Effective bandwidth and fast simulation of ATM intree networks
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Analysis of an importance sampling estimator for tandem queues
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Proceedings of the 35th conference on Winter simulation: driving innovation
Efficient simulation of buffer overflow probabilities in jackson networks with feedback
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the efficiency of RESTART for multidimensional state systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
WSC '05 Proceedings of the 37th conference on Winter simulation
Efficient heuristics for the simulation of population overflow in series and parallel queues
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Efficient simulation of population overflow in parallel queues
Proceedings of the 38th conference on Winter simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Tandem queue with server slow-down
ACM SIGMETRICS Performance Evaluation Review
Simulation of a Jackson tandem network using state-dependent importance sampling
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Asymptotically optimal importance sampling for Jackson networks with a tree topology
Queueing Systems: Theory and Applications
State-dependent importance sampling for a Jackson tandem network
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A variant of importance splitting for rare event estimation: Fixed number of successes
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The rare event simulation method RESTART: efficiency analysis and guidelines for its application
Network performance engineering
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The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.