The random walk construction of uniform spanning trees and uniform labelled trees
SIAM Journal on Discrete Mathematics
Stationarity detection in the initial transient problem
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Randomized algorithms
What do we know about the Metropolis algorithm?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Exact sampling and approximate counting techniques
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Blocking probability estimates in a partitioned sector TDMA system
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
Generating random spanning trees
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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Analysis of machine scheduling problem can get very complicated even for simple scheduling policies and simple arrival processes. The problem becomes even harder if the scheduler and the arrival process are complicated, or worse still, given to us as a black box. In such cases it is useful to obtain a typical state of the system which can then be used to deduce information about the performance of the system or to tune the parameters for either the scheduling rule or the arrival process. We consider two general scheduling problems and present an algorithm for extracting an exact sample from the stationary distribution of the system when the system forms an ergodic Markov chain. We assume no knowledge of the internals of the arrival process or the scheduler. Our algorithm assumes that the scheduler has a natural monotonic property, and that the job service times are geometric/exponential. We use the Coupling From The Past paradigm due to Propp and Wilson to obtain our result. In order to apply their general framework to our problems, we perform a careful coupling of the different states of the Markov chain.