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Analysis of a discrete-time queue with general service demands and phase-type service capacities

Michiel De Muynck (UGent) , Herwig Bruneel (UGent) and Sabine Wittevrongel (UGent)
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Abstract
In this paper, we analyze a non-classical discrete-time queueing model where customers demand variable amounts of work from a server that is able to perform this work at a varying rate. The service demands of the customers are integer numbers of work wilds. They are assumed to be independent and identically distributed (i.i.d.) random variables. The service capacities, i.e., the numbers of work units that the server can process in the consecutive slots, are also assumed to be i.i.d. and their common probability generating function (pgf) is assumed to be rational. New customers arrive in the queueing system according to a general independent arrival process. For this queueing model we present an analysis method, which is based on complex contour integration. Expressions are obtained for the pgfs, the mean values and the tail probabilities of the customer delay and the system content in steady state. The analysis is illustrated by means of some numerical examples.
Keywords
SYSTEMS, ARRIVAL, MODEL, Queueing theory, discrete time, service demands, service capacities, probability generating functions

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Citation

Please use this url to cite or link to this publication:

MLA
De Muynck, Michiel, Herwig Bruneel, and Sabine Wittevrongel. “Analysis of a Discrete-time Queue with General Service Demands and Phase-type Service Capacities.” JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 13.4 (2017): 1901–1926. Print.
APA
De Muynck, M., Bruneel, H., & Wittevrongel, S. (2017). Analysis of a discrete-time queue with general service demands and phase-type service capacities. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 13(4), 1901–1926.
Chicago author-date
De Muynck, Michiel, Herwig Bruneel, and Sabine Wittevrongel. 2017. “Analysis of a Discrete-time Queue with General Service Demands and Phase-type Service Capacities.” Journal of Industrial and Management Optimization 13 (4): 1901–1926.
Chicago author-date (all authors)
De Muynck, Michiel, Herwig Bruneel, and Sabine Wittevrongel. 2017. “Analysis of a Discrete-time Queue with General Service Demands and Phase-type Service Capacities.” Journal of Industrial and Management Optimization 13 (4): 1901–1926.
Vancouver
1.
De Muynck M, Bruneel H, Wittevrongel S. Analysis of a discrete-time queue with general service demands and phase-type service capacities. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION. Springfield: Amer Inst Mathematical Sciences-aims; 2017;13(4):1901–26.
IEEE
[1]
M. De Muynck, H. Bruneel, and S. Wittevrongel, “Analysis of a discrete-time queue with general service demands and phase-type service capacities,” JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, vol. 13, no. 4, pp. 1901–1926, 2017.
@article{8538262,
  abstract     = {In this paper, we analyze a non-classical discrete-time queueing model where customers demand variable amounts of work from a server that is able to perform this work at a varying rate. The service demands of the customers are integer numbers of work wilds. They are assumed to be independent and identically distributed (i.i.d.) random variables. The service capacities, i.e., the numbers of work units that the server can process in the consecutive slots, are also assumed to be i.i.d. and their common probability generating function (pgf) is assumed to be rational. New customers arrive in the queueing system according to a general independent arrival process. For this queueing model we present an analysis method, which is based on complex contour integration. Expressions are obtained for the pgfs, the mean values and the tail probabilities of the customer delay and the system content in steady state. The analysis is illustrated by means of some numerical examples.},
  author       = {De Muynck, Michiel and Bruneel, Herwig and Wittevrongel, Sabine},
  issn         = {1547-5816},
  journal      = {JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION},
  keywords     = {SYSTEMS,ARRIVAL,MODEL,Queueing theory,discrete time,service demands,service capacities,probability generating functions},
  language     = {eng},
  number       = {4},
  pages        = {1901--1926},
  publisher    = {Amer Inst Mathematical Sciences-aims},
  title        = {Analysis of a discrete-time queue with general service demands and phase-type service capacities},
  url          = {http://dx.doi.org/10.3934/jimo.2017024},
  volume       = {13},
  year         = {2017},
}

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