A new polynomial-time algorithm for linear programming
Combinatorica
Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Spatial averages of coverage characteristics in large CDMA networks
Wireless Networks
Perfect simulation of monotone systems for rare event probability estimation
WSC '05 Proceedings of the 37th conference on Winter simulation
Introduction to Discrete Event Systems
Introduction to Discrete Event Systems
Perfect simulation and monotone stochastic bounds
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Perfect simulation and non-monotone Markovian systems
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Coupling from the past in hybrid models for file sharing peer to peer systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
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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Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events in the system have monotonicity property. However, in the general (non-monotone) case, this technique needs to consider the whole state space, which limits its application only to chains with a state space of small cardinality. Here, we propose a new approach for the general case that only needs to consider two trajectories. Instead of the original chain, we use two bounding processes (envelopes) and we show that, whenever they meet, one obtains a sample under the stationary distribution of the original chain. We show that this new approach is particularly effective when the state space can be partitioned into pieces where envelopes can be easily computed. We further show that most Markovian queueing networks have this property and we propose efficient algorithms for some of them.