A Markovian Game Theoretic Framework for Analysing a Queueing System with Multiple Servers

This paper introduces a Markov game theoretic framework designed to analyze a Markovian queueing system equipped with multiple servers. Our focus lies in modelling a message transmission system, where messages traverse various transmission options, each associated with a cost and governed by a decision process. The primary objective is to investigate the impact of cooperation and communication, or their absence, among servers. The inherent uncertainty regarding the characteristics of the available transmission alternatives is mathematically captured through a Markovian game formulation. Within this framework, we quantify the inefficiency resulting from the self-interested management of individual servers and the associated loss attributed to the decision-making process. Our analysis encompasses diverse scenarios of signaling exchange among servers, providing valuable insights into the system's behavior under varying conditions.