Overflow Models for Dimension PBX Feature Packages

In this paper we present numerical results for some traffic overflow systems with queuing. Traffic is offered by two independent streams to two groups of trunks with a finite number of waiting spaces for each, and some overflow capability from the primary group to the secondary group. The holding times of the calls are independent, and exponentially distributed. In two of the three systems considered, the overflow capability models feature packages (FP) offered in Dimension® PBX. The third system, which is considered for comparison, differs from the other two systems in that no overflow is permitted if there is a waiting space available in the primary queue. Since there are a finite number of trunks and waiting spaces in each group, arriving calls may be blocked and cleared from the system. For given offered loads and unit mean holding time, we determine the 661 number of trunks and waiting spaces in the two groups so that the blocking probabilities and the average delays of queued calls do not exceed prescribed values. We also calculate various other quantities, such as the occupancies of the trunk groups and the probability of overflow from the primary group to the secondary group. In addition, we examine the effect on the blocking probabilities and the average delays of varying the loads offered to a given system. The numerical results are based on different techniques developed by Kaufman 1 and Morrison.2,3 The basic problem is to solve a large sparse system of linear equations for the steady-state probabilities of the number of calls in the two groups.