Network traffic modeled on path dependent queues

Abstract

Network traffic modeled as queues where the probability of a new entry depends on the history of the arrival process is analyzed. Based on this characteristic, we propose to use the generalized Polya stochastic processes (GPPs). The theoretical background of such type of queue is reviewed and the heavy-tailed epochs property is shown to hold for the arrival rates we consider. The probability of instability or congestion for the GPP/M/1 and GPP/GPP/1 queues is analyzed from simulations. The results agree with theoretical results for the Polya process, and show interesting similarities and differences when a recently proposed arrival rate distinct from that of Polya is used. Simulation results and possible further directions are discussed.