Analysis of the discrete-time bulk-service queue Geo/GY/1/N+B

Chaudhry, M. L.; Chang, Seok Ho

doi:10.1016/j.orl.2003.09.006

Cited by 29 publications

(15 citation statements)

References 9 publications

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“…In real systems, the maximum batch size or service capacity is often variable and stochastic, which has been studied in only a few papers. In many of these papers, the service capacity is generically distributed and does not depend on any parameter of the system, like the number of customers waiting in the queue, see the papers of Chaudhry and Chang 2004;Germs and Foreest 2010;Pradhan et al 2015;Sikdar and Samanta 2016. A more detailed description of these papers can be found in our paper (Baetens et al 2016).…”

Section: Introductionmentioning

confidence: 99%

System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation

Baetens

Steyaert

Claeys

et al. 2017

ECMS 2017 Proceedings Edited by Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, Ján

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In many queueing systems the server processes several customers simultaneously. Although the capacity of a batch, that is the number of customers that can be processed simultaneously, is often variable in practice, nearly all batch-service queueing models in literature consider a constant capacity. In this paper, we extend previous work on a batch-service queueing model with variable server capacity, where customers of two classes are accommodated in a common first-come-first-served single-server queue. We include correlation between the classes of consecutive customers, and the service times are geometrically distributed. We establish the equations that govern the system behaviour, the stability condition, and an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. In addition, some numerical results are shown to study the impact of the mean service times and of the customer-based correlation in the arrival process on the performance of the queueing system.

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Section: Introductionmentioning

confidence: 99%

System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation

Baetens

Steyaert

Claeys

et al. 2017

ECMS 2017 Proceedings Edited by Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, Ján

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“…However, in practice, the maximum batch size or capacity of the server can be variable and stochastic, a feature that has been incorporated in only a few papers. Chaudhry and Chang analysed the system content at various epochs in the Geo/G Y /1/N + B model in discrete time, where Y denotes the stochastic capacity of the server, which is upper-bounded by B, and N is the maximum queue capacity [6]. Furthermore, Pradhan et al obtained closed-form expressions for the queue length distribution at departure epochs for the discrete-time M/G Y r /1 queue where the service process depends on the batch size [7].…”

Section: Introductionmentioning

confidence: 99%

System Occupancy of a Two-Class Batch-Service Queue with Class-Dependent Variable Server Capacity

Baetens

Steyaert

Claeys

et al. 2016

Analytical and Stochastic Modelling Techniques and Applications

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Abstract. Due to their wide area of applications, queueing models with batch service, where the server can process several customers simultaneously, have been studied frequently. An important characteristic of such batch-service systems is the size of a batch, that is the number of customers that are processed simultaneously. In this paper, we analyse a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common first-come-first served single-server queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the number of consecutive same-class customers. After establishing the system equations that govern the system behaviour, we deduce an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. Also, some numerical examples are given that provide further insight in the impact of the different parameters on the system performance.

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“…Taking Y = b, a constant, in particular, (2) and (3) reduce to (16) and (17) of Gupta and Goswami [5], respectively. Taking a = 1, on the other hand, they reduce to the results corresponding to (4)-(6) of Chaudhry and Chang [4]. Note that our results are much simpler than those of Chaudhry and Chang that are additionally involved with the distribution of a certain random variable.…”

Section: Relationship Between Random-epoch and Departure-epoch Distrimentioning

confidence: 48%

“…This batch-service rule is introduced by Powell and Humblet [8] and referred to as a versatile batch-service rule by Kim et al [7]. Recently, special cases of the Geo/G a,Y /1/K queue, namely, the Geo/G a,b /1/K and Geo/G Y /1/K queues were analyzed by Gupta and Goswami [5] and Chaudhry and Chang [4], respectively. Note that the Geo/G a,b /1/K queue has a constant service capacity, i.e., Y = b a constant, and the Geo/G Y /1/K queue has no particular threshold policy, i.e., a = 1.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue

Kim

Yoon

et al. 2007

European Journal of Operational Research

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Analysis of the discrete-time bulk-service queue Geo/GY/1/N+B

Cited by 29 publications

References 9 publications

System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation

System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation

System Occupancy of a Two-Class Batch-Service Queue with Class-Dependent Variable Server Capacity

Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue

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