The Superposition-Traffic Game

Abstract

We consider a queuing game where a set of sources or players strategically send jobs to a single shared server. The traffic sources have disparate coefficients of variation of the interarrival times, and the sources are strategic in their choice of mean inter-arrival times (or the arrival rates). For every job completion, each player receives a benefit that potentially depends on the number of other players using the server (capturing network effects due to using the same server). However, the players experience a delay due to their jobs waiting in the queue. Assuming the service times have a general distribution with a finite second moment, we model the delay experienced by the superposed traffic using a Brownian approximation. In our first contribution, we show that the total rate of job arrivals at a Nash equilibrium with n sources is larger when the sources have heterogeneous coefficients of variation, while the average delay experienced by a job is smaller, compared to the equilibrium with an equal number of homogeneous sources. In the second contribution, we characterize the equilibrium behavior of the queuing system when the number of homogeneous sources scales to infinity in terms of the rate of growth of the benefits due to network effects.