Identifying critical transient traffic intensity in a queuing system
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.
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