Commuting and internet traffic congestion

Berliant, Marcus (2023): Commuting and internet traffic congestion.

Abstract

We examine the fine microstructure of commuting in a game-theoretic setting with a continuum of commuters. Commuters' home and work locations can be heterogeneous. A commuter transport network is exogenous. Traffic speed is determined by link capacity and by local congestion at a time and place along a link, where local congestion at a time and place is endogenous. The model can be reinterpreted to apply to congestion on the internet. We find sufficient conditions for existence of equilibrium, that multiple equilibria are ubiquitous, and that the welfare properties of morning and evening commute equilibria differ on a generalization of a directed tree.

• Item Type: MPRA Paper
• Language: English
• Keywords: Commuting; Internet traffic; Congestion externality; Efficient Nash equilibrium
• Subjects: L - Industrial Organization > L8 - Industry Studies: Services > L86 - Information and Internet Services ; Computer Software; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R4 - Transportation Economics > R41 - Transportation: Demand, Supply, and Congestion ; Travel Time ; Safety and Accidents ; Transportation Noise

References

Anas, A., 2007. "The Trips-to-Flows Riddle in Static Traffic Equilibrium: How to drive a BMW?" Unpublished manuscript.

Arnott, R., A. de Palma and R. Lindsey, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand." American Economic Review 83, 161-179.

Baillon, J.-B. and R. Cominetti, 2008. "Markovian Traffic Equilibrium." Mathematical Programming Series B 111, 33-56.

Beckmann, M., C.B. McGuire and C.B. Winsten, 1956. Studies in the Economics of Transportation. Yale University Press: New Haven.

Berg, N. and G. Gigerenzer, 2010. "As-if Behavioral Economics: Classical Economics in Disguise?" History of Economic Ideas 18, 133-165.

Berliant, M., 2024. "Daily Commuting." Research in Transportation Economics 130. https://doi.org/10.1016/j.retrec.2023.101392

Bertsimas, D., V. Gupta and I. Ch. Paschalidis, 2015. "Data-driven Estimation in Equilibrium Using Inverse Optimization." Mathematical Programming Series A 153, 595-633.

Biles, D.C., M. Federson and R. López Pouso, 2014. "A Survey of Recent Results for the Generalizations of Ordinary Differential Equations." Abstract and Applied Analysis http://dx.doi.org/10.1155/2014/260409.

Braess, D., 1968. "Uber ein Paradoxonder Verkehrsplanung." Unternehmensforschung 12, 258-268.

Bressan, A., 1988. "Unique Solutions for a Class of Discontinuous Differential Equations." Proceedings of the American Mathematical Society 104, 772-778.

Bressan, A., 2000. Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem. Oxford University Press: Oxford.

Bressan, A. and W. Shen, 1998. "Uniqueness for Discontinuous ODE and Conservation Laws." Nonlinear Analysis 34, 637-652.

Colombo, R.M. and A. Marson, 2003. "A Hölder Continuous ODE Related To Traffic Flow." Proceedings of the Royal Society of Edinburgh 133A, 759-772.

Cominetti, R., M. Scarsini, M. Schröder and N. Stier-Moses, 2022. "Approximation and Convergence of Large Atomic Congestion Games." Mathematics of Operations Research 48, 784--811.

Daganzo, C.F., 2008. Fundamentals of Transportation and Traffic Operations. Emerald Group Publishing: Bingley, UK.

de Palma, A. and M. Fosgerau, 2011. "Dynamic Traffic Modeling." In A Handbook of Transport Economics, edited by A. de Palma, R. Lindsey, E. Quinet and R. Vickerman. Edward Elgar: Cheltenham, UK. Ch. 9, pp. 188-212.

Debreu, G., 1952. "A Social Equilibrium Existence Theorem." Proceedings of the National Academy of Sciences 38, 886-893.

Filippov, A.F., 1973. Differential Equations with Discontinuous Righthand Sides. Kluwer: Dordrecht, Netherlands.

Frascaria, D. and N. Oliver, 2022. "Algorithms for Flows Over Time with Scheduling Costs." Mathematical Programming Series B 192, 177-206.

Friedrich, J., O. Kolb and S. Göttlich, 2018. "A Godunov Type Scheme for a Class of Scalar Conservation Laws with Non-local Flux." Working paper.

Garavello, M. and B. Piccoli, 2006. Traffic Flow on Networks: Conservation Laws Model. American Institute of Mathematical Sciences: Springfield, MO.

Han, K., T.L. Friesz and T. Yao, 2013. "Existence of Simultaneous Route and Departure Choice Dynamic User Equilibrium." Transportation Research Part B 53, 17-30.

Han, K., B. Piccoli and T.L. Friesz, 2015. "Continuity of the Path Delay Operator for LWR-Based Network Loading with Spillback." Working Paper.

Heydecker, B.G. and J.D. Addison, 2005. "Analysis of Dynamic Traffic Equilibrium with Departure Time Choice." Transportation Science 39, 39-57.

Hofbauer, J. and W.H. Sandholm, 2007. "Evolution in Games with Randomly Disturbed Payoffs." Journal of Economic Theory 132, 47-69.

Hu, D., 2010. "Equilibrium and Dynamics of the Discrete Corridor Problem." Unpublished manuscript.

Ito, T., 1979. "A Filippov Solution of a System of Differential Equations with Discontinuous Right-Hand Sides." Economics Letters 4, 349-354.

Jacobsson, K., 2008. Dynamic Modeling of Internet Congestion Control. Doctoral Thesis, KTH School of Electrical Engineering: Stockholm.

Kelly, F.P., A.K. Maulloo and D.K.H. Tan, 1998. "Rate Control for Communication Networks: Shadow Prices, Proportional Fairness, and Stability." Journal of the Operational Research Society 49, 237-252.

Khan, M.A., 1989. "On Cournot-Nash Equilibrium Distributions for Games with a Nonmetrizable Action Space and Upper Semicontinuous Payoffs." Transactions of the American Mathematical Society 315, 127-146.

Koch, R. and M. Skutella, 2011. "Nash Equilibria and the Price of Anarchy for Flows over Time." Theory of Computing Systems 49, 71-97.

Konishi, H., 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters." Transportation Science 38, 315-330.

Levinson, D., 2005. "Micro-foundations of Congestion and Pricing: A Game Theory Perspective." Transportation Research Part A 39, 691-704.

Malone, J.B., A. Nevo and J.W. Williams, 2017. "The Tragedy of the Last Mile: Economic Solutions to Congestion in Broadband Networks." Unpublished manuscript.

Marson, A., 2004. "Nonconvex Conservation Laws and Ordinary Differential Equations." Journal of the London Mathematical Society 69, 428-440.

McMillen, D.P. and S.C. Smith, 2003. "The Number of Subcenters in Large Urban Areas." Journal of Urban Economics 53, 321-338.

Merchant, D.K. and G.L. Nemhauser, 1978. "A Model and an Algorithm for the Dynamic Traffic Assignment Problems." Transportation Science 12, 183-199.

Milchtaich, I., 2006. "Network Topology and the Efficiency of Equilibrium." Games and Economic Behavior 57, 321-346.

Ostrovsky, M. and M. Schwarz, 2018. "Carpooling and the Economics of Self-Driving Cars." NBER Working Paper 24349.

Rath, K.P., 1994. "Some Refinements of Nash Equilibria of Large Games." Games and Economic Behavior 7, 92-103.

Rath, K.P., 1998. "Perfect and Proper Equilibria of Large Games." Games and Economic Behavior 22, 331-342.

Rosenthal, R.W., 1973. "A Class of Games Possessing Pure-Strategy Nash Equilibria." International Journal of Game Theory 2, 65-67.

Ross, S.L. and J. Yinger, 2000. "Timing Equilibria in an Urban Model with Congestion." Journal of Urban Economics 47, 390-413.

Roughgarden, T., 2016. Twenty Lectures in Algorithmic Game Theory. Cambridge University Press: Cambridge, UK.

Sandholm, W.H., 2001. "Potential Games with Continuous Player Sets." Journal of Economic Theory 97, 81-108.

Sandholm, W.H., 2007. "Pigouvian Pricing and Stochastic Evolutionary Implementation." Journal of Economic Theory 132, 367--382.

Schmeidler, D., 1973. "Equilibrium Points of Non-Atomic Games." Journal of Statistical Physics 7, 295-301.

Schrank, D., B. Eisele and T. Lomax, 2019. 2019 Urban Mobility Report. Texas A&M Transportation Institute: College Station.

Smart, D.R., 1974. Fixed Point Theorems. Cambridge University Press: Cambridge, UK.

Strub, I.S. and A.M. Bayen, 2006. "Mixed Initial-Boundary Value Problems for Scalar Conservation Laws: Application to the Modeling of Transportation Networks." In Hybrid Systems: Computation and Control, Lecture Notes in Computer Science Volume 3927, edited by J. Hespanha and A. Tiwari, pp. 552-567. Springer Verlag: Berlin.

Verhoef, E., 1999. "Time, Speeds, Flows and Densities in Static Models of Road Traffic Congestion and Congestion Pricing." Regional Science and Urban Economics 29, 341-369.

Vickrey, W., 1963. "Pricing in Urban and Suburban Transport." American Economic Review 53, 452-465.

Vickrey, W., 1969. "Congestion Theory and Transport Investment." American Economic Review 59, 251-261.

Wardrop, J.G., 1952. "Some Theoretical Aspects of Road Traffic Congestion." Proceedings of Institute of Civil Engineers 1, 325-378.

Zhang, X. and H.M. Zhang, 2010. "Simultaneous Departure Time/Route Choices in Queuing Networks and a Novel Paradox." Networks and Spatial Economics 10, 93-112.

Zhu, D. and P. Marcotte, 2000. "On the Existence of Solutions to the Dynamic User Equilibrium Problem." Transportation Science 34, 402-414.