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Delay analysis of a queue with general service demands and correlated service capacities

Michiel De Muynck (UGent) , Herwig Bruneel (UGent) and Sabine Wittevrongel (UGent)
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Abstract
We present the study of a non-classical discrete-time queueing model in which the customers each request a variable amount of service, called their “service demand”, from a server which is able to execute a variable amount of work, called its “service capacity”, during each time slot. We assume that the numbers of arrivals in consecutive time slots and the service demands of consecutive customers form two independent and identically distributed sequences. However, we allow the service capacities in consecutive time slots to be correlated according to a discrete-batch Markovian process. We study this model analytically and obtain an expression for the probability generating function of the delay of an arbitrary customer in steady state. The results are illustrated with several numerical examples.
Keywords
Discrete-time queueing theory · Service demands Correlated service capacities · Discrete-batch Markovian service process

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MLA
De Muynck, Michiel, et al. “Delay Analysis of a Queue with General Service Demands and Correlated Service Capacities.” Queueing Theory and Network Applications, QTNA 2018, vol. 10932, Springer, 2018, pp. 64–85.
APA
De Muynck, M., Bruneel, H., & Wittevrongel, S. (2018). Delay analysis of a queue with general service demands and correlated service capacities. In Queueing theory and network applications, QTNA 2018 (Vol. 10932, pp. 64–85). Tsukuba, Japan: Springer.
Chicago author-date
De Muynck, Michiel, Herwig Bruneel, and Sabine Wittevrongel. 2018. “Delay Analysis of a Queue with General Service Demands and Correlated Service Capacities.” In Queueing Theory and Network Applications, QTNA 2018, 10932:64–85. Springer.
Chicago author-date (all authors)
De Muynck, Michiel, Herwig Bruneel, and Sabine Wittevrongel. 2018. “Delay Analysis of a Queue with General Service Demands and Correlated Service Capacities.” In Queueing Theory and Network Applications, QTNA 2018, 10932:64–85. Springer.
Vancouver
1.
De Muynck M, Bruneel H, Wittevrongel S. Delay analysis of a queue with general service demands and correlated service capacities. In: Queueing theory and network applications, QTNA 2018. Springer; 2018. p. 64–85.
IEEE
[1]
M. De Muynck, H. Bruneel, and S. Wittevrongel, “Delay analysis of a queue with general service demands and correlated service capacities,” in Queueing theory and network applications, QTNA 2018, Tsukuba, Japan, 2018, vol. 10932, pp. 64–85.
@inproceedings{8636416,
  abstract     = {We present the study of a non-classical discrete-time queueing
model in which the customers each request a variable amount of
service, called their “service demand”, from a server which is able to
execute a variable amount of work, called its “service capacity”, during
each time slot. We assume that the numbers of arrivals in consecutive
time slots and the service demands of consecutive customers form two
independent and identically distributed sequences. However, we allow the
service capacities in consecutive time slots to be correlated according to
a discrete-batch Markovian process. We study this model analytically
and obtain an expression for the probability generating function of the
delay of an arbitrary customer in steady state. The results are illustrated
with several numerical examples.},
  author       = {De Muynck, Michiel and Bruneel, Herwig and Wittevrongel, Sabine},
  booktitle    = {Queueing theory and network applications, QTNA 2018},
  isbn         = {9783319937359},
  issn         = {0302-9743},
  keywords     = {Discrete-time queueing theory · Service demands Correlated service capacities · Discrete-batch Markovian service process},
  language     = {eng},
  location     = {Tsukuba, Japan},
  pages        = {64--85},
  publisher    = {Springer},
  title        = {Delay analysis of a queue with general service demands and correlated service capacities},
  url          = {http://dx.doi.org/10.1007/978-3-319-93736-6_5},
  volume       = {10932},
  year         = {2018},
}

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