Identifying critical transient traffic intensity in a queuing system

Abstract

We simulate an M/M/1 queue system with a single server using a Monte Carlo method. Individual agents are tracked in the queue and their mean waiting times T_w as a function of their arrival times t_arr are obtained for different traffic intensities ρ. The intensity ρ is defined as the ratio of the arrival rate λ and the service rate μ. We find that T_w = T_w (t_arr) can be approximately described by a logistic function parametrized by three factors that can provide useful insights in the transient response of the system. From these factors, we identify a critical traffic intensity ρ_c that points to a transition from a cooperative to competitive queuing conditions.