A Stackelberg strategy for routing flow over time

Abstract

Routing games are used to to understand the impact of individual users' decisions on network efficiency. Most prior work on routing games uses a simplified model of network flow where all flow exists simultaneously, and users care about either their maximum delay or their total delay. Both of these measures are surrogates for measuring how long it takes to get all of a user's traffic through the network. We attempt a more direct study of how competition affects network efficiency by examining routing games in a flow over time model. We give an efficiently computable Stackelberg strategy for this model and show that the competitive equilibrium under this strategy is no worse than a small constant times the optimal, for two natural measures of optimality. * {umang,lkf}@cs.dartmouth.edu.

Dynamic Flows with Adaptive Route Choice

“…Consider the network in Figure 2 (left). There are two source nodes s 1 and s 2 with constant inflow rates u 1 (θ) ≡ 3 for θ ∈ [0, 1) and u 2 (θ) ≡ 4 for θ ∈ [1,2). Commodity 1 (red) has two simple paths connecting s 1 with the sink t. Since both have equal length ( e τ e = 3), in an IDE both can be used by commodity 1.…”

“…Proof. First, it is possible to determine the queue lengths at time θ k using Constraint (1) and from those the labels v (θ k ) can be obtained. Applying Lemma 3.1 on the nodes in order of increasing v (θ k ) values, we obtain the outflow rates and, therefore, the slope a v of label v for some interval right after θ k .…”

“…Very recently, Cominetti, Correa and Olver [5] shed light on the behavior of steady state queues assuming single commodity networks and constant inflow rates. Sering and Vargas-Koch [19] analyzed the impact of spillbacks in the fluid queuing model and Bhaskar et al [1] devised Stackelberg strategies in order to improve the efficiency of dynamic equilibria.…”

Algorithms for Flows over Time with Scheduling Costs

“…Dynamic equilibria, which is the flow over time equivalent of Wardrop equilibria for static flows, are key objects of study. Existence, uniqueness, structural and algorithmic issues, and much more have been receiving increasing recent interest from the optimization community [4,5,6,7,16,22,23].…”

“…Consider for a moment the model where users cannot choose their departure time, but instead are released from the source at a fixed rate u 0 , and simply wish to reach the destination as early as possible. This is the game-theoretic model that has received the most attention from the flow-overtime perspective [4,6,7,16,22]. Our construction of optimal tolls is applicable to this model as well.…”