Conditional stochastic decompositions in the M/M/c queue with server vacations

Tian, Naishuo; Li, Quan‐Lin; Cao, Jiling

doi:10.1080/15326349908807540

Cited by 57 publications

(27 citation statements)

References 7 publications

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“…In terms of Laplace-Stieltjes transforms, it can be shown that W (c) decomposes on two contributions; one of them is the corresponding counterpart in the standard M/M/c queue and the second contribution gives the additional delay due to the setup times (see [18,19]). …”

Section: Then Equation (27) Readily Yieldsmentioning

confidence: 99%

Analysis of a Multiserver Queue with Setup Times

2005

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This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length.

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Section: Then Equation (27) Readily Yieldsmentioning

confidence: 99%

Analysis of a Multiserver Queue with Setup Times

2005

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“…Chao and Zhao [1] investigated multiserver vacation models and provided some algorithms for computing the stationary performance measures for multiple vacation and single vacation policies. Tian, Li, and Cao [11] and Zhang and Tian [13,14] also studied several multiserver vacation models. However, these previous studies on multiserver vacation models focus on an "all idle server vacation" policy in which all idle servers start processing the NQ-jobs (or taking vacations) when the number of idle servers reaches a critical number.…”

Section: Introductionmentioning

confidence: 98%

Quantifying the performance effects of idle time utilization in multiserver systems

Tian

Zhang

2006

Naval Research Logistics

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Abstract:In many practical multiserver queueing systems, servers not only serve randomly arriving customers but also work on the secondary jobs with infinite backlog during their idle time. In this paper, we propose a c-server model with a two-threshold policy, denoted by (e d), to evaluate the performance of this class of systems. With such a policy, when the number of idle servers has reached d (Ͻc), then e (Ͻd) idle agents will process secondary jobs. These e servers keep working on the secondary jobs until they find waiting customers exist in the system at a secondary job completion instant. Using the matrix analytic method, we obtain the stationary performance measures for evaluating different (e, d) policies.

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“…In the M/PH/1 queue with working vacations, the stationary queue length is distributed as the conditional sum of the stationary queue length in an M/PH/1 queue without vacations and the number of customers in the system at an arbitrary time during the vacation. Note that, the block forms of the MSP are based on two types of phases of the MSP and similar factorizations (decompositions) have been obtained for vacation models in Refs [19,20].…”

Section: Introductionmentioning

confidence: 99%

“…We refer to the service process as a Markovian service process (MSP) and study MAP/MSP/1 queues. In Refs [19,20], the idea of using two types of states (phases) was used in analyzing queueing models with vacations. This idea is extended to a general service discipline in our model.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Queues with Markovian Service Processes

Ozawa

2004

Stochastic Models

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Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N -policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary queue length. The MAP/MSP/1 queue is a very tractable model since its behavior is represented as a quasi-birth-and-death process.

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Conditional stochastic decompositions in the M/M/c queue with server vacations

Cited by 57 publications

References 7 publications

Analysis of a Multiserver Queue with Setup Times

Analysis of a Multiserver Queue with Setup Times

Quantifying the performance effects of idle time utilization in multiserver systems

Analysis of Queues with Markovian Service Processes

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