Analysis of first-come first-served queuing systems with peaked inputs

This paper treats the problem of analyzing a first-come first-served queuing system, in equilibrium, when subjected to a peaked input (e.g., traffic overflowing a trunk group with Poisson input). The basic GI/M/N (renewal input to N exponential servers) queuing result is used, together with each of two models for representing peaked traffic, the Equivalent Random (E-R) model and the Interrupted Poisson Process (IPP) model. The equilibrium virtual delay distribution is derived and compared with the equilibrium distribution of delays seen by arriving calls. Numerical examples are presented, along with comparisons of results using both the above models. The results show that delays can be quite sensitive to peakedness.