Peakedness of traffic carried by a finite trunk group with renewal input

Abstract

In trunking theory, peakedness is defined conventionally as the variance-to-mean ratio of a traffic load when carried on an infinite trunk group. For analysis of switching machine delays, it has proven useful to define a peakedness measure associated with the Carried Arrival Process (CAP), the stream of call arrivals carried on an incoming trunk group. The peakedness of the CAP is defined to be the conventional peakedness of a fictitious traffic-load process generated by associating with each carried arrival an independent exponentially distributed holding time with mean equal to the mean of calls actually carried on the trunk group. The problem considered is the effect of trunk group congestion on the peakedness of the CAP for traffic consisting of renewal inputs offered on a blocked-calls-cleared basis to a finite trunk group with exponential holding times. The CAP is characterized as a semi-Markov process. This model leads to the determination of the peakedness of the CAP. Numerical results illustrate the reduction of peakedness, or smoothing, introduced by the congestion.