Sojourn times in a processor sharing queue with service interruptions
Queueing Systems: Theory and Applications
On performance bounds for the integration of elastic and adaptive streaming flows
Proceedings of the joint international conference on Measurement and modeling of computer systems
Perturbation analysis of an M/M/1 queue in a diffusion random environment
Queueing Systems: Theory and Applications
Fluid models of integrated traffic and multipath routing
Queueing Systems: Theory and Applications
Performance implications of fluctuating server capacity
Computer Communications
Optimal robust policies for bandwidth allocation and admission control in wireless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Perturbation analysis of an M/M/1 queue in a diffusion random environment
Queueing Systems: Theory and Applications
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We study in this paper the integration of elastic and streaming traffic on a same link in an IP network. We are specifically interested in the computation of the mean bit rate obtained by a data transfer. For this purpose, we consider that the bit rate offered by streaming traffic is low, of the order of magnitude of a small parameter @e@?1 and related to an auxiliary stationary Markovian process (X(t)). Under the assumption that data transfers are exponentially distributed, arrive according to a Poisson process, and share the available bandwidth according to the ideal processor sharing discipline, we derive the mean bit rate of a data transfer as a power series expansion in @e. Since the system can be described by means of an M/M/1 queue with a time-varying server rate, which depends upon the parameter @e and process (X(t)), the key issue is to compute an expansion of the area swept under the occupation process of this queue in a busy period. We obtain closed formulas for the power series expansion in @e of the mean bit rate, which allow us to verify the validity of the so-called reduced service rate at the first order. The second order term yields more insight into the negative impact of the variability of streaming flows.