A heavy traffic limit theorem for networks of queues with multiple customer types
Mathematics of Operations Research
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
A most probable path approach to queueing systems with general Gaussian input
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Testing the Gaussian approximation of aggregate traffic
Proceedings of the 2nd ACM SIGCOMM Workshop on Internet measurment
Sample-path large deviations for generalized processor sharing queues with Gaussian inputs
Performance Evaluation - Long range dependence and heavy tail distributions
A note on large-buffer asymptotics for generalized processor sharing with Gaussian inputs
Queueing Systems: Theory and Applications
A performance analysis of discrete-time tandem queues with Markovian sources
Performance Evaluation
Large deviations theory: basic principles and applications to communication networks
Network performance engineering
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Tandem systems are seen in many places and at various hierarchical levels in high-speed communication networks, from router architectures to protocol stacks. If the traffic fed into the system is generated by independent or weakly dependent sources and the smallest relevant time scale is not too fine, the central limit theorem suggests that the input traffic is (close to) Gaussian. This paper considers tandem queues fed by Gaussian processes with stationary increments. Relying on the generalized version of Schilder's sample-path large-deviations theorem, we derive the many-sources asymptotics of the overflow probabilities in the second queue; 'Schilder' reduces this problem to finding the most probable path along which the second queue reaches overflow. The general form of these paths is described by recently obtained results on infinite-intersections of events in Gaussian processes; for the special cases of fractional Brownian motion and integrated Ornstein-Uhlenbeck input, the most probable path can be explicitly determined, as well as the corresponding exponential decay rate. As the computation of the decay rate is numerically involved, we introduce an explicit approximation ('rough full-link approximation'). Based on this approximation, we propose performance formulae for network provisioning purposes. Simulation is used to assess the accuracy of the formulae. As an example, we show how the methods can be applied to dimensioning the interface between a line card and a switch fabric.