Blocking probability computation in reversible Markovian bufferless multi-server systems

Abstract

We study the blocking probability in a Markovian bufferless queuing system with a finite number of servers when the packet arrival process is a Markov-modulated Poisson process (MMPP), a superposition of a finite number N of independent MMPPs. We present an algorithm to compute the blocking probability in the system. The algorithm is exact if some related Quasi-birth-and-death (QBD) processes are reversible. We prove that the complexity of our algorithm scales linearly with N , whereas that of the standard solution does it exponentially. We illustrate the use of our algorithm in a bufferless multi-server system receiving long-range dependent (LRD) input traffic. This problem finds applications in the study of the blocking probability in bufferless optical packet switching (OPS) and optical burst switching (OBS) networks. We emulate LRD traffic with an MMPP, a superposition of N independent ON/OFF sources, which are also MMPPs. Our algorithm is in this case approximative since the reversibility condition is not fulfilled with the proposed MMPP. An extensive numerical analysis suggests that our algorithm can accurately approximate the blocking probability in the original queueing system with LRD input traffic. We provide an insight into the reason why our approximation is accurate.