Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

D. Perry; W. Stadje; S. Zacks

doi:10.1016/S0167-6377(00)00043-2

Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

D. Perry, W. Stadje, S. Zacks

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let (V(t))_t≥0 be the virtual waiting time process, let S_n be the time required for a full service of the nth customer and let τ_n be his arrival time. In both models there is a capacity bound v* ∈(0, ∞). In Model I the amount of service given to the nth customer is equal to min[S_n, v*-V(τ_n-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(τ_n-) exceeds v*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods.

Original language	English
Pages (from-to)	163-174
Number of pages	12
Journal	Operations Research Letters
Volume	27
Issue number	4
DOIs	https://doi.org/10.1016/S0167-6377(00)00043-2
State	Published - Nov 2000

Bibliographical note

Funding Information:
This research was carried out while the first author (D. Perry) was a visiting professor at the University of Osnabrück. The support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/S0167-6377(00)00043-2

Cite this

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title = "Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility",

abstract = "We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let (V(t))t≥0 be the virtual waiting time process, let Sn be the time required for a full service of the nth customer and let τn be his arrival time. In both models there is a capacity bound v* ∈(0, ∞). In Model I the amount of service given to the nth customer is equal to min[Sn, v*-V(τn-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(τn-) exceeds v*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods.",

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AU - Perry, D.

AU - Stadje, W.

AU - Zacks, S.

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N2 - We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let (V(t))t≥0 be the virtual waiting time process, let Sn be the time required for a full service of the nth customer and let τn be his arrival time. In both models there is a capacity bound v* ∈(0, ∞). In Model I the amount of service given to the nth customer is equal to min[Sn, v*-V(τn-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(τn-) exceeds v*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods.

AB - We consider two models of M/G/1 and G/M/1 type queueing systems with restricted accessibility. Let (V(t))t≥0 be the virtual waiting time process, let Sn be the time required for a full service of the nth customer and let τn be his arrival time. In both models there is a capacity bound v* ∈(0, ∞). In Model I the amount of service given to the nth customer is equal to min[Sn, v*-V(τn-)], i.e. the full currently free workload is assigned to the new customer. In Model II the customer is rejected iff the currently used workload V(τn-) exceeds v*, but the service times of admitted customers are not censored. We obtain closed-form expressions for the Laplace transforms of the lengths of the busy periods.

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Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility

Abstract

Bibliographical note

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