Equilibria for multiclass routing in multi-agent networks

Eitan Altman · Hisao Kameda

51 citations0/0 files storedIEEE Conference on Decision and Control (CDC)

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Game Theory and Applications

Abstract

We study optimal static routing problems in open multiclass networks with state-independent arrival and service rates. Our goal is to study the uniqueness of optimal routing under different scenarios. We consider first the overall optimal policy that is the routing policy whereby the overall mean cost of a job is minimized. We then consider an individually optimal policy whereby jobs are routed so that each job may feel that its own expected cost is minimized if it knows the mean cost for each path. This is related to the Wardrop equilibrium concept in a multiclass framework. We finally study the case of class optimization, in which each of several class of jobs tries to minimize the averaged cost per job within that class; this is related to the Nash equilibrium concept. For all three settings, we show that the routing decisions at optimum need not be unique, but that the utilizations in some large class of links are uniquely determined.

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References

1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1994The Traffic Assignment Problem: Models and Methods 1968Über ein Paradoxon aus der Verkehrsplanung 1993Competitive routing in multiuser communication networks 1985Optimal static load balancing in distributed computer systems 1985On the relationship between Nash—Cournot and Wardrop equilibria 1972The Traffic Assignment Problem for Multiclass-User Transportation Networks

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2005Topological Conditions for Uniqueness of Equilibrium in Networks 2003Social optimality and cooperation in nonatomic congestion games 2007Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users 2002Non-cooperative routing in loss networks 2002NASH EQUILIBRIA IN LOAD BALANCING IN DISTRIBUTED COMPUTER SYSTEMS 2019Pricing Traffic Networks with Mixed Vehicle Autonomy 2019Nash Equilibrium in a Road Network with Many Groups of Users

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