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An approximate analysis of a bernoulli alternating service model

Arnaud Devos (UGent) , Dieter Fiems (UGent) , Joris Walraevens (UGent) and Herwig Bruneel (UGent)
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Abstract
We consider a discrete-time queueing system with one server and two types of customers, say type-1 and type-2 customers. The server serves customers of either type alternately according to a Bernoulli pro- cess. The service times of the customers are deterministically equal to 1 time slot. For this queueing system, we derive a functional equation for the joint probability generating function of the number of type-1 and type-2 customers. The functional equation contains two unknown partial generating functions which complicates the analysis. We investigate the dominant singularity of these two unknown functions and propose an approximation for the coefficients of the Maclaurin series expansion of these functions. This approximation provides a fast method to compute approximations of various performance measures of interest.
Keywords
Queueing Theory

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MLA
Devos, Arnaud, et al. “An Approximate Analysis of a Bernoulli Alternating Service Model.” Queueing Theory and Network Applications, 14th International Conference, QTNA 2019, Proceedings, vol. 11688, Springer, 2019, pp. 314–29.
APA
Devos, A., Fiems, D., Walraevens, J., & Bruneel, H. (2019). An approximate analysis of a bernoulli alternating service model. In Queueing theory and network applications, 14th International Conference, QTNA 2019, Proceedings (Vol. 11688, pp. 314–329). Cham: Springer.
Chicago author-date
Devos, Arnaud, Dieter Fiems, Joris Walraevens, and Herwig Bruneel. 2019. “An Approximate Analysis of a Bernoulli Alternating Service Model.” In Queueing Theory and Network Applications, 14th International Conference, QTNA 2019, Proceedings, 11688:314–29. Cham: Springer.
Chicago author-date (all authors)
Devos, Arnaud, Dieter Fiems, Joris Walraevens, and Herwig Bruneel. 2019. “An Approximate Analysis of a Bernoulli Alternating Service Model.” In Queueing Theory and Network Applications, 14th International Conference, QTNA 2019, Proceedings, 11688:314–329. Cham: Springer.
Vancouver
1.
Devos A, Fiems D, Walraevens J, Bruneel H. An approximate analysis of a bernoulli alternating service model. In: Queueing theory and network applications, 14th International Conference, QTNA 2019, Proceedings. Cham: Springer; 2019. p. 314–29.
IEEE
[1]
A. Devos, D. Fiems, J. Walraevens, and H. Bruneel, “An approximate analysis of a bernoulli alternating service model,” in Queueing theory and network applications, 14th International Conference, QTNA 2019, Proceedings, Ghent, 2019, vol. 11688, pp. 314–329.
@inproceedings{8628443,
  abstract     = {We consider a discrete-time queueing system with one server
and two types of customers, say type-1 and type-2 customers. The server
serves customers of either type alternately according to a Bernoulli pro-
cess. The service times of the customers are deterministically equal to
1 time slot. For this queueing system, we derive a functional equation
for the joint probability generating function of the number of type-1 and
type-2 customers. The functional equation contains two unknown partial
generating functions which complicates the analysis. We investigate the
dominant singularity of these two unknown functions and propose an
approximation for the coefficients of the Maclaurin series expansion of
these functions. This approximation provides a fast method to compute
approximations of various performance measures of interest.},
  author       = {Devos, Arnaud and Fiems, Dieter and Walraevens, Joris and Bruneel, Herwig},
  booktitle    = {Queueing theory and network applications, 14th International Conference, QTNA 2019, Proceedings},
  isbn         = {9783030271800},
  issn         = {0302-9743},
  keywords     = {Queueing Theory},
  language     = {eng},
  location     = {Ghent},
  pages        = {314--329},
  publisher    = {Springer},
  title        = {An approximate analysis of a bernoulli alternating service model},
  url          = {http://dx.doi.org/10.1007/978-3-030-27181-7_19},
  volume       = {11688},
  year         = {2019},
}

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