TY - JOUR
T1 - On the Price of Anarchy for Flows over Time
AU - Correa, José R.
AU - Cristi, Andrés
AU - Oosterwijk, Tim
N1 - Tim Oosterwijk, Computational experiments for the monotonicity conjecture for Flows over Time, 2020, School of Business and Economics, Maastricht University: Pure; https://drive.google.com/open?id=1BTxc7J4I0uS1mg-lBcgT8BlPCCd-8abB and https://docs.google.com/spreadsheets/d/1Rp_brX85lDr0ndrG1Fdw-e6EoOqSZeJy?
PY - 2021
Y1 - 2021
N2 - Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper we study dynamic equilibria in the deterministic fluid queuing model in single-source single-sink networks, arguably the most basic model for flows over time. In the last decade we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the Price of Anarchy, measured as the worst case ratio between the minimum time required to route a given amount of flow from the source to the sink, and the time a dynamic equilibrium takes to perform the same task. Our main result states that if we could reduce the inflow of the network in a dynamic equilibrium, then the Price of Anarchy is bounded by a factor, parameterized by the longest path length, that converges to e/(e − 1) ≈ 1.582 and this is tight. This significantly extends a result by Bhaskar, Fleischer, and Anshelevich (SODA 2011). Furthermore, our methods allow us to determine that the Price of Anarchy in parallel-link and parallel-path networks is exactly 4/3. Finally, we argue that if a certain very natural monotonicity conjecture holds, the Price of Anarchy in the general case is exactly e/(e − 1).
AB - Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper we study dynamic equilibria in the deterministic fluid queuing model in single-source single-sink networks, arguably the most basic model for flows over time. In the last decade we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the Price of Anarchy, measured as the worst case ratio between the minimum time required to route a given amount of flow from the source to the sink, and the time a dynamic equilibrium takes to perform the same task. Our main result states that if we could reduce the inflow of the network in a dynamic equilibrium, then the Price of Anarchy is bounded by a factor, parameterized by the longest path length, that converges to e/(e − 1) ≈ 1.582 and this is tight. This significantly extends a result by Bhaskar, Fleischer, and Anshelevich (SODA 2011). Furthermore, our methods allow us to determine that the Price of Anarchy in parallel-link and parallel-path networks is exactly 4/3. Finally, we argue that if a certain very natural monotonicity conjecture holds, the Price of Anarchy in the general case is exactly e/(e − 1).
KW - flows over time
KW - price of anarchy
KW - dynamic equilibrium
M3 - Article
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
SN - 0364-765X
ER -