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Discrete-time modified number- and time-limited vacation queues

Dieter Claeys (UGent) and Stijn De Vuyst (UGent)
(2019) QUEUEING SYSTEMS . 91(3-4). p.297-318
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Abstract
A vast amount of literature has appeared on vacation queues. In the well-known number- and time-limited vacation policies, the server goes on vacation if the number of customers, respectively, work (time slots) served since the previous vacation reaches a specified value, or if the system becomes empty, whichever occurs first. However, in practice, the server does not always go on vacation when the system is empty if the number of customers/work to be served has not yet reached the specified amount. Therefore, we study modified number- and time-limited vacation policies, where we account for this feature. We complement our recent work on these vacation policies by considering a discrete time, instead of a continuous-time, setting. We therefore adopt a different analysis approach, which enables us to obtain similar as well as new results as compared to our previous work. The results in this paper are valid for a memoryless distribution, but also for distributions with finite support, and a mixture of geometric distributions.
Keywords
Management Science and Operations Research, Computational Theory and Mathematics, Computer Science Applications

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Citation

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

MLA
Claeys, Dieter, and Stijn De Vuyst. “Discrete-time Modified Number- and Time-limited Vacation Queues.” QUEUEING SYSTEMS 91.3-4 (2019): 297–318. Print.
APA
Claeys, Dieter, & De Vuyst, S. (2019). Discrete-time modified number- and time-limited vacation queues. QUEUEING SYSTEMS , 91(3-4), 297–318.
Chicago author-date
Claeys, Dieter, and Stijn De Vuyst. 2019. “Discrete-time Modified Number- and Time-limited Vacation Queues.” Queueing Systems 91 (3-4): 297–318.
Chicago author-date (all authors)
Claeys, Dieter, and Stijn De Vuyst. 2019. “Discrete-time Modified Number- and Time-limited Vacation Queues.” Queueing Systems 91 (3-4): 297–318.
Vancouver
1.
Claeys D, De Vuyst S. Discrete-time modified number- and time-limited vacation queues. QUEUEING SYSTEMS . Springer Nature; 2019;91(3-4):297–318.
IEEE
[1]
D. Claeys and S. De Vuyst, “Discrete-time modified number- and time-limited vacation queues,” QUEUEING SYSTEMS , vol. 91, no. 3–4, pp. 297–318, 2019.
@article{8588046,
  abstract     = {A vast amount of literature has appeared on vacation queues. In the well-known
number- and time-limited vacation policies, the server goes on vacation if the number
of customers, respectively, work (time slots) served since the previous vacation reaches
a specified value, or if the system becomes empty, whichever occurs first. However,
in practice, the server does not always go on vacation when the system is empty if
the number of customers/work to be served has not yet reached the specified amount.
Therefore, we study modified number- and time-limited vacation policies, where we
account for this feature. We complement our recent work on these vacation policies by
considering a discrete time, instead of a continuous-time, setting. We therefore adopt
a different analysis approach, which enables us to obtain similar as well as new results
as compared to our previous work. The results in this paper are valid for a memoryless
distribution, but also for distributions with finite support, and a mixture of geometric
distributions.},
  author       = {Claeys, Dieter and De Vuyst, Stijn},
  issn         = {0257-0130},
  journal      = {QUEUEING SYSTEMS },
  keywords     = {Management Science and Operations Research,Computational Theory and Mathematics,Computer Science Applications},
  language     = {eng},
  number       = {3-4},
  pages        = {297--318},
  publisher    = {Springer Nature},
  title        = {Discrete-time modified number- and time-limited vacation queues},
  url          = {http://dx.doi.org/10.1007/s11134-018-9596-8},
  volume       = {91},
  year         = {2019},
}

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