Because it is more intuitively understandable than the previously existing convolution algorithms, Mean Value Analysis (MVA) has gained great popularity as an exact solution technique for separable queueing networks. However, the derivations of MVA presented to date apply only to closed queueing network models. Additionally, the problem of the storage requirement of MVA has not been dealt with satisfactorily. In this paper we address both these problems, presenting MVA solutions for open and mixed load independent networks, and a storage maintenance technique that we postulate is the minimum possible of any “reasonable” MVA technique.
This paper is concerned with how coupling can be used to enhance the efficiency of a certain class of terminating simulations, in Markov process settings in which the stationary distribution is known. We are able to theoretically establish that our coupling-based estimator is often more efficient than the naive estimator. In addition, we discuss extensions of our methodology to Markov process settings in which conventional coupling fails and show (for Doeblin chains) that knowledge of the stationary distribution is sometimes unnecessary.
In this paper we consider the use of coupling ideas
in efficiently computing a certain class of transient performance
measures. Specifically, we consider the setting in which
the stationary distribution is unknown, and for which no
exact means of generating stationary versions of the process
is known. In this context, we can approximate the stationary
distribution from empirical data obtained from a first-stage
steady-state simulation. This empirical approximation is
then used in place of the stationary distribution in implementing
our coupling-based estimator. In addition to the empirically
based coupling estimator itself, we also develop an associated
confidence interval procedure.
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