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Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times

Jens Baetens (UGent) , Bart Steyaert (UGent) , Dieter Claeys (UGent) and Herwig Bruneel (UGent)
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Abstract
Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain. We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved.
Keywords
Modelling and Simulation, Computer Networks and Communications, Hardware and Architecture, Software, MARKOVIAN ARRIVAL PROCESS, BULK-SERVICE, FINITE-BUFFER, GLOBAL FCFS, MODEL, DELAY, SERVERS, SYSTEMS, PROBABILITIES, PERFORMANCE, Batch service, Two-class, Variable service capacity, Correlated customer types

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MLA
Baetens, Jens, et al. “Analysis of a Batch-Service Queue with Variable Service Capacity, Correlated Customer Types and Generally Distributed Class-Dependent Service Times.” PERFORMANCE EVALUATION, vol. 135, 2019.
APA
Baetens, J., Steyaert, B., Claeys, D., & Bruneel, H. (2019). Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times. PERFORMANCE EVALUATION, 135.
Chicago author-date
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2019. “Analysis of a Batch-Service Queue with Variable Service Capacity, Correlated Customer Types and Generally Distributed Class-Dependent Service Times.” PERFORMANCE EVALUATION 135.
Chicago author-date (all authors)
Baetens, Jens, Bart Steyaert, Dieter Claeys, and Herwig Bruneel. 2019. “Analysis of a Batch-Service Queue with Variable Service Capacity, Correlated Customer Types and Generally Distributed Class-Dependent Service Times.” PERFORMANCE EVALUATION 135.
Vancouver
1.
Baetens J, Steyaert B, Claeys D, Bruneel H. Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times. PERFORMANCE EVALUATION. 2019;135.
IEEE
[1]
J. Baetens, B. Steyaert, D. Claeys, and H. Bruneel, “Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times,” PERFORMANCE EVALUATION, vol. 135, 2019.
@article{8624996,
  abstract     = {Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain.
We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved.},
  articleno    = {102012},
  author       = {Baetens, Jens and Steyaert, Bart and Claeys, Dieter and Bruneel, Herwig},
  issn         = {0166-5316},
  journal      = {PERFORMANCE EVALUATION},
  keywords     = {Modelling and Simulation,Computer Networks and Communications,Hardware and Architecture,Software,MARKOVIAN ARRIVAL PROCESS,BULK-SERVICE,FINITE-BUFFER,GLOBAL FCFS,MODEL,DELAY,SERVERS,SYSTEMS,PROBABILITIES,PERFORMANCE,Batch service,Two-class,Variable service capacity,Correlated customer types},
  language     = {eng},
  title        = {Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times},
  url          = {http://dx.doi.org/10.1016/j.peva.2019.102012},
  volume       = {135},
  year         = {2019},
}

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