Controlling road congestion via a low-complexity route reservation approach

Abstract This work introduces a novel route reservation architecture to manage road traffic within an urban area. The developed routing architecture decomposes the road infrastructure into slots in the spatial and temporal domains and for every vehicle, it makes the appropriate route reservations to avoid traffic congestion while minimizing the traveling time. Under this architecture, any road segment is admissible to be traversed only during time-slots when the accumulated reservations do not exceed its critical density. A road-side unit keeps track of all reservations which are subsequently used to solve the routing problem for each vehicle. Through this routing mechanism, vehicles can either be delayed at their origin or are routed through longer but non-congested routes such that their traveling time is minimized. In this work, the proposed architecture is presented and the resulting route reservation problem is mathematically formulated. Through a complexity analysis of the routing problem, it is shown that for certain cases, the problem reduces to an NP-complete problem. A heuristic solution to the problem is also proposed and is used to conduct realistic simulations across a particular region of the San Francisco area, demonstrating the promising gains of the proposed solution to alleviate traffic congestion.

[1]  Andy H.F. Chow Properties of system optimal traffic assignment with departure time choice and its solution method , 2009 .

[2]  Nikolas Geroliminis,et al.  Optimal Perimeter Control for Two Urban Regions With Macroscopic Fundamental Diagrams: A Model Predictive Approach , 2013, IEEE Transactions on Intelligent Transportation Systems.

[3]  Stelios Timotheou,et al.  Congestion Free Vehicle Scheduling Using a Route Reservation Strategy , 2015, 2015 IEEE 18th International Conference on Intelligent Transportation Systems.

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Xi-Ren Cao,et al.  Perturbation analysis of discrete event dynamic systems , 1991 .

[6]  S. P. Hoogendoorn,et al.  Routing Strategies Based on Macroscopic Fundamental Diagram , 2012 .

[7]  Ismail Chabini,et al.  Discrete Dynamic Shortest Path Problems in Transportation Applications: Complexity and Algorithms with Optimal Run Time , 1998 .

[8]  Yang Du,et al.  Finding Fastest Paths on A Road Network with Speed Patterns , 2006, 22nd International Conference on Data Engineering (ICDE'06).

[9]  Nikolaos Geroliminis,et al.  Properties of a well-defined Macroscopic Fundamental Diagram for urban traffic , 2011 .

[10]  Nikolas Geroliminis,et al.  Approximating Dynamic Equilibrium Conditions with Macroscopic Fundamental Diagrams , 2014 .

[11]  Maria Grazia Scutellà,et al.  Dynamic shortest paths minimizing travel times and costs , 2001, Networks.

[12]  Nikolaos Geroliminis,et al.  Perimeter and boundary flow control in multi-reservoir heterogeneous networks , 2013 .

[13]  Ariel Orda,et al.  Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length , 1990, JACM.

[14]  Markos Papageorgiou,et al.  Exploiting the fundamental diagram of urban networks for feedback-based gating , 2012 .

[15]  Nikolaos Geroliminis,et al.  On the stability of traffic perimeter control in two-region urban cities , 2012 .

[16]  Peter Sanders,et al.  Time-Dependent Route Planning with Generalized Objective Functions , 2012, ESA.

[17]  P. Wagner,et al.  Metastable states in a microscopic model of traffic flow , 1997 .

[18]  Stelios Timotheou,et al.  On the Complexity of Congestion Free Routing in Transportation Networks , 2015, 2015 IEEE 18th International Conference on Intelligent Transportation Systems.

[19]  Nikolaos Geroliminis,et al.  On the spatial partitioning of urban transportation networks , 2012 .

[20]  Nikolaos Geroliminis,et al.  Clustering of Heterogeneous Networks with Directional Flows Based on “Snake” Similarities , 2016 .

[21]  Daniele Condorelli,et al.  Efficient and equitable airport slot allocation , 2007 .

[22]  Lili Du,et al.  Coordinated Online In-Vehicle Navigation Guidance Based on Routing Game Theory , 2015 .

[23]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[24]  Carlos F. Daganzo,et al.  Urban Gridlock: Macroscopic Modeling and Mitigation Approaches , 2007 .

[25]  Dirk Helbing,et al.  The spatial variability of vehicle densities as determinant of urban network capacity , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[26]  Stelios Timotheou,et al.  Improved Road Usage Through Congestion-Free Route Reservations , 2017 .

[27]  Nikolas Geroliminis,et al.  Multiple Concentric Gating Traffic Control in Large-Scale Urban Networks , 2015, IEEE Transactions on Intelligent Transportation Systems.

[28]  Robert L. Smith,et al.  Fastest Paths in Time-dependent Networks for Intelligent Vehicle-Highway Systems Application , 1993, J. Intell. Transp. Syst..

[29]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[30]  H Lieu,et al.  TRAFFIC-FLOW THEORY , 1999 .

[31]  Hesham A Rakha,et al.  Multivariate calibration of single regime speed-flow-density relationships [road traffic management] , 1995, Pacific Rim TransTech Conference. 1995 Vehicle Navigation and Information Systems Conference Proceedings. 6th International VNIS. A Ride into the Future.

[32]  Pravin Varaiya,et al.  Causes and cures of highway congestion , 2001 .

[33]  Lin Xiao,et al.  Adaptive Vehicle Navigation With En Route Stochastic Traffic Information , 2014, IEEE Transactions on Intelligent Transportation Systems.

[34]  Marta C. González,et al.  Understanding congested travel in urban areas , 2016, Nature Communications.

[35]  Andrew V. Goldberg,et al.  Route Planning in Transportation Networks , 2015, Algorithm Engineering.

[36]  Daniel Krajzewicz,et al.  SUMO - Simulation of Urban MObility An Overview , 2011 .

[37]  Meead Saberi,et al.  Urban Network Gridlock: Theory, Characteristics, and Dynamics , 2013 .

[38]  Christos G. Cassandras,et al.  A sample path approach for solving the ground-holding policy problem in air traffic control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[39]  Nikolaos Geroliminis,et al.  Estimating MFDs in Simple Networks with Route Choice. , 2013 .

[40]  Markos Papageorgiou,et al.  Traffic flow optimisation in presence of vehicle automation and communication systems – Part I: A first-order multi-lane model for motorway traffic , 2015 .

[41]  Nikolas Geroliminis,et al.  Equilibrium analysis and route guidance in large-scale networks with MFD dynamics , 2015 .

[42]  Nikolas Geroliminis,et al.  Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control , 2015 .