Peakedness of Traffic Carried by a Finite Trunk Group With Renewal Input

This paper is concerned with characterizing the traffic offered to a switching machine, taking into account both the alternate routing t h a t the traffic may have undergone and the smoothing of the traffic resulting from congestion on the trunk group incoming to the machine. In trunking theory, peakedness is defined conventionally as the variance-to-mean ratio of a traffic load carried on an infinite trunk group. It is well known t h a t trunk group blocking of peaked traffic, such as overflow traffic, can be substantially larger t h a n the blocking seen by Poisson traffic with the same intensity. Similarly, switching machine* delay and capacity can be quite sensitive to the peakedness * Throughout this paper, when we refer to a switching machine we mean the common control devices in a switching machine. 1617 1618 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , N O V E M B E R 1 9 7 3 of t h e incoming traffic. 1 To determine t h e peakedness of t h e traffic offered to a switching machine, we must t a k e into account the smoothing effect of the incoming t r u n k groups. To this end, we consider t h e process of arrivals offered to a t r u n k group which are carried by t h a t t r u n k group. We call this process t h e Carried Arrival Process, or CAP. To illustrate the CAP, consider the alternate routing network shown in Fig. 1. Here traffic overflowing t r u n k group AB is then offered to t r u n k group AC [Fig. 1(c)]. Those calls finding free circuits on iC then appear at node C as requests for service.