Bayesian game analysis of a queueing system with multiple candidate servers

Abstract

We combine queueing theory and game theory to evaluate the performance of a queueing system with multiple strategic candidate servers. The intent is to model a transmission system where packets can be sent via multiple options, each incurring a cost and controlled by a distributed management. Our purpose is to analyze the effects of the presence or the lack of both cooperation and communication between servers. The mathematical characterization of the uncertainty about the characteristics of the transmission alternatives available is captured through a Bayesian game formulation. In this setup, we compute both the Price of Anarchy, quantifying the inherent inefficiency arising from selfish management of each server, and the Price of Stability, which is the loss due to distributed system management, under different conditions of signaling exchange among the servers.

The Value of Communication and Cooperation When Servers Are Strategic

“…In addition, we prove that this is the only threshold Nash equilibrium strategy. This is different from the conclusion stated by Guglielmi and Badia [2] that all pairs satisfying p * 1 p * 2 = c are Nash equilibria. Also, we calculate the expression for social welfare for the threshold strategies and obtain the best-case allocation.…”

“…Guglielmi and Badia [2] proposed and analysed a transmission system of two servers. Each server has to make a decision whether to be "active", that is, available for the service, or "inactive", that is, not available for the service.…”

“…Unfortunately, the analysis of Guglielmi and Badia [2] contained some errors. In this paper we correct these errors and change the order so that we look at the most straightforward case first.…”

“…Game theory, which has already been applied to study telecommunication problems [3], provides a mathematical framework with which to model and analyse this situation, since it considers the behaviour of individuals given that everyone's best strategy is affected by the strategies adopted by other participants in the system. In this paper we will take another look at the system that was studied by Guglielmi and Badia [2] and derive somewhat different results.…”

“…The paper is organized as follows. In Section 2 we describe the strategic server system proposed by Guglielmi and Badia [2]and compare our analysis with theirs. In Section 3 we introduce some preliminaries on game theory and describe how we use them to obtain the main results.…”