Analysis of First-Come First-Served Queuing Systems With Peaked Inputs

It is well known, from analysis of blocking in trunk groups, that the blocking seen by peaked traffic (e.g., traffic overflowing a first-choice trunk group with Poisson input) can be significantly larger than blocking seen by Poisson traffic with the same intensity. In this paper, we are interested in determining the effect peaked traffic has on delays in queuing systems. The analysis was motivated by a study of sender attachment delay in Crossbar Tandem switching machines receiving alternate routed (peaked) traffic. We treat the problem of analyzing a first-come first-served queuing system with peaked input for the situation where there is no idle server if there is a waiting customer. The basic tool is the G I / M / N queuing result which requires a characterization of the input process in terms of the Laplace-Stieltjes transform of the interarrival time distribution. This characterization is provided using Wilkinson's Equivalent Random 1 (E-R) model where the peaked input is modeled as an overflow process from a finite trunk group with Poisson input. 1215