are wireline (fixed-to-fixed),wide area wireless (fixed-to-mobile), dedicated short range communications (fixed-to-mobile), and vehicle-to-vehicle (mobile-to-mobile). Wireline technology, such as leased or

owned twisted wire pairs, coaxial cable, or fiber optics, can be used by a traffic management

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Wayside

CentresTravellers

PersonalInformation

Access

RemoteTravellerSupport

ArchivedData

Management

InformationService

Provider

Roadway

EmissionsManagement

Vehicles

CommercialVehicle

EmergencyVehicle

CommercialVehicle

Administration

Toll Collection

ParkingManagement

CommercialVehicleCheck

Vehicle

TransitVehicle

Roadway

DedicatedShortRange

Communications

IntermodalTerminal

IntermodalContainer

VehicletoVehicleCommunications

MaintenanceVehicle

TransitManagement

Fleet andFreight

Management

Wireline (Fixed-Point to Fixed-Point) CommunicationsWide Area Wireless

(Mobile) Communications

EmergencyManagement

TrafficManagement

TollAdministration

MaintenanceManagement

New Modified

FIGURE 6.1 The Canadian physical architecture and communications connections.

center to gather information and monitor and control roadway subsystem equipment packages(e.g., traffic surveillance sensors, traffic signals, changeable message signs). Although wire-less communications technologies can also be used in this case, they are used to providefixed-to-fixed communications and consequently the architecture recognizes them as wirelinecommunications media. One- or two-way wide area wireless (fixed-to-mobile) communica-tions are suited for services and applications where information is disseminated to users whoare not located near the source of transmission and who require seamless coverage, such asis the case for traveler information and route guidance dissemination. Short-range wirelessis concerned with information transfer of localized interest. Two types of short-range wireless

communication are identified by the architecture: vehicle-to-vehicle communication, whichsupports automated highway systems (AHS), and dedicated short-range communications(DSRC), used in applications such as automated toll collection.

In conclusion, the basic benefit of the architecture is to provide a structure that supportsthe development of open standards. This results in numerous benefits: the architecture makesintegration of complex systems easier, ensures compatibility, and supports multiple rangesof functionality and designs.

ITS and Potential Economic Stimulation. As mentioned above, ITS is more than justsolutions to traffic problems. Investments in the ITS industry are actually large scale infra-structure investments that feature wide-spread application of high technology. The arguablequestion is whether ITS would promote national level economic growth. Information tech-nology-related industries are increasingly becoming the heart of the economy of many in-

dustrialized nations worldwide. Directing information technology investments towards large-





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6.10 CHAPTER SIX

scale infrastructure developments has the potential to promote new industries that wouldhave an impact on long-term economic growth. This might take place for several reasons(Transportation Infastructures 1995). First, such investments would create large economiesof scale for new computing and communications products even before they could attain suchscale economies in the marketplace. This would offer more rapid returns on investment to

supporters of such industries. Second, as a consequence of such success, capital markets,which are usually risk-averse, might be more inclined to support such industries and makelarger funds available for their expansion. Third, this would speed the adoption of newgenerations of communications and computing technology.

Governments can play critical roles in accelerating the growth of the ITS industry. Publicinvestments could shape the setting of system architectures and standards and influence thedevelopment of applications that would encourage private sector investments by loweringthe risk perceived by private investors. A national ITS mandate would likely reduce someof the risks and result in private companies taking a longer-range view of returns to theircapital spending. The role of governmental leadership in the ITS industry can be easilyappreciated if one contrasts the rapid growth of the ITS industry in a country like the UnitedStates with that in its neighbor Canada, for example. In the United States, ISTEA promoted

and accelerated ITS research and development using federal funds, and resulted in large-scale involvement from the private sector. In Canada, on the other hand, the absence of asimilar federal ITS mandate is severely crippling the growth of the ITS industry and therelated job market, forcing Canadian talents and entrepreneurs in the ITS field to be export-oriented, shifting focus and effort toward the American market and the international marketin general.

Sustainability. A 1987 United Nations-sponsored report entitledOur Common Futurede-fined sustainable development as development that meets the needs of the present withoutcompromising the ability of future generations to meet their own needs. Thus, any economicor social development should improve rather than harm the environment. Sustainability hasonly recently begun to be applied to cities. With increasing environmental awareness, urban

transportation planning process becomes more concerned with the air, land, and water andthe likely ecological impact of transportation facilities.Thus, sustainable transportation planning states that cities can become more livable, more

humane, more healthy places, but they must learn how to achieve this by using fewer naturalresources, creating less waste, and decreasing the impact on the environment.

Cities are increasingly involved in pursuing this sustainability agenda. For this purpose,specific indicators are defined to guide cities to move towards more livable communitieswhile reducing their impact on the earth and the ecosystem. Examples of such indicators aretaken from Newman and Kenworthy (1998):

Energy and air quality (e.g., the reduction of energy use per capita, air pollutants, green-house gases)

Water, materials, and waste (e.g., the reduction of total water user per capita, solid waste,consumption of building materials per capita)

Land, green spaces, and biodiversity (e.g., preserve agricultural land and natural landscapeand green space; increase proportion of urban redevelopment to new developments, in-crease density of population and employment in transit-oriented locations)

Transportation (e.g., reduce auto use per capita; increase transit, walk, bike, and carpool;decrease parking spaces)

Livability: human amenities and health (e.g., decrease infant mortality, increase educationalattainment, decrease transport fatalities, increase proportion of cities allowing mixed-useand higher-density urban villages).

The above indicators are a scaled-down version of the original 150 indicators suggested bythe World Bank and the UN Center for Human Settlements. They serve as evidence of how





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cities are contributing to global problems, namely greenhouse gases and oil depletion. Everyparticular city has to define the indicators that are applicable to its conditions, and conse-quently manage both local and global issues.

In order to meet the sustainability indicators, cities have to develop sustainability plans,known also as Local Agenda 21 plans, as stated in Agenda 21:

Each Local authority should enter into a dialogue with its citizens, local organizations and privateenterprises and adopt a local Agenda 21. Local authorities should learn from citizens and local,civic, community, business, and industrial organizations the information needed for formulatingthe best strategies. This process will also increase household awareness of sustainable developmentissues (Sitarz 1994, 177)

Sustainability plans require two central approaches, namely integrated planning as wellas community participation. The integrated planning deals with the fusion of cities physicaland environmental planning with economic planning. On the other hand, community partic-ipation calls for public participation in planning. In other words, urban plans should be

designed with local citizens to meet their local needs.Auto-dependency is recognized as a great threat to sustainability. In fact, one of the centralarguments for sustainable development is concerned with the critical impact of an automo-bile-based transportation system on a society. Thus, changes in travel behavior must occurin order to minimize transportations impact on the environment (Newman and Kenworthy1998). Three general approaches are to be implemented simultaneously to limit auto-dependency and consequently change cities over time to become more sustainable:

Automobile technological improvements:the development of less-polluting cars to reduceair pollutants and emissions.

Economic instruments:setting the right road user charges to meet the real cost of autousage, such as pollution costs, health costs, road and parking costs, etc.

Planning mechanisms:the need of a non-automobile-dependent planning. The New Ur-banism trend encourages environment-friendly commuting modes, such as transit, cycling,and walking. This can be achieved by changing the urban fabric to become denser andmixed land use.

In addition, in order to reduce auto-dependency in cities, five policies should be followed.These policies bring together the processes of traffic calming, state-of-the-art transit, bicycleplanning, and transit-oriented development, the neo-traditional urban design of streets forpedestrians, in particular the design of urban villages, growth management, as well as eco-nomic penalties for private transportation.

6.2 TRAFFIC STREAM PARAMETERS AND THEIR MEASUREMENT

6.2.1 Characteristics of Traffic Flow

Traffic flow can be divided into two primary types: interrupted flow and uninterrupted flow.Uninterrupted flow occurs when vehicles traversing a length of roadway are not required

to stop by any cause external to the traffic stream, such as traffic control devices. Uninter-rupted flow is regulated by vehicle-vehicle interactions on one side and by the interactionsbetween vehicles and the roadway environment and geometry on the other side. An instanceof uninterrupted flow includes vehicles traveling on an interstate highway or on other limited

access facilities where there are no traffic signals or signs to interrupt the traffic. Uninter-rupted flow can also occur on long sections of rural surface highway between signalized





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6.12 CHAPTER SIX

intersections. Even when such facilities are experiencing congestion, breakdowns in the traf-fic stream are the results of internal rather than external interactions in the traffic stream.

Interrupted flow occurs when flow is periodically interrupted by external means, primarilytraffic control devices such as stop and yield signs and traffic signals. Under interrupted flowconditions, traffic control devices play a primary role in defining the traffic flow, while

vehicle-vehicle interactions and vehicle-roadway interactions play only a secondary role. Forinstance, traffic signals allow designated movements to occur only part of the time. In ad-dition, because of the repeated stopping and restarting of traffic stream on such facilities,flow occurs in platoons.

6.2.2 Traffic Stream Parameters

Traffic stream parameters represent the engineers quantitative measure for understandingand describing traffic flow. Traffic stream parameters fall into two broad categories: macro-scopic parameters, which characterize the traffic stream as a whole, and microscopic para-meters, which characterize the behavior of individual vehicles in the traffic stream with

respect to each other.The three macroscopic parameters that describe traffic stream are volume or rate of flow,

speed, and density.

Volume and Flow. Volume is simply the number of vehicles that pass a given point on theroadway or a given lane or direction of a highway in a specified period of time. The unit ofvolume is simply vehicles, although it is often expressed as annual, daily, hourly peak andoff-peak. The subsequent sections explain the range of commonly used daily volumes, hourlyvolumes, and subhourly volumes.

Daily Volumes. Daily volumes are frequently used as the basis for highway planning,for general trend observations, as well as for traffic volume projections. Four daily volumeparameters are widely used: average annual daily traffic (AADT), average annual weekday

traffic (AAWT), average daily traffic (ADT), and average weekday traffic (AWT).

AADT is the average 24-hour traffic volume at a given location over a full year, that is,the total number of vehicles passing the site in a year divided by 365. AADT is normallyobtained from permanent counting stations, typically bidirectional flow data rather thanlane-specific flow data.

AAWT is the average 24-hour traffic volume occurring on weekdays over a full year.AAWT is normally obtained by dividing the total weekday traffic for the year by the annualweekdays (usually 260 days). This volume is of particular importance since weekend trafficis usually low; thus, the average higher weekday volume over 365 days would hide theimpact of the weekday traffic.

ADT is the average 24-hour traffic volume at a given location for a period of time lessthan a year (e.g., summer, six months, a season, a month, a week). ADT is valid only forthe period of time over which it was measured.

AWT is the average 24-hour traffic volume occurring on weekdays at a given location fora period of time less than a year, such as a month or a season.

The unit describing all these volumes is vehicles per day (veh/day). Daily volumes areoften not differentiated per lane or direction but rather are given as totals for an entire facilityat a particular location.

Hourly Volumes. As mentioned previously, daily volumes are used mainly for planningapplications. They cannot be used alone for design and operational analysis. Hourly volumesare designed to reflect the variation of traffic over the different time period of a day. They

are also used to identify single hour or period of highest volume in a day occurring during





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the morning and evening commute, that is, rush hours. The single hour of the day corre-sponding to the highest hourly volume is referred to as peak hour. The peak hour trafficvolume is a critical input in the design and operational analysis of transportation facilities.The peak hour volume is usually a directional traffic, that is, the direction of flows is sep-arated. Highway design as well as other operations analysis, such as signal design, must

adequately serve the peak-hour flow corresponding to the peak direction.Peak hour volumes can sometimes be estimated from AADT, as follows:

DDHV AADT K D

where DDHV directional design hourly volume (veh/hr)AADT average annual daily traffic (24 hours) (veh/day)

K factor for proportion of daily traffic occurring at peak hourD factor for proportion of traffic in peak direction

KandDvalues vary depending on the regional characteristics of the design facilities, namely,rural versus urban versus suburban. Koften represents the AADT proportions occurringduring the thirtieth or fiftieth highest peak hour of the year. Kfactor is inversely proportional

to the density of development surrounding the highway. In design and analysis of rural areas,the thirtieth highest peak-hour volume is used, while in urbanized areas the fiftieth highestis used. The Dfactor depends on both the concentration of developments and the specificrelationship between the design facility and the major traffic generators in the area. TheHighway Capacity Manual 2000 provides ranges for Kand D factors depending on thefacility types and the corresponding regional characteristics of the area.

Subhourly Volumes. Subhourly volumes represent traffic variation within the peak hour,i.e., short-term fluctuations in traffic demand. In fact, a facility design may be adequate fordesign hour, but breakdown may occur due to short-term fluctuations. Typical designs andoperational analyses are based on 15-minute peak traffic within the peak hour (e.g., level ofservice analysis using Highway Capacity Manual).

The peak-hour factor (PHF) is calculated to relate the peak flow rate to hourly volumes.

This relationship is estimated as follows:

VPHF

4 V15

where PHF peak hour factorV peak hour volume (veh/hr)

V15 volume for peak 15-min period (veh)

The PHF describes trip-generation characteristics. When PHF is known, it can be used toconvert a peak-hour volume to an estimated peak rate of flow within an hour:

Vv PHF

where v peak rate of flow within hour (veh/hr)V peak hourly volume (veh/hr)

PHF peak hour factor

Speed. The speed of a vehicle is defined as the distance it travels per unit of time. It isthe inverse of the time taken by a vehicle to traverse a given distance. Most of the time,each vehicle on the roadway will have a speed that is somewhat different from the speed ofthe vehicles around it. In quantifying the traffic stream, the average speed of the traffic isthe significant variable. The average speed, called the space mean speed, can be found by

averaging the individual speeds of all of the vehicles in the study area.





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6.14 CHAPTER SIX

Space Mean versus Time Mean Speed. Two different ways of calculating the averagespeed of a set of vehicles are reported, namely the space mean speed and the time meanspeed. This difference in computing the average speed leads to two different values withdifferent physical significance. While the time mean speed (TMS) is defined as the averagespeed of all vehicles passing a point on a highway over a specified time period, the space

mean speed (SMS) is defined as the average speed of all vehicles occupying a given sectionof a highway over a specified time period. TMS is a point measure and SMS is a measurerelating to a length of highway or lane. TMS and SMS may be computed from a series ofmeasured travel times over a measured distance. TMS takes the arithmetic mean of theobservation. It is computed as:

d tiTMS

n

SMS could be calculated by taking the harmonic mean of speeds measured at a point overtime. It is computed by dividing the distance by an average travel time, as shown below:

d ndSMS

t ti in

where TMS time mean speed (fps or mph)SMS space mean speed (fps or mph)

d distance traversed (ft or mi)n number of travel times observedti travel time for the ith vehicles (sec or hr)

Density. Density is the number of vehicles present on a given length of roadway or lane.

Normally, density is reported in terms of vehicles per mile or per kilometer. High densitiesindicate that individual vehicles are very close to each other, while low densities implygreater distances between vehicles. Density is a difficult parameter to measure directly inthe field. Direct measurements of density can be obtained through aerial photography, whichis an expensive method, or it can be estimated from the density, flow, and speed relationshipas explained in the paragraphs below.

Flow, Speed, Density Relationship. Speed, flow, and density are all related to each otherand are fundamental for measuring the operating performance and level of service of trans-portation facilities, such as freeway sections. Under uninterrupted flow conditions, speed,density, and flow are all related by the following equation:

Flow Density Speed: v S D

where v flow (veh/hr)S space mean (average running) speed (mph, km/hr)

D density (veh/mile, veh/hr)

The general form of relationships between speed, density, and flow is illustrated in Figure6.2, also known as the fundamental diagrams of traffic flow. The relationship between speedand density is consistently decreasing. As density increases, speed decreases. This diagramas well as the above formula show that flow is zero under two different conditions:

When density is zero: thus, there is no vehicle on the road

When speed is zero: vehicles are at complete stop because of traffic congestion.





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FIGURE 6.2 Fundamental flow-speed-density diagram.

In the first case, the speed corresponds to the theoretical maximum value: the free flow speedv0, while in the second the density assumes the theoretical maximum value: the jam density,Kjam. The peak of the density flow curve (and speed-flow curve) occurs at the theoreticalmaximum flow (i.e., capacity) of the facility. The corresponding speed vcand density kcarereferred to as the critical speed and the critical density at which maximum capacity occurs.

Density is the most important of the three traffic-stream parameters, since it is the measuremost directly related to traffic demand and congestion levels. In fact, traffic is generatedfrom various land uses, bringing trips on a highway segment. Generated trips produce trafficdensity, which in turn produces flow rate and speeds. Density also gives an indication of thequality of flow on the facilities. It is the measure of proximity of vehicles and is also thebasis for LOS on uninterrupted facilities. In addition, density readings, in contrast to flowmeasurements, clearly distinguish between congested or uncongested conditions.

6.2.3 Other: Gap, Headway, and Occupancy

Flow, speed, and density are macroscopic parameters characterizing the traffic stream as awhole. Headway, gap, and occupancy are microscopic measures for describing the spacebetween individual vehicles. These parameters are discussed in the paragraphs below.

Headway. Headway is a measure of the temporal space between two vehicles, or, morespecifically, the time that elapses between the arrival of the leading vehicle and the followingvehicle at the designated test point along the lane. Headway between two vehicles is mea-sured by starting a chronograph when the front bumper of the first vehicle crosses the selectedpoint and subsequently recording the time that the second vehicles front bumper crossesover the designated point. Headway is usually reported in units of seconds.

Average value of headway is related to macroscopic parameters as follows:





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6.16 CHAPTER SIX

Headway, h (sec)

Spacing , S (ft or m)

Gap (sec)

Clearance (ft or m)

Headway, h (sec)

Spacing , S (ft or m)

Gap (sec)

Clearance (ft or m)

FIGURE 6.3 Illustration of gap and headway definition.

3600Average headway 1/flow or v

ha

where v rate of flowha average headway

Gap. Gap is very similar to headway, except that it is a measure of the time that elapsesbetween the departure of the first vehicle and the arrival of the second at the designated testpoint. Gap is a measure of the time between the rear bumper of the first vehicle and thefront bumper of the second vehicle, where headway focuses on front-to-front times. Gap isalso reported in units of seconds. Figure 6.3 illustrates the difference between gap andheadway.

Occupancy. Occupancy denotes the proportion or percentage of time a point on the roadis occupied by vehicles. It is measured, using loop detectors, as the fraction of time thatvehicles are on the detector. Therefore, for a specific time interval T, occupancy is the sumof the time that vehicles cover the detector, divided by T. For each individual vehicle, thetime spent on the detector is determined as function of the vehicles speed, its headway, itslength L, plus the length of the detector itself C. That is, the detector is affected by thevehicle from the time the front bumper crosses the start of the detection zone until the timethe rear bumper clears the end of the detection zone. Occupancy is computed as follows:

(L C)/speedLO (L C) density k (L C)

headway

Assuming flow density speed

where LO lane occupancy, i.e., percentage of time a lane is occupied with vehicles divided

by total study timeK density of flowL average vehicle lengthC length of detector

Therefore, if occupancy is measured as above, density can be estimated as:

LOk

(L C)





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Magnetic Flux

BuriedInductive Loop

Detector

Electronics

in Cabinet

Terminal Connections

Lead In Cable

AC current flow direction in loop

Terminal connection between loop and lead in

FIGURE 6.4 Car passing over inductive loop buried in pavement. Theloop system becomes active when the detector unit sends an electriccurrent through the cable, creating a magnetic field in the loop. When avehicle passes over the loop, the metal of the vehicle disturbs the mag-netic field over the loop, which causes a change in the loops inductance.Inductance is an electrical property that is proportional to the magneticfield. The induced magnetic field increases the frequency of oscillationthat is sensed by the detector unit. The loop sensor thus detects a vehicle.

6.2.4 Loop Detector as Measuring Device

The inductive loop detector is by far the most common form of detector used for both trafficcounting and traffic management purposes. It is used to measure traffic volume, flow rate,vehicle speed, and occupancy. Inductance loops are widely used detector systems and are

known for their reliability in data measurement, flexibility in design, and relatively low cost.The loop detectors principal components (see Figure 6.4) include:

One or more turns of insulated wire buried in a narrow, shallow saw-cut in the roadway

Lead-in cable that connects the loop to the detector via a roadside pull-out box

Detector unit (or amplifier) that interprets changes in the electrical properties of the loopwhen a vehicle passes over it

Data that can be determined from inductive loop detectors include lane occupancy, trafficdensities, traffic composition, average and instantaneous vehicle velocities, presence of con-gestion, and length and duration of traffic jams. Depending on the technology used, thesedata can be directly or indirectly determined by the inductive loop detectors. Additional data

include historical data, weather condition measurements, time of day (rush hour or other-wise), and type of day (weekday, weekend, public holiday).





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6.18 CHAPTER SIX

Loop detectors are also necessary to measure the data that will be used to construct atraffic model and calibrate this model, as we will see in the next section (i.e., checkingwhether the behavior predicted by the model corresponds accurately enough to the realbehavior of the system).

6.3 TRAFFIC FLOW THEORY

Knowledge of fundamental traffic flow characteristics (speed, volume, and density) and therelated analytical techniques are essential requirements in planning, design, and operation oftransportation systems. Fundamental traffic flow characteristics have been studied at the mi-croscopic, mesoscopic, and macroscopic, levels. Existing traffic flow models are based ontime headway, flow, time-space trajectory, speed, distance headway, and density. These mod-els lead to the development of a range of analytical techniques, such as demand-supplyanalysis, capacity and level of service analysis, traffic stream modeling, shock wave analysis,queuing analysis, and simulation modeling (May 1990).

Traffic simulation models are also classified as microscopic, macroscopic, and mesoscopicmodels. Microscopic simulation models are based on car-following principles and are typi-cally computationally intensive but accurate in representing traffic evolution. Macroscopicmodels are based on the movement of traffic as a whole by employing flow rate variablesand other general descriptors representing flow at a high level of aggregation without distin-guishing its parts. This aggregation improves computational performance but reduces thedetail of representation. Mesoscopic models lie between the other two approaches and bal-ance accuracy of representation and computational performance. They represent averagemovement of a group of vehicles (packets) on a link. Microscopic analysis may be selectedfor moderate-size systems where there is a need to study the behavior of individual units inthe system. Macroscopic analysis may be selected for higher-density, large-scale systems inwhich a study of behavior of groups of units is adequate. Knowledge of traffic situations

and the ability to select the more appropriate modeling technique is required for the specificproblem. In addition, simulation models differ in the effort needed for the calibration process.Microscopic models are the most difficult to calibrate, followed by mesoscopic models.Macroscopic models are easily calibrated.

6.3.1 Traffic Flow Models

Microscopic traffic flow modeling is concerned with individual time and space headwaybetween vehicles, while macroscopic modeling is concerned with macroscopic flow char-acteristics. The latter are expressed as flow rates with attention given to temporal, spatial,and modal flows (May 1990). This section describes the best-known macroscopic, mesosopic,

and microscopic traffic flow models.

Macro Models. In a macroscopic approach, the variables to be determined are:

The flow q(x,t) (or volume) corresponding to the number of vehicles passing a specificlocation xin a time unit and at time period t

The space mean speed v(x,t) corresponding to the instantaneous average speed of vehiclesin a length increment

The traffic density k(x,t) corresponding to the number of vehicles per length unit

These macroscopic variables are defined by the well-known equation:





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FIGURE 6.5 Three-dimensional fundamental diagram. (Source:Hall 1998.)

q(x,t) k(x,t) v(x,t)

The static characteristics of the flow are completely defined by a fundamental diagram(as shown in Figure 6.5). The macroscopic approach considers traffic stream parameters anddevelops algorithms that relate flow to density and space mean speed. Various speed-density

models have been developed and are shown also to fit experimental data. These models areexplained below.

Greenshields Model. The first steady-state speed-density model was introduced byGreenshields, who proposed a linear relationship between speed and density as follows:

uu u k

kj

where u velocity at any timeu free-flow speed

k density at that instant

kj

maximum density

As mentioned above, in these equations, as the flow increases, density increases and thespeed decreases. At optimum density, flow becomes maximum (qm) at u u/2 and k kj/ 2.





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6.20 CHAPTER SIX

Greenberg Model. A second early model was suggested by Greenberg (1959), showinga logarithmic relationship as follows:

u cln (k/k)j

where u velocity at any timec a constant (optimum speed)k density at that instantkj maximum density

Three-Dimensional Models. The idea of considering all three fundamental variables (q,k, v) simultaneously first appeared in TRB SR-165. The notion of a three-dimensional modelappeared in the form of Figure 6.5, where v q/k represents the surface of admissibletraffic stream models. The surface shown in Figure 6.5 is a continuous one; thus, by acceptingthat the u q/krelationship holds the entire range of traffic operations, one can reasonablyconclude that it suffices to study traffic modeling as a two-dimensional problem (Hall 1998).

Lighthill and Whitham(LW) Model. The continuous-flow approach, proposed by Ligh-thill and Whitham (LW) (1955), represents the aggregate behavior of a large number ofvehicles. This model is applicable to the distribution of traffic flow on long and crowdedroads. The LW model reproduces qualitatively a remarkable amount of real traffic phenom-ena, such as the decreasing speeds with increasing densities and shock wave formation.

The LW model is derived from the physical law of incompressible fluid and is based onthe following three fundamental principles (Cohen 1991):

1. Continuous representation of variables:It considers that at a given location xand timet, the traffic mean speed u(x,t), the flow q(x,t) and traffic density values k(x,t) are contin-uous variables and satisfy the relation u(x,t) q(x,t) /k(x,t).

2. The law of conservation of mass: This is a basic speculation of the simple continuummodel, which states that vehicles are not created or lost along the road. The law of theconservation of the number of vehicles leads to the continuity equation for the densityk(x,t):

k(x,t) q(x,t) 0

t x

3. The statement of fundamental diagrams:The fundamental hypothesis of the theory is thatat any point on the road, the speed uis a function of the density. In addition, speed is adecreasing function of concentration: u u(k).

Therefore, the law of traffic at a given section of the road during a given time period canbe expressed in terms of an equation relating two out of the three variables flow, concentra-tion, and speed (Cohen 1991).

For the macroscopic description of the theory the flow q(veh/hr), the densityk(veh/km),and the mean speed u(km/hr) are considered as differentiable functions of timetand spacex(Papageorgiou 1998).

From the continuity equation with the flow-density relation (q q(k)) and the basicrelation between traffic variables (q u k), a differential equation of the density (k) isderived as follows:

k(x,t) k(x,t) q(k) 0

t x

The kinematic waves theory attempts to solve this partial differential equation to predict theconcentration of flow at any point on the road at any time.

Figure 6.6 shows how the propagation speed of the shock wave corresponds to the slopeof the tangent on the fundamental diagram. This hypothesis implies that slight changes in





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Time, t

Distance,x

Time, t

Distance,x

Flo

w (

q)

Density (k) kc (Critical Density)

qm Max. Flow Rate

A

Flo

w (

q)


qm

A

Flo

w (

q)


qm Max. Flow Rateqm Max. Flo Rate

A

FIGURE 6.6 Speed and kinematic waves. (Source:Cohen 1991.)

traffic flow are propagated through the stream of vehicles along kinematic waves. Waves arepropagated either:

Forward, when density k is less than the critical density kc, which corresponds to theuncongested region of the flow-density diagram, or

Backward, when kis greater than critical density kc, which corresponds to the congestedregion of the flow-density diagram.

This property leads to a distinction between two types of flow, namely uncongested flow(for k kc) and congested flow (k kc). In practice, once congestion occurs, disturbancepropagates backward from downstream.

Under several assumptions and simplifications, the LW model is consistent with a classof car-following models. With regard to urban traffic flow in signalized networks, the LWmodel is more than sufficient because traffic flow dynamics are dominated by external events(red traffic lights) rather than by the inherent traffic flow dynamics (Papageorgiou 1998). Forfreeway traffic flow, the LW model achieves a certain degree of qualitative accuracy and iscertainly an improvement over purely static approaches. However, the LW model includes anumber of simplifications and fails to reproduce some real dynamic phenomena observed onfreeways.

Shock Waves. Flow-speed-density states changes over space and time (May 1990). Withthe prompt occurrence of such change, a boundary is established that marks a discontinuityof flow and density from one side of the boundary in respect to the other. This discrepancyis explained by the generation of shock waves. Basically, a shock wave exists whenever thetraffic conditions change abruptly. As such, shock waves can be generated by collisions,sudden increases in speed caused by entering free-flow conditions, or a number of othermeans. A shock, then represents a mathematical discontinuity (abrupt change) in k, q, or u.

Figure 6.7, from May (1990), shows two different densities, flows and speed of vehiclesmoving along a highway. The line separating these two flows represents the shock wave andis moving at a speed wAB.

The propagation velocity of shock waves is

w (q q) / (k k)AB B A B A

where wAB propagation velocity of shock wave (mph or km/hr)qB flow prior to change in conditions (veh/hr)qA flow after change in conditions (veh/hr)kB traffic density prior to change in conditions (veh/mile or veh/km)kA traffic density after change in conditions (veh/mile or veh/km)

Thus, the shock wave separating the two flows travels at an intermediate speed. Since the





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6.22 CHAPTER SIX

FIGURE 6.7 Shock wave analysis fundamentals. (Source:May 1990.)

Shock wave

FIGURE 6.8 Shock wave diagrams.

shock wave in Figure 6.7 is moving with the direction of the traffic, it is a positive forward-moving shock wave. On the other hand, a backward-moving shock wave or negative shockwave travels upstream or against the traffic stream.

Figure 6.8, from Cohen (1991), demonstrates the use of traffic waves in identifying theoccurrence of a shock wave and following its trajectory. The figure on the left represents a

flow-concentration curve. The figure on the right represents the occurrence of a shock waveand following its trajectory. On the qkcurve, point Arepresents a situation where traffictravels at near capacity, implying that speed is well below the free-flow speed. Point Brepresents an uncongested condition where traffic travels at a higher speed because of thelower density. Tangents at points Aand Brepresent the wave velocities of these two situa-tions. The line connecting the two points on the qkcurve represents the velocity of theshock wave. In the space-time diagram the intersection of these two sets of waves has aslope equal to the slope of the line connecting the two points Aand Bon the qkcurve.This intersection represents the velocity of the shock wave.

Second-Order Model: Payne Model. Payne (1971) proposed a method for relating mac-roscopic variables and car-following theories. Payne developed an extended continuum modelthat takes into consideration drivers reaction time and uses a dynamic speed equation as

shown below:

D()dV 2 (V() V) e

dt x

where the term (Ve() V) / is denoted by the relaxation term and the term (D() /)(/x) is denoted by the anticipation term.

The relaxation term allows for the delayed adjustment of the stream to a prespecifiedspeed Ve() as a result of reaction time and braking or acceleration procedures. The antic-





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FIGURE 6.9 Car-following model.

ipation term allows the drivers to adjust their speeds in advance to changes in density lyingahead.

The 2nd-order model provides the possibility of a more realistic description of traffic flow(Kim 2002). The shock wave problem is alleviated through the application of the diffusionterms. Moreover, unstable congested states are derived by the interplay between anticipation

and relaxation effects in the model. The 2nd-order model has a critical density, above whichuniform flow conditions are unstable and the wave is oscillating with ever-increasing am-plitude. In addition, the presence of oscillating waves, explains stop-and-go traffic conditions.

Microscopic Models. Much research has been devoted to the concept that traffic streambehavior can be analyzed at the microscopic level. At this level the behavior of individualdrivers must be examined and modeled. Microscopic models use car following laws to de-scribe the behavior of each driver-vehicle system in the traffic stream as well as their inter-action. Examples of microscopic models include car-following models, General Motors mod-els, and cell transmission and cellular automata models.

Car-Following. These models are based on supposed mechanisms describing the processof one vehicle following another, called follow-the-leader models (Lieberman and Rathi

1998). From the overall driving task, the subtask that is most relevant to traffic flow is thetask of one vehicle following another on a single lane of roadway (car following). Thisparticular driving subtask is relatively simple to describe by mathematical models as com-pared to other driving tasks. Car-following models describe the process of car-following insuch a way as to approximate the macroscopic behavior of a single lane of traffic. Hence,car-following models form a bridge between individual car-following behavior and the mac-roscopic world of a line of vehicles and their corresponding flow and stability properties.

Pipes and Forbes Car-Following Models. Car-following theories were developed in the1950s and 1960s. Early models employed simple rules for determining the distance gapbetween vehicles. For example, Pipes (1953) argued that the rule that drivers actually followis the following, as suggested by the California Motor Vehicle Code: The gap that a drivershould maintain should be at least one car length for every 10 mph of speed at which he is

traveling.Using the notation shown in Figure 6.9 for the gap and the vehicle speed, the resultingdistance headway dcan be written as:

x (t)n1d [x(t) x (t)] L L min n n1 min n n(10)(1.47)According to Pipes car-following theory, the minimum safe distance headways increaselinearly with distance.





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6.24 CHAPTER SIX

FIGURE 6.10 Simple car-following General Motors principle.

General Motors Models. In reality, drivers conform to the behavior of the immediatelyleading vehicle. Under this notion, a stimulus response relationship exists that describes thecontrol process of the driver-vehicle system. Researchers at General Motors (GM) havedeveloped car-following models and tested these models using real-world data. The impor-tance of these models lies in the discovery of the mathematical bridge linking the microscopic

and macroscopic theories of traffic flow (May 1990).The GM research team developed five generations of car-following models in terms ofresponse-stimuli relationship. The general stimulus-response equation expresses the conceptthat a driver of a vehicle responds to a given stimulus according to a relation (May, 1990):

Response Function {Sensitivity, Stimuli}

where Response acceleration or deceleration of the vehicle, which is dependent on thesensitivity of the automobile and the driver himself

Sensitivity ability of the driver to perceive and react to the stimuliStimuli relative velocity of the lead and following vehicle.

The stimulus function may be composed of many factors: speed, relative speed, intervehiclespacing, accelerations, vehicle performance, driver thresholds, etc. The relative velocity isthe most used term. It is generally assumed in car-following modeling that a driver attemptsto (a) keep up with the vehicle ahead and (b) avoid collisions. The response is the reactionof the driver to the motion of the vehicle immediately in front of him/her. The response ofsuccessive drivers is to react (i.e., accelerate or decelerate) proportionally to the stimulus.

From the notation of Figure 6.10, assuming that the driver of the following vehicle willspace himself/herself from the leading vehicle at a distance, such that in case the leadingvehicle comes to an emergency stop he/she will be able to come to a rest without crashing.Thus, the spacing of the two vehicles at time twill be:

d(t) [x(t) x (t)] T x (t t) b L bn n1 n1 n1 n

where bis the stopping distance of the vehicle.Assuming equal braking distances for the two vehicles and differentiating with respect to

time t, we obtain:

[x(t) x (t t)] T x (t t)n n1 n1

or





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1x (t t) [x(t) x (t t)]n1 n n1

t

where b is the stopping distance of the vehicle, andt reaction time (reciprocal of sensitivity).

The response of the following vehicle is to decelerate by an amount proportional to thedifference of speeds. The measure of sensitivity is the reciprocal of the perception-reactiontime of the driver. The response function is taken as the deceleration of the following vehicle.The response is lagged by the perception and reaction time of the following driver.

Another form in the simple car-following model is to distinguish the reaction time fromthe sensitivity by introducing a sensitivity term as follows:

x (t t) [x(t) x (t)]n1 n n1

The unit of the sensitivity term is sec1. The stimuli term (t)] could be positive,[x(t) xn n1negative, or zero, causing the response to be respectively either an acceleration, deceleration,or constant speed.

The two parameters (sensibility term) and t(reaction time) must be selected in sucha way that traffic behaves realistically. The choice of these terms is associated with theconcept of stability, which is explained below.

Traffic Stability. There are two important types of stability in the car-following system:local stability and asymptotic stability. Local stability is concerned with the response of afollowing vehicle to a fluctuation in the motion of the vehicle directly in front of it, i.e., itis concerned with the localized behavior between pairs of vehicles. Asymptotic stability isconcerned with the manner in which a fluctuation in the motion of any vehicle, say the leadvehicle of a platoon, is propagated through a line of vehicles. The analysis of traffic stabilitydetermines the range of the model parameters over which the traffic stream is stable.

Improvements over the First Generation of the General Motors Model. The first GMmodel was derived using a functional value for acceleration with the assumption that driver

sensitivity is constant for all vehicles (May 1990). In a revised version of the GM model,discrepancy from field values indicated that the sensitivity of the driver was higher wheneverthe headway was less. Accordingly, the GM model was adjusted to account for this error.

Further improvements about the sensitivity were introduced by the speed difference, i.e.,relative velocity, because as the speed difference increases, the sensitivity increases. Everysystem has a time lag to react to changes occurring ahead of it. This is accounted for by theterm t, which represents the reaction time on the part of the following vehicle to accelerateand decelerate. Finally, the powers of the terms of speed and headway of the vehicle aheadwere proposed and these constants were called speed component (m) and headway compo-nent (l). The resulting equation represents the fifth and final GM model and is stated asfollows:

m x (t t)l,m n1x (t t) [x(t) x (t)]n1 n n1l[x(t) x (t)]n n1

This is the generalized model, and all previous GM models can be considered a special caseof this model (May 1990).

Macro-to-Micro Relationship. Gazis, Herman, and Potts (1959) studied the relationshipbetween car-following models and macroscopic traffic stream models. They demonstratedthat almost all macroscopic models were related to almost all car-following theory models(May 1990). Gazis, Herman, and Potts derived a generalized macroscopic model from thecar-following models:

1m 1m l1v v [1 (k/k) ] j

For instance, the Greenshields model lies within the following feasible range: when m 0





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6.26 CHAPTER SIX

FIGURE 6.11 Speed-density relationships for various values ofmand l. (Source:May 1990.)

and l 2. Figure 6.11 shows the speed-density relationship for a number of cases withm 1 and l 2.0 to 3.0.

New Trends in Microscopic Traffic Flow Modeling. Cell-transmission models of highwaytraffic, developed by Daganzo (1994), are discrete versions of the simple continuum (kine-matic wave) model of traffic flow that are convenient for computer implementation. They

are in the Godunov family of finite difference approximation methods for partial differentialequations. In cell-transmission models, the speed is calculated from the updated flow anddensity rather than being directly updated.

In the cell-transmission scheme the highway is partitioned into small sections (cells). Theanalyst then keeps track of the cell contents (number of vehicles) as time passes. The recordis updated at closely spaced instants (clock ticks) by calculating the number of vehicles thatcross the boundary separating each pair of adjoining cells during the corresponding clockinterval. This average flow is the result of a comparison between the maximum number ofvehicles that can be sent by the cell directly upstream of the boundary and those that canbe received by the downstream cell.

The sending (receiving) flow is a simple function of the current traffic density in theupstream (downstream) cell. The particular form of the sending and receiving functions

depends on the shape of the highways flow-density relation, the proximity of junctions, andwhether the highway has special lanes (e.g., turning lanes) for certain vehicles (e.g., exitingvehicles). Although the discrete and continuum models are equivalent in the limit of van-ishing small cells and clock ticks, the need for practically sized cells and clock intervalsgenerates numerical errors in actual applications.

The cell-transmission representation can be used to predict traffics evolution over timeand space, including transient phenomena such as the building, propagation, and dissipationof queues.

Recently there has been growing interest in studying traffic flow with cellular automata(CA) models. CA models are conceptually simple rules that can be used to simulate a





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complex physical process by considering a description at the level of the basic componentsof the system (Jiang). Only the essential features of the real interactions are taken intoaccount in the evolution rules. Through the use of powerful computers, these models cancapture the complexity of the real-world traffic behavior and produce clear physical patternsthat are similar to real phenomenon.

Nagel and Schreckenberg (1992) introduced the CA model for traffic. The rationale ofCA is not to try to describe a complex system from a global point of view, as it is describedusing for instance differential equations, but rather modeling this system starting from theelementary dynamics of its interacting parts. In other words, CA does not describe a complexsystem with complex equations; rather, it lets the complexity emerge by interaction of simpleindividuals following simple rules. These simple models have been shown to reproduce, atleast qualitatively, the features of real traffic flow.

TRANSIMS microsimulation has adapted CA techniques for representing driving dynam-ics and simulating traffic in entire cities. In these models, the basic idea is to formulate amodel in space and time. The space is the road divided into grid points or cells (typically7.5-m length, which corresponds to the length that a car uses up in a jam). A cell is eitherempty or occupied by exactly one vehicle. In addition, car positions are updated synchro-

nously, in successive iterations (discrete time steps) (Dupuis and Chopard 1998). During themotion, each car can be at rest or jump to the nearest neighbor site along the direction ofmotion. The rule is simply that a car moves only if its destination cell is empty. In essence,drivers do not know whether the car in front will move or is stuck by another car. That is,the state of a cell s(t) at a given time depends only on its own state one time step previously,and the states of its nearby neighbors at the previous time step. This dynamic can be sum-marized by the following relation:

s (t 1) s(t) (1 s(t) ) s(t)s(t)i i1 i i i1

where tis the discrete time step.All cells are updated together. Movement takes place byhoppingfrom one cell to another,

using a 1-second time step, which agrees with the reaction-time arguments. Different vehiclespeeds are represented by different hopping distances (Nagel and Rickert 2001). This impliesfor example that a hopping speed of 5 cells per time step corresponds to 135 km/hr. Ac-cordingly, the rules for car following in the CA are:

1. If no car is ahead: linear acceleration occurs up to maximum speed.

2. If a car is ahead: velocity is adjusted so that it is proportional to the distance betweenthe cars (constant time headway).

3. Sometimes vehicles are randomly slower than what would result from 1 and 2.

Lane changing is done as pure sideways movement in a sub-time step, before the forward

movement of the vehicles, i.e., each time-step is subdivided into two sub-time steps (Nageland Rickert 2001). The first sub-time-step is used for lane changing, while the second sub-time-step is used for forward motion. Lane-changing rules for TRANSIMS are symmetricand consist of two simple elements: decide that you want to change lanes, and check if thereis enough gap to get in. A reason to change lanes is either that the other lane is faster orthat the driver wants to make a turn at the end of the link and needs to get into the correctlane. In the latter case, the accepted gap decreases with decreasing distance to the intersec-tion, that is, the driver becomes more and more desperate. In addition, details of the system,including lane changing, complex turns, and intersection configurations, are fully representedand each driver is given a destination and a preferred path.

In more advanced work, Nagel and Rickert (2001) proposed the parallel implementationof the TRANSIMS traffic microsimulation. In this parallelism, the road network is partitioned

across many processors. This means that each CPU of the parallel computer is responsible





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6.28 CHAPTER SIX

for a different geographical area of the simulated region. The results show a significant speed-up in the computation efficiency.

Meso Models. The mesoscopic models fall in between macroscopic and microscopic mod-eling. The mesoscopic traffic flow models describe the microscopic vehicle dynamics as a

function of macroscopic fields. The gas-kinematic model, which is the most used mesoscopictraffic flow model, treats vehicles as a gas of interacting particles (Nagatani 2002). As such,when the number of vehicles is large, traffic flows is modeled in terms of one compressiblegas. Prigogine and Herman have proposed the following Boltzmann equation for the traffic:

(x,v,t) (x,v,t) (x,v,t) (x,t)F (v) (x,v,t)des v

t x trel int

where the first-term on the right-hand side represents the relaxation of the velocity distri-bution function (x,v,t), to the desired velocity distribution (x,t)Fdes(v), with the relaxationtime rel, in the absence of the interactions of vehicles. The second-term on the right-handside takes into account the change arising from the interactions among vehicles.

Recently, the kinetic theories of a single-lane highway have been extended to two-dimensional flow for urban traffic and multilane traffic.

6.3.2 Traffic-Simulation Models

Computer simulation modeling has been a valuable tool for analyzing and designing complextransportation systems. Simulation models are designed to mimic the behavior of these sys-tems and processes. These models predict system performance based on representations ofthe temporal and/or spatial interactions between system components (normally vehicles,events, control devices), often characterizing the stochastic nature of traffic flow. In general,the complex simultaneous interactions of large transportation system components cannot be

adequately described in mathematical or logical forms. Properly designed models integratethese separate entity behaviors and interactions to produce a detailed, quantitative descriptionof system performance.

In addition, simulation models are mathematical/ logical representations (or abstractions)of real-world systems, which take the form of software executed on a digital computer inan experimental fashion (Lieberman and Rathi 1998). The inherent value of computer sim-ulation is that it allows experimentation to take place off-line without having to go out inthe real world to test or develop a solution. Specifically, simulation offers the benefits ofbeing able to control input conditions, treat variables independently even though they maybe coupled in real life, and, most importantly, repeat the experiment many times to testmultiple alternative performance (Middleton and Cooner 1999). The user of traffic simulationsoftware specifies a scenario (e.g., highway network configuration, traffic demand) as

model inputs. The simulation model results describe system operations in two formats: (1)statistical and (2) graphical. The numerical results provide the analyst with detailed quanti-tative descriptions of what is likely to happen. Traffic simulation models may be classifiedaccording to the level of detail with which they represent the transportation performance, aswell as flow representation, namely (see Table 6.2):

In microscopicmodels, traffic is represented discretely (single vehicles); individual trajec-tories can be explicitly traced. Disaggregate performance measures are calculated basedon explicit modeling of driver behavior.

In mesoscopic models, traffic is represented discretely (vehicles or group of vehicles);individual trajectories can be explicitly traced as for microscopic models. However, ag-gregate performance measures are calculated as for macroscopic models.





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TABLE 6.2 Classification and Examples of Traffic-Simulation Models

Performance functions

Aggregate Disaggregate

Flow representation Continuous

Discrete

MACROSCOPICe.g., FREFLO, AUTOS,METANET

MESOSCOPICe.g., DYNASMART,DYNAMIT,INTEGRATION

MICROSCOPICe.g., INTRAS, CORSIM,PARAMICS, CORSIM,AIMSUN2, TRANSIMS,VISSIM, MITSIM

FIGURE 6.12 Scale and level of detail of simulation models. (Source:Institute of TransportationStudies, University of California, Irvine).

In macroscopic models, traffic is represented continuously followi

traffic engineering analysis

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