Likelihood Ratio Derivative Estimation for Finite-Time Performance Measures in Generalized Semi-Markov Processes

AbstractA method for determining the upper and lower bounds for performance measures for certain types of Generalised Semi-Markov Processes has been described in Taylor and Coyle [8]. A brief description of this method and its use in finding an upper bound for the time congestion of a GI/M/n/n queueing system will be given. This bound turns out to have a simple form which is quickly calculated and easy to use in practice.

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Tight bounds on the sensitivity of generalised semi-Markov processes with a single generally distributed lifetime

Journal of Applied Probability ◽

10.1017/s0021900200102578 ◽

1995 ◽

Vol 32 (01) ◽

pp. 63-73

Author(s):

A. J. Coyle ◽

P. G. Taylor

Keyword(s):

Performance Measures ◽

Markov Processes ◽

Queueing System ◽

Mean Value ◽

Performance Measure ◽

Upper And Lower Bounds ◽

Lifetime Distributions ◽

Actual Distribution ◽

The Mean ◽

Semi Markov Processes

There are some generalised semi-Markov processes (GSMP) which are insensitive, that is the value of some performance measures for the system depend only on the mean value of lifetimes and not on their actual distribution. In most cases this is not true and a performance measure can take on a number of values depending on the lifetime distributions. In this paper we present a method for finding tight bounds on the sensitivity of performance measures for the class of GSMPs with a single generally distributed lifetime. Using this method we can find upper and lower bounds for the value of a function of the stationary distribution as the distribution of the general lifetime ranges over a set of distributions with fixed mean. The method is applied to find bounds on the average queue length of the Engset queue and the time congestion in theGI/M/n/nqueueing system.

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Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices

Operations Research ◽

10.1287/opre.39.5.724 ◽

1991 ◽

Vol 39 (5) ◽

pp. 724-738 ◽

Cited By ~ 44

Author(s):

Paul Glasserman

Keyword(s):

Perturbation Analysis ◽

Finite Time ◽

Performance Indices ◽

Derivative Estimation ◽

Time Performance

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Tight bounds on the sensitivity of generalised semi-Markov processes with a single generally distributed lifetime

Journal of Applied Probability ◽

10.2307/3214921 ◽

1995 ◽

Vol 32 (1) ◽

pp. 63-73 ◽

Cited By ~ 2

Author(s):

A. J. Coyle ◽

P. G. Taylor

Keyword(s):

Performance Measures ◽

Markov Processes ◽

Queueing System ◽

Mean Value ◽

Performance Measure ◽

Upper And Lower Bounds ◽

Lifetime Distributions ◽

Actual Distribution ◽

The Mean ◽

Semi Markov Processes

There are some generalised semi-Markov processes (GSMP) which are insensitive, that is the value of some performance measures for the system depend only on the mean value of lifetimes and not on their actual distribution. In most cases this is not true and a performance measure can take on a number of values depending on the lifetime distributions. In this paper we present a method for finding tight bounds on the sensitivity of performance measures for the class of GSMPs with a single generally distributed lifetime. Using this method we can find upper and lower bounds for the value of a function of the stationary distribution as the distribution of the general lifetime ranges over a set of distributions with fixed mean. The method is applied to find bounds on the average queue length of the Engset queue and the time congestion in the GI/M/n/n queueing system.

Download Full-text