The Impact of Spillback on the Price of Anarchy for Flows over Time

Israel, Jonas; Sering, Leon

doi:10.1007/978-3-030-57980-7_8

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…In this sense, highly congested parts of the network now can have an impact on previous edges as traffic users might spill back to other parts of the network while queuing. Additional properties of this model have been shown by Israel and Sering (2020). Ziemke et al recently presented experiments that indicate a strong connection of the limit of the MATSim flow model for decreasing vehicle and time step size and Nash flows over time with spillback (Ziemke et al 2021).…”

Section: Introductionmentioning

confidence: 81%

Recent Developments in Mathematical Traffic Models

Schmand

2021

Dynamics in Logistics

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Predictions such as forecasts of congestion effects in transportation networks can be based on complex simulations that include many aspects of actual transportation systems. On the other hand, rigorous mathematical traffic models give rise to theoretical analyses, very general statements, and various traffic optimization opportunities. There has been a huge development in the last years to make mathematical traffic models more realistic. This chapter provides an overview of the mathematical traffic models developed recently and some state-of-the-art results.

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Section: Introductionmentioning

confidence: 81%

Recent Developments in Mathematical Traffic Models

Schmand

2021

Dynamics in Logistics

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“…Regarding the price of anarchy of dynamic equilibria, Koch and Skutella [15] derived the first results on the price of anarchy for dynamic equilibria, which were recently improved by Correa, Cristi and Oosterwijk [4] devising a tight bound of e e−1 , provided that a certain monotonicity conjecture holds. Israel and Sering [13] investigated the price of anarchy for the model with spillbacks. Bhaskar, Fleischer and Anshelevich [1] devised Stackelberg strategies in order to improve the efficiency of dynamic equilibria.…”

Section: Further Related Workmentioning

confidence: 99%

The Price of Anarchy for Instantaneous Dynamic Equilibria

Graf¹,

Harks²

2020

Preprint

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We consider flows over time within the deterministic queueing model and study the solution concept of instantaneous dynamic equilibrium (IDE) in which flow particles select at every decision point a currently shortest path. The length of such a path is measured by the physical travel time plus the time spent in queues. Although IDE have been studied since the eighties, the efficiency of the solution concept is not well understood. We study the price of anarchy for this model and show an upper bound of order O(U • τ ) for single-sink instances, where U denotes the total inflow volume and τ the sum of edge travel times. We complement this upper bound with a family of quite complex instances proving a lower bound of order Ω(U • log τ ).

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“…There are many works investigating properties of equilibria in this model [BFA15], [CCL15], [CCO21], [CCO19], [Kai22], [Koc12], [KS11], [OSVK22], [SS18] and in generalized models [IS20], [PS20], [SVK19], [Ser20]. We will discuss some of these later in Section II-E.…”

Section: Introductionmentioning

confidence: 99%

Convergence of Approximate and Packet Routing Equilibria to Nash Flows Over Time

Olver,

Sering,

Koch

2023

2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)

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We consider a dynamic model of traffic that has received a lot of attention in the past few years. Infinitesimally small agents aim to travel from a source to a destination as quickly as possible. Flow patterns vary over time, and congestion effects are modeled via queues, which form based on the deterministic queueing model whenever the inflow into a link exceeds its capacity.Are equilibria in this model meaningful as a prediction of traffic behavior? For this to be the case, a certain notion of stability under ongoing perturbations is needed. Real traffic consists of discrete, atomic "packets", rather than being a continuous flow of non-atomic agents. Users may not choose an absolutely quickest route available, if there are multiple routes with very similar travel times. We would hope that in both these situations -a discrete packet model, with packet size going to 0, and ε-equilibria, with ε going to 0 -equilibria converge to dynamic equilibria in the flow over time model. No such convergence results were known.We show that such a convergence result does hold in singlecommodity instances for both of these settings, in a unified way. More precisely, we introduce a notion of "strict" ε-equilibria, and show that these must converge to the exact dynamic equilibrium in the limit as ε → 0. We then show that results for the two settings mentioned can be deduced from this with only moderate further technical effort.

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The Impact of Spillback on the Price of Anarchy for Flows over Time

Cited by 5 publications

References 20 publications

Recent Developments in Mathematical Traffic Models

Recent Developments in Mathematical Traffic Models

The Price of Anarchy for Instantaneous Dynamic Equilibria

Convergence of Approximate and Packet Routing Equilibria to Nash Flows Over Time

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