Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
An Efficient Method for Generating Discrete Random Variables with General Distributions
ACM Transactions on Mathematical Software (TOMS)
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Perfect simulation of monotone systems for rare event probability estimation
WSC '05 Proceedings of the 37th conference on Winter simulation
Perfect simulation and non-monotone Markovian systems
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Perfect sampling of phase-type servers using bounding envelopes
ASMTA'11 Proceedings of the 18th international conference on Analytical and stochastic modeling techniques and applications
On the efficiency of perfect simulation in monotone queueing networks
ACM SIGMETRICS Performance Evaluation Review - Special Issue on IFIP PERFORMANCE 2011- 29th International Symposium on Computer Performance, Modeling, Measurement and Evaluation
Acceleration of perfect sampling by skipping events
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Tradeoff between accuracy and efficiency in the time-parallel simulation of monotone systems
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Tradeoff between accuracy and efficiency in the time-parallel simulation of monotone systems
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
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We consider open Jackson queueing networks with mixed finite and infinite buffers and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain has a large or even infinite state space. The main idea is to use a Jackson network with infinite buffers (that has a product form stationary distribution) to bound the number of initial conditions to be considered in the coupling from the past scheme. We also provide bounds on the sampling time of this new perfect sampling algorithm under hyper-stability conditions (to be defined in the paper) for each queue. These bounds show that the new algorithm is considerably more efficient than existing perfect samplers even in the case where all queues are finite. We illustrate this efficiency through numerical experiments.