4,404 research outputs found
Regenerative Simulation for Queueing Networks with Exponential or Heavier Tail Arrival Distributions
Multiclass open queueing networks find wide applications in communication,
computer and fabrication networks. Often one is interested in steady-state
performance measures associated with these networks. Conceptually, under mild
conditions, a regenerative structure exists in multiclass networks, making them
amenable to regenerative simulation for estimating the steady-state performance
measures. However, typically, identification of a regenerative structure in
these networks is difficult. A well known exception is when all the
interarrival times are exponentially distributed, where the instants
corresponding to customer arrivals to an empty network constitute a
regenerative structure. In this paper, we consider networks where the
interarrival times are generally distributed but have exponential or heavier
tails. We show that these distributions can be decomposed into a mixture of
sums of independent random variables such that at least one of the components
is exponentially distributed. This allows an easily implementable embedded
regenerative structure in the Markov process. We show that under mild
conditions on the network primitives, the regenerative mean and standard
deviation estimators are consistent and satisfy a joint central limit theorem
useful for constructing asymptotically valid confidence intervals. We also show
that amongst all such interarrival time decompositions, the one with the
largest mean exponential component minimizes the asymptotic variance of the
standard deviation estimator.Comment: A preliminary version of this paper will appear in Proceedings of
Winter Simulation Conference, Washington, DC, 201
Exponential inequalities for unbounded functions of geometrically ergodic Markov chains. Applications to quantitative error bounds for regenerative Metropolis algorithms
The aim of this note is to investigate the concentration properties of
unbounded functions of geometrically ergodic Markov chains. We derive
concentration properties of centered functions with respect to the square of
the Lyapunov's function in the drift condition satisfied by the Markov chain.
We apply the new exponential inequalities to derive confidence intervals for
MCMC algorithms. Quantitative error bounds are providing for the regenerative
Metropolis algorithm of [5]
Wide sense one-dependent processes with embedded Harris chains and their applications in inventory management
In this paper we consider stochastic processes with an embedded Harris chain. The embedded Harris chain describes the dependence structure of the stochastic process. That is, all the relevant information of the past is contained in the state of the embedded Harris chain. For these processes we proved a powerful reward theorem. Futher, we show how we can control these type of processes and give a formulation similar to semi-Markov decision processes. Finally we discuss a number of applications in inventory management.
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