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Analysis of a discrete-time queue with time-limited overtake priority

Sofian De Clercq (UGent) , Bart Steyaert (UGent) , Sabine Wittevrongel (UGent) and Herwig Bruneel (UGent)
(2016) ANNALS OF OPERATIONS RESEARCH . 238(1-2). p.69-97
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Abstract
In this paper, we investigate a single-server discrete-time queueing system subject to two independent batch Bernoulli arrival processes, each supplying the queue with different customer classes. The two classes of customers have different priority levels in the queue, and different service-time distributions. The studied priority mechanism is time-limited, i.e., customers of the high-priority class cannot overtake customers of lower priority if the latter arrived at least N slots earlier than the former. The parameter N makes the mechanism versatile, spanning a bridge between absolute (fixed) priority and slot-bound priority (see De Clercq et al. in Math Probl Eng. doi: 10.1155/2012/425630, 2012). The time-limited overtake priority mechanism maintains levels of fairness that are unattainable by a pure absolute priority mechanism, and offers more service differentiation than the slot-bound priority alternative studied earlier. By using a censoring argument, we obtain expressions for the steady-state probability generating functions of the delays of both customer classes, as well as the steady-state joint probability generating function of the system content, by using a censoring argument.
Keywords
Queueing theory, Priority, Slot-bound priority, Probability generating function, Censored Markov chains, Priority jumps, Earliest-due-date, Dynamic priority

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Chicago
De Clercq, Sofian, Bart Steyaert, Sabine Wittevrongel, and Herwig Bruneel. 2016. “Analysis of a Discrete-time Queue with Time-limited Overtake Priority.” Annals of Operations Research 238 (1-2): 69–97.
APA
De Clercq, Sofian, Steyaert, B., Wittevrongel, S., & Bruneel, H. (2016). Analysis of a discrete-time queue with time-limited overtake priority. ANNALS OF OPERATIONS RESEARCH , 238(1-2), 69–97.
Vancouver
1.
De Clercq S, Steyaert B, Wittevrongel S, Bruneel H. Analysis of a discrete-time queue with time-limited overtake priority. ANNALS OF OPERATIONS RESEARCH . Springer Nature; 2016;238(1-2):69–97.
MLA
De Clercq, Sofian, Bart Steyaert, Sabine Wittevrongel, et al. “Analysis of a Discrete-time Queue with Time-limited Overtake Priority.” ANNALS OF OPERATIONS RESEARCH 238.1-2 (2016): 69–97. Print.
@article{8507846,
  abstract     = {In this paper, we investigate a single-server discrete-time queueing system subject to two independent batch Bernoulli arrival processes, each supplying the queue with different customer classes. The two classes of customers have different priority levels in the queue, and different service-time distributions. The studied priority mechanism is time-limited, i.e., customers of the high-priority class cannot overtake customers of lower priority if the latter arrived at least N slots earlier than the former. The parameter N makes the mechanism versatile, spanning a bridge between absolute (fixed) priority and slot-bound priority (see De Clercq et al. in Math Probl Eng. doi: 10.1155/2012/425630, 2012). The time-limited overtake priority mechanism maintains levels of fairness that are unattainable by a pure absolute priority mechanism, and offers more service differentiation than the slot-bound priority alternative studied earlier. By using a censoring argument, we obtain expressions for the steady-state probability generating functions of the delays of both customer classes, as well as the steady-state joint probability generating function of the system content, by using a censoring argument.},
  author       = {De Clercq, Sofian and Steyaert, Bart and Wittevrongel, Sabine and Bruneel, Herwig},
  issn         = {0254-5330},
  journal      = {ANNALS OF OPERATIONS RESEARCH },
  keyword      = {Queueing theory,Priority,Slot-bound priority,Probability generating function,Censored Markov chains,Priority jumps,Earliest-due-date,Dynamic priority},
  language     = {eng},
  number       = {1-2},
  pages        = {69--97},
  publisher    = {Springer Nature},
  title        = {Analysis of a discrete-time queue with time-limited overtake priority},
  url          = {http://dx.doi.org/10.1007/s10479-015-2000-8},
  volume       = {238},
  year         = {2016},
}

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