On the self-similar nature of Ethernet traffic
SIGCOMM '93 Conference proceedings on Communications architectures, protocols and applications
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Superposition of Markov sources and long range dependence
BC '98 Proceedings of the IFIP TC6/WG6.2 Fourth International Conference on Broadband Communications: The future of telecommunications
BROADNETS '04 Proceedings of the First International Conference on Broadband Networks
A multifractal wavelet model with application to network traffic
IEEE Transactions on Information Theory
Performance analyses of optical burst-switching networks
IEEE Journal on Selected Areas in Communications
On the use of fractional Brownian motion in the theory of connectionless networks
IEEE Journal on Selected Areas in Communications
Optical burst switching: a new area in optical networking research
IEEE Network: The Magazine of Global Internetworking
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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.