A network partitioning methodology for distributed traffic management applications

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  • This article was downloaded by: [Cranfield University]On: 23 April 2014, At: 13:38Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

    Transportmetrica A: Transport SciencePublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/ttra21

    A network partitioning methodologyfor distributed traffic managementapplicationsHamideh Etemadniaa, Khaled Abdelghanya & Ahmed Hassanaa Bobby B. Lyle School of Engineering, Southern MethodistUniversity, PO Box 750340, Dallas, TX 75275-0340, USAAccepted author version posted online: 22 Apr 2013.Publishedonline: 15 Jul 2013.

    To cite this article: Hamideh Etemadnia, Khaled Abdelghany & Ahmed Hassan (2014) A networkpartitioning methodology for distributed traffic management applications, Transportmetrica A:Transport Science, 10:6, 518-532, DOI: 10.1080/23249935.2013.795200

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  • Transportmetrica A: Transport Science, 2014Vol. 10, No. 6, 518532, http://dx.doi.org/10.1080/23249935.2013.795200

    A network partitioning methodology for distributed trafficmanagement applications

    Hamideh Etemadnia1*, Khaled Abdelghany and Ahmed Hassan

    Bobby B. Lyle School of Engineering, Southern Methodist University, PO Box 750340,Dallas, TX 75275-0340, USA

    (Received 31 January 2012; final version received 9 April 2013)

    This paper presents a multi-way network partitioning methodology for distributed traffic man-agement applications. The methodology can be used to partition a typical urban transportationnetwork such that: (a) the inter-flow among the resulting subnetworks is minimised; (b) thesubnetworks are balanced in terms of their sizes/flow activities; and (c) each subnetwork isconnected. Two heuristics are presented. The first adopts a recursive iterative procedure todetermine the networks sparsest cuts that maintain the balance and connectivity requirements.The second heuristic adopts a greedy network coarsening technique to determine the mostflow-independent subnetworks. The solution quality of these two heuristics is evaluated usinghypothetical and real networks with different configurations. The results show that the heuristicscan obtain near-optimal solution in significantly shorter execution times.

    Keywords: distributed traffic management; network partitioning; network coarsening;sparsest cut

    IntroductionUrban areas in the USA and in many countries around the world have rapidly grown in sizeand population resulting in the formation of mega-cities with congested transportation networks.For instance, the Los Angeles (LA) metropolitan area in California has grown at a rate of about35% from 1982 to 2007 recording a total population of 17.8 millions living in 189 cities thatextend over an area of 4850 square miles. With an average annual delay of 70 h per traveller, theLA metropolitan area is ranked as the most congested urban area in the USA (Schrank and Lomax2009). Traffic management in such large congested urban areas is considerably challenging. Itrequires the development of traffic management capabilities that effectively alleviate recurrentand non-recurrent congestion. A holistic approach to develop these capabilities would follow acentralised architecture through which the entire traffic network is managed using one centralcontroller. This controller is equipped with the capabilities to collect real-time information onthe current congestion pattern across the entire network, generate a suitable traffic managementscheme, and disseminate this scheme to the traffic control devices for implementation (e.g. traf-fic light, dynamic message signs, traveller information, etc.). However, the large size of theseurban areas represents a barrier in face of adopting the centralised architecture. It requires an

    *Corresponding author. Email: hetemadnia@mail.smu.edu1Present affiliation: Department of Agricultural Economics, Sociology and Education, Pennsylvania StateUniversity, University Park, PA 16802-5602.

    2013 Hong Kong Society for Transportation Studies Limited

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    extensive wired and wireless communication infrastructure to interconnect these large areas. Fur-thermore, the large network sizes make it algorithmically difficult to develop a global optimaltraffic management scheme, especially if this scheme needs to be generated in real-time (Peetaand Ziliaskopoulos 2001).

    A plausible alternative approach is to adopt a decentralised traffic management architecture. Thearchitecture builds on an existing infrastructure for data collection and traffic management withineach local jurisdiction. Extensive research work has been devoted to describe the framework andmethodological aspects of the decentralised traffic management architecture (Cuena, Hernandez,and Molina 1995; Hawas and Mahmassani 1995; Pavlis and Papageorgiou 1999; Hernandez,Ossowski, and Garcia-Serrano 2002; Logi and Ritchie 2002; Daganzo 2007). For example, Hawasand Mahmassani (1995) proposed a decentralised architecture in which the network is managedby multiple distributed controllers. Each controller manages traffic within a pre-defined subarea.The route guidance instructions and other control strategies are generated by each controller usingtraffic surveillance data for the portion of the network within the controllers locality. Each localcontroller is assumed to estimate the network conditions outside its boundaries based on availablehistorical information. Chiu and Mahmassani (2002) present a hybrid framework that integratesthe centralised and the decentralised approaches. Travellers are split in terms of their source ofroute guidance instructions (centralised versus decentralised). The centralised controller providesroute guidance instructions based on the predicted network conditions, while the decentralisedcontrollers provide route guidance instructions that react to the actual traffic conditions withinthe locality of each controller. Also, Hernandez, Ossowski, and Garcia-Serrano (2002) present aknowledge-based approach to develop a distributed architecture in which a structural cooperationmechanism is used to model the coordination among local controllers.

    Nonetheless, one should expect the quality of a traffic management scheme using a distributedarchitecture to depend primarily on the boundaries of the local controllers, and their interfaces withthe main traffic movements in the network (i.e. traffic hand-off points). Most existing researchwork that adopts distributed traffic management architectures seems to overlook such dimen-sion of the problem assuming that the boundaries of the local controllers are predefined. In arecent research work (Wen 2009; Villalobos, Chiu, and Mirchandani), network decompositionis proposed as a strategy to achieve scalable dynamic traffic assignment (DTA) implementation.To reduce the computational complexity of the existing DTA methodologies, Wen (2009) andVillalobos, Chiu, and Mirchandani propose solution techniques to improve the scalability of DTAmodels for on-line applications. Boundary construction and adjustment algorithm are proposed inJi and Geroliminis (2011, 2012) to obtain partitioning results such that each subnetwork has well-defined macroscopic fundamental diagrams. Several criteria should be considered to determinethe boundaries of the distributed controllers in the decentralised architecture. For example, thenetwork should be partitioned such that the subnetworks are flow-independent. In other words,the partition minimises inter-flow among adjacent subnetworks in order to reduce the need fortraffic management schemes that require intensive communication/coordination among adjacentcontrollers. In addition, the network partitioning should maintain a balance in terms of the amountof traffic management activities required by each local controller. For instance, the partitioningshould be conducted such that the subnetworks are relatively close in size (spatial balance), and/orthey are similar in terms of the amount of served traffic within their boundaries (flow balance). Thebalance criterion would likely enable the decentralised architecture to achieve the real-time com-putational requirement as it distributes the computation effort, associated with developing thetraffic management activities, equally among controllers. Furthermore, the partitioning shouldensure the spatial connectivity of each subnetwork. The boundaries of each subnetwork shouldenvelope all control devices (e.g. traffic lights) that are operated by the controller to facilitatecommunication among these control devices, especially if wireless communication is used.

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  • 520 H. Etemadnia et al.

    In this paper, we investigate the problem of network partitioning for distributed traffic man-agement applications. We present a methodology in which the network is divided such that theabove-mentioned criteria are considered. As the problem is proved to be nondeterministic poly-nomial time-hard (NP-hard), two heuristics are developed to solve it efficiently. The first heuristicrecursively determines a near-optimal sparsest cut through solving the maximum concurrent flow(MCF) problem while maintaining the balance and connectivity requirements. The second heuris-tic adopts a greedy-based network coarsening technique to determine the most flow-independentsubnetworks. The paper contributes to the existing literature by providing a mathematical formu-lation to the traffic network partitioning problem. In addition, the presented methodology is novelas it simultaneously ensures independency and load balance of the obtained partitions. The paperis organised as follows. A literature review of the network partition problem is presented in thenext section. A formal definition of the network partitioning problem in the form of an integermathematical program is presented. We then describe the two heuristics that are developed tosolve this problem. The results of a set of experiments that illustrate their performance are alsopresented. Finally, conclusions and planned research extensions are discussed.

    Literature reviewConsidering its numerous applications, several versions of the network partitioning problem havebeen studied in the graph theory literature (Shmoys 1997). For example, the minimum multicutproblem determines the minimum cost cut in a network such that the source and the sink nodes ofany predefined sourcesink pair are located in two different partitioned components. The sparsestcut problem determines the minimum density cut in the network. It determines the cut with theminimum ratio between the cost of the cut and the total demand between sourcesink pairs thatare disconnected due to this cut. The -balanced cut problem aims at determining the minimumcost cut by separating the network into two components such that one component includes nnodes, where n is the number of nodes in the network. The bisection cut problem is a specialcase of the -balanced cut where is equal to 0.5. The network partitioning problem, includingthe versions mentioned above, has been proven to be NP-hard (Garey and Johnson 1979; Matulaand Shahrokhi 1990). Therefore, an approximate solution that is based on solving a relaxed linearapproximation of the problem is proposed (Matula and Shahrokhi 1990). For example, the dualof the linear approximation of the sparsest cut problem is the MCF problem. Linial, London,and Rabinovich (1995) and independently Garg, Vazirani, and Yannakakis (1996) have shownthat these approximated algorithms could run in polynomial expected time, and are guaranteed toproduce a cut of sparsity ratio of O(log k) factor of the optimal solution, where k is the numberof sourcesink pairs in the network. Rao (1987) emphasised the importance of the sparsest cutin computing a balanced cut. For any cut S, the sparsity ratio is equal to the ratio of: (I) the totalcost of the cut (e Ce, where e is the list of links in the cut S, and Ce is the cost of link e);nd(II) the total disconnected demand (k df , where k is a disconnected sourcesink pair and df isthe demand of this pair). By solving the special case of the sparsest cut problem in which weconsider ( n2 ) sourcesink pairs, and setting the demand between every pair to be one unit (theall pairs unit-demand sparsest cut problem), the denominator of the sparsity ratio is maximisedby having two separated components of roughly equal size which results in a balanced cut. Inorder to achieve a cut that is as close as possible to the required -balance value, an iterativeheuristic approach that adopts a greedy-ratio strategy is proposed. This greedy-ratio heuristic hasbeen proved to find an optimal -balanced cut for any 13 (Shmoys 1997).

    Another approach that adopts a multi-level recursive heuristic is proposed by Hauck and Bor-riello (1995), Karypis, Kumar, and Shekhar (1999), Alpert, Huang, and Kahng (1997), Wichlundand Einar (1998) and Karypis and Kumar (2000). The heuristic recursively creates a coarser

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    version of the network through combining its nodes to reduce the network size. The coarsen-ing step is conducted such that a predefined global objective is achieved. For example, for acost-minimisation partitioning, nodes that are connected with high-cost links are combined torepresent a coarser node in the next iteration. The remaining leas...

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