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

This paper approximates the Markovian model to investigate the router’s loss behavior using the PBS mechanism with self-similar variable length input traffic and voids using the MAP / M /1/ K queueing system. As previously stated, the Broadband integrated digital service network (B-ISDN) is expected to support a variety of services including voice, data, video, and possible combinations of these. Because of this integration and demand, there may be network congestion. Some priority handling queueing mechanisms can help to alleviate network congestion. Buffer access control (B.A.C. ), also known as space priority, is one of these mechanisms. This scheme works on both low and high priority packets. All arriving packets share a portion of the Buffer that is on or below the threshold. When the buffer occupancy exceeds the threshold, arriving low priority packets are rejected by the queueing system. Only when the Buffer is full are high priority packets lost. The significant design issue for a space priority queueing system is determining an appropriate threshold. If the threshold is set too high, high priority packets will be lost more frequently than expected. Low priority packets will be lost excessively if the threshold is set too low. Quality of service (QoS) requirements are not guaranteed in either case. As a result, setting the threshold is a trade-off between queue utilization and guaranteed QoS. When the packet length is variable, however, voids will occur in the router buffer, and the router’s performance will suffer as voids incur excess loads. We assume that the length of voids follows a uniform distribution and the length of packets follows an exponential distribution. The input traffic in this paper is self-similar and is modelled as the Markovian arrival process (M.A.P.). Assume that packet lengths have an exponential distribution and voids have a uniform distribution. In that case, the sum does not have to be exponential, and Difficulties in calculating performance measures As a result, we assume that the sum of the packet length distribution and the void length distribution are exponential, but with modified parameters that include both the exponential and uniform distribution parameters. Using matrix analytic methods, we compute performance measures such as packet loss probability versus threshold, buffer capacity, traffic intensity, and optimal threshold. To improve performance even further, one could use the analysis of mean lengths of the critical and non-critical periods to initialize the related call admission control schemes in the router.

Author (S) Details

Dr. Mallikarjuna Reddy Doodipala
Department of Mathematics, School of Science, GITAM, Hyderabad, India.

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