The queue M/G/1 with Markov modulated arrivals and services
Mathematics of Operations Research
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Wide-area traffic: the failure of Poisson modeling
SIGCOMM '94 Proceedings of the conference on Communications architectures, protocols and applications
Self-similarity in World Wide Web traffic: evidence and possible causes
Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Fluid queues and regular variation
Performance Evaluation
IEEE/ACM Transactions on Networking (TON)
Tail probabilities for M/G/\infty input processes (I): Preliminary asymptotics
Queueing Systems: Theory and Applications
On a reduced load equivalence for fluid queues under subexponentiality
Queueing Systems: Theory and Applications
Invited Fluid queues with long-tailed activity period distributions
Computer Communications
On the use of fractional Brownian motion in the theory of connectionless networks
IEEE Journal on Selected Areas in Communications
Modeling integration of streaming and data traffic
Performance Evaluation
Erlang loss queueing system with batch arrivals operating in a random environment
Computers and Operations Research
An infinite-server queue influenced by a semi-Markovian environment
Queueing Systems: Theory and Applications
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We consider an M/M/1 queue in a semi-Markovian environment. The environment is modeled by a two-state semi-Markov process with arbitrary sojourn time distributions F0(x) and F1(x). When in state i = 0, 1, customers are generated according to a Poisson process with intensity λi and customers are served according to an exponential distribution with rate μi. Using the theory of Riemann-Hilbert boundary value problems we compute the z-transform of the queue-length distribution when either F0(x) or F1(x) has a rational Laplace-Stieltjes transform and the other may be a general --- possibly heavy-tailed --- distribution. The arrival process can be used to model bursty traffic and/or traffic exhibiting long-range dependence, a situation which is commonly encountered in networking. The closed-form results lend themselves for numerical evaluation of performance measures, in particular the mean queue-length.