IPP Overflow Traffic on a Two-stage Queueing Network

Abstract

In a two-stage queueing network the state space is very large such that the exact analytic solution is very hard to obtain. The concept of the IPP overflow stream is a good method to decompose the two-cascade-stage network into two independent queueing systems. The transition matrix will reduce from the size with all the states in the state space of the system to the size depending on the size of the trunk group and the number of the operators in the service centres. In order to present the characteristic of the call stream passing the trunk group, the approximate analytic method revises the concept of the overflow stream to match it. Using the call stream and the IPP overflow call stream from the other service centre, the blocking probability of the second stage can be obtained. Then, the blocking probability of the first stage is also calculated after reducing the mutual effect between the two stages. The overall blocking probability of this network can be calculated very easily.