Open queueing systems in light traffic
Mathematics of Operations Research
A single server model for packetwise transmission of messages
Queueing Systems: Theory and Applications
Interpolation approximations of sojourn time distributions
Operations Research
A simple relationship between light and heavy traffic limits
Operations Research - Supplement to Operations Research: stochastic processes
Correlation effects in ATM queues due to data format conversions
Performance Evaluation
On the relevance of long-range dependence in network traffic
IEEE/ACM Transactions on Networking (TON)
Tail probabilities for M/G/\infty input processes (I): Preliminary asymptotics
Queueing Systems: Theory and Applications
Heavy traffic limits associated with M/G/∞ input processes
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Performance evaluation of a queue fed by a Poisson Pareto burst process
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
The impact of the service discipline on delay asymptotics
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Generalized processor sharing with light-tailed and heavy-tailed input
IEEE/ACM Transactions on Networking (TON)
Long-Range Dependence: Ten Years of Internet Traffic Modeling
IEEE Internet Computing
Asymptotic optimality of the Round---Robin policy in multipath routing with resequencing
Queueing Systems: Theory and Applications
Fluid Queues with Heavy-Tailed M/G/∞ Input
Mathematics of Operations Research
Modeling video traffic using M/G/∞ input processes: a compromise between Markovian and LRD models
IEEE Journal on Selected Areas in Communications
Performance analysis of a Poisson-Pareto queue over the full range of system parameters
Computer Networks: The International Journal of Computer and Telecommunications Networking
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We examine the impact of network traffic dependencies on queueing performance in the context of a popular stochastic model, namely the infinite capacity discrete-time queue with deterministic service rate and M|G|~ arrival process. We propose approximations to the stationary queue size distribution which are generated by interpolating between heavy and light traffic extremes. This is done under both long- and short-range dependent network traffic. Under long-range dependence, the heavy traffic results can be expressed in terms of Mittag-Leffler special functions which generalize the exponential distribution and yet display power-law decay. Numerical results from exact expressions (when available), approximations and simulations support the following conclusions: Network traffic dependencies need to be carefully accounted for, but whether this is accomplished through a short- or long-range dependent stochastic model bears little impact on queueing performance. The differences between exponential and power-law queueing are negligible at the ''head'' of the distribution, and manifest themselves only for large buffers.