Bounds for performance characteristics: a systematic approach via cost structures

G.J.J.A.N. Houtum, van; W.H.M. Zijm; I.J.B.F. Adan; J. Wessels

doi:10.1080/15326349808807467

Bounds for performance characteristics: a systematic approach via cost structures

G.J.J.A.N. Houtum, van, W.H.M. Zijm, I.J.B.F. Adan, J. Wessels

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Abstract

In this paper we present a systematic approach to the construction of bounds for the average costs in Markov chains with possibly infinitely many states. The technique used to prove the bounds is based on dynamic programming. Most performance characteristics of Markovian systems can be represented by the average costs for some appropriately chosen cost structure. Therefore, the approach can be used to generate bounds for relevant performance characteristics. The approach is demonstrated for the shortest queue model. It is shown how for this model several bounds for the mean waiting time can be constructed. We include numerical results to demonstrate the quality of these bounds

Original language	English
Pages (from-to)	205-224
Journal	Communications in Statistics. Part C, Stochastic Models
Volume	14
Issue number	1/2
DOIs	https://doi.org/10.1080/15326349808807467
Publication status	Published - 1998

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abstract = "In this paper we present a systematic approach to the construction of bounds for the average costs in Markov chains with possibly infinitely many states. The technique used to prove the bounds is based on dynamic programming. Most performance characteristics of Markovian systems can be represented by the average costs for some appropriately chosen cost structure. Therefore, the approach can be used to generate bounds for relevant performance characteristics. The approach is demonstrated for the shortest queue model. It is shown how for this model several bounds for the mean waiting time can be constructed. We include numerical results to demonstrate the quality of these bounds",

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AU - Wessels, J.

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DO - 10.1080/15326349808807467

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JF - Communications in Statistics. Part C, Stochastic Models

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Bounds for performance characteristics: a systematic approach via cost structures

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