Identifying critical transient traffic intensity in a queuing system

  • Kit Laurence Lacanaria Guial National Institute of Physics, University of the Philippines Diliman
  • Johnrob Yap Bantang National Institute of Physics, University of the Philippines Diliman
  • Caesar Aya-ay Saloma National Institute of Physics, University of the Philippines Diliman
Keywords: Stochastic processes, Queue systems, Monte Carlo

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 Tw as a function of their arrival times tarr 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 Tw = Tw (tarr) 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 ρc that points to a transition from a cooperative to competitive queuing conditions.

Published
2017-06-07
Section
Poster Session B (Complex Systems, Simulations, and Theoretical Physics)