Markovian Model for Internet Router Employing PBS Mechanism under Self-Similar Traffic

Broadband integrated service digital 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 network can be dealt with some priority handling queueing mechanisms. One of such mechanisms is buffer access control (BAC) also called space priority. There are strategies by which one can implement this space priority mechanism, one of such strategies is partial buffer sharing (PBS) scheme. In this scheme, a limit (or threshold) is imposed on both low and high priority packets. The part of buffer on or below the threshold is shared by all arriving packets. When the buffer occupancy is above the threshold, the arriving low priority packets will be rejected by queueing system. 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 performance of router degrades as voids will incur excess loads. We assume that voids length follows uniform distribution and packet length follows exponential distribution. In this paper, loss behavior of the router employing PBS mechanism under Markovian modeled self-similar variable length input traffic by taking voids into consideration is investigated using queueing system. Here the input traffic is self-similar in nature and modeled as Markovian arrival process (MAP). If the packet lengths follow exponential distribution, and voids follow uniform distribution, then 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 is exponential, but with modified parameter which involves both the parameters of exponential distribution and uniform distribution. We compute the performance measures such as packet loss probability against threshold, buffer capacity and traffic intensity and optimal threshold using matrix analytic methods.