Transient behavior of the M/M/1 queue: starting at the origin
Queueing Systems: Theory and Applications
Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Towards a polynomial-time randomized algorithm for closed product-form networks
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)
Analysis of Queueing Networks with Blocking
Analysis of Queueing Networks with Blocking
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Perfect Generation, Monotonicity and Finite Queueing Networks
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Approximation Algorithm and Perfect Sampler for Closed Jackson Networks with Single Servers
SIAM Journal on Computing
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
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We consider Jackson queueing networks with finite buffer constraints (JQN) and analyze the efficiency of sampling from their stationary distribution. In the context of exact sampling, the monotonicity structure of JQNs ensures that such efficiency is of the order of the coupling time (or meeting time) of two extremal sample paths. In the context of approximate sampling, it is given by the mixing time. Under a condition on the drift of the stochastic process underlying a JQN, which we call hyper-stability, in our main result we show that the coupling time is polynomial in both the number of queues and buffer sizes. Then, we use this result to show that the mixing time of JQNs behaves similarly up to a given precision threshold. Our proof relies on a recursive formula relating the coupling times of trajectories that start from network states having "distance one", and it can be used to analyze the coupling and mixing times of other Markovian networks, provided that they are monotone. An illustrative example is shown in the context of JQNs with blocking mechanisms.