A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Sharing a Processor Among Many Job Classes
Journal of the ACM (JACM)
Modeling TCP Reno performance: a simple model and its empirical validation
IEEE/ACM Transactions on Networking (TON)
Fair end-to-end window-based congestion control
IEEE/ACM Transactions on Networking (TON)
Impact of fairness on Internet performance
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
State-dependent Importance Sampling and large Deviations
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
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We consider a network supporting elastic traffic, where the service capacity is shared among the various classes according to an alpha-fair sharing policy. Assuming Poisson arrivals and exponentially distributed service requirements for each class, the dynamics of the user population may be described by a Markov process. We focus on the probability that, given that the network is in some state n0 at time 0, the network is in some set of states A at time T. In particular, we assume that the underlying event is rare, i.e., the probability of interest is small. As in general no explicit expressions are known for this probability, an attractive approach may be to resort to Monte-Carlo (MC) simulation. However, due to the rarity of the event under consideration, MC simulation is infeasible. A natural approach to speed up the simulation is to use Importance Sampling (IS). We present an IS algorithm to accelerate the simulation that is based on large deviations results. With extensive simulation experiments we assess the performance of the algorithm; under rather general conditions a considerable speed-up is achieved.