Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Approximation Algorithm and Perfect Sampler for Closed Jackson Networks with Single Servers
SIAM Journal on Computing
Perfect sampling of Markov chains with piecewise homogeneous events
Performance Evaluation
Perfect sampling of networks with finite and infinite capacity queues
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Efficiency of simulation in monotone hyper-stable queueing networks
Queueing Systems: Theory and Applications
| Hi-index | 0.00 |
We consider Jackson queueing networks (JQN) with finite capacity constraints and analyze the temporal computational complexity of sampling from their stationary distribution. In the context of perfect sampling, the monotonicity of JQNs ensures that it is the coupling time of extremal sample-paths. In the context of approximate sampling, it is given by the mixing time. We give a sufficient condition to prove that the coupling time of JQNs with M queues is O(M ∑Mi=1 Ci), where Ci denotes the capacity (buffer size) of queue i. This condition lets us deal with networks having arbitrary topology, for which the best bound known is exponential in the Ci's or in M. Then, we use this result to show that the mixing time of JQNs is log2 1/∈ O(M ∑Mi=1 Ci), where ∈ is a precision threshold. The main idea of our proof relies on a recursive formula on the coupling times of special sample-paths and provides a methodology for analyzing the coupling and mixing times of several monotone Markovian networks.