An Approximate Markovian Model for Cyberspace Switches Using PBS Mechanism under Self-similar Type Variable Length Input Traffic

Abstract

This paper approximates the Markovian model to study the router's loss behaviour employing the PBS mechanism under self-similar variable length input traffic by considering voids using the queueing system . As we know that the Broadband integrated digital service network (B-ISDN) is expected to support various kinds of services such as voice, data, video, and possible combinations of these. Because of this integration and demand, there may be congestion problem in networking. Congestion problem in the network can be dealt with some priority handling queueing mechanisms. One of such mechanisms is buffer access control (B.A.C.), also called space priority. There are strategies by which one can implement this space priority mechanism. One of such strategies is the partial buffer sharing (PBS) scheme. A limit (or threshold) is imposed on both low and high priority packets in this scheme. All arriving packets share the part of Buffer on or below the threshold. When the buffer occupancy is above the threshold, the queueing system's arriving low priority packets will be rejected. The high priority packets are lost only when the Buffer is full. Determination of an appropriate threshold is the significant design issue for a space priority queueing system. If the threshold is relatively high, then high priority packets will be lost more than expectedly. If the threshold is relatively low, low priority packets will be lost excessively. Either way, qualities of service (QoS) requirements are not guaranteed. Hence the threshold setting is a trade-off between the queue utilization and the guaranteed QoS. On the other hand, when the packet length is variable, voids will occur in the router buffer, and the performance of the router degrades as voids will incur excess loads. We assume that voids length follows uniform distribution and packet length follows an exponential distribution. Here, in this paper, the input traffic is self-similar and modelled as the Markovian arrival process (M.A.P.). Suppose the packet lengths follow an exponential distribution, and voids follow a uniform distribution. In that case, the sum of them need not be exponential and presents difficulties in the computation of performance measures. Hence, we assume that sum of packet length distribution and void length distribution are exponential, but with modified parameters that involve both the parameters of exponential distribution and uniform distribution. We compute the performance measures such as packet loss probability against the threshold, buffer capacity, traffic intensity, and optimal threshold using matrix analytic methods. One could utilize the analysis of mean lengths of the critical and non-critical period to initialize the related call admission control schemes in the router to improve performance further.