Importance sampling for stochastic simulations
Management Science
IEEE/ACM Transactions on Networking (TON)
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)
Estimating small cell-loss ratios in ATM switches via importance sampling
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Simulating GI/GI/1 queues and insurance risk processes with subexponential distributions
Proceedings of the 32nd conference on Winter simulation
Cross-entropy and rare events for maximal cut and partition problems
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue: Rare event simulation
Proceedings of the 33nd conference on Winter simulation
Simulating heavy tailed processes using delayed hazard rate twisting
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient simulation of a tandem Jackson network
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Multilevel Splitting for Estimating Rare Event Probabilities
Operations Research
Combining importance sampling and temporal difference control variates to simulate Markov Chains
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient simulation of buffer overflow probabilities in jackson networks with feedback
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Analysis of state-independent importance-sampling measures for the two-node tandem queue
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
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
Networks with cascading overloads
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
| Hi-index | 0.00 |
In this article, we propose state-dependent importance sampling heuristics to estimate the probability of population overflow in Jackson queueing networks. These heuristics capture state-dependence along the boundaries (when one or more queues are empty), which is crucial for the asymptotic efficiency of the change of measure. The approach does not require difficult (and often intractable) mathematical analysis and is not limited by storage and computational requirements involved in adaptive importance sampling methodologies, particularly for a large state space. Experimental results on tandem, parallel, feed-forward, and feedback networks with a moderate number of nodes suggest that the proposed heuristics may yield asymptotically efficient estimators, possibly with bounded relative error, when applied to queueing networks wherein no other state-independent importance sampling techniques are known to be efficient. The heuristics are robust and remain effective for larger networks. Moreover, insights drawn from the basic networks considered in this article help understand sample path behavior along the boundaries, conditional on reaching the rare event of interest. This is key to the application of the methodology to networks of more general topologies. It is hoped that empirical findings and insights in this paper will encourage more research on related practical and theoretical issues.