An approximate analysis of a bernoulli alternating service model
- Author
- Arnaud Devos (UGent) , Dieter Fiems (UGent) , Joris Walraevens (UGent) and Herwig Bruneel (UGent)
- Organization
- 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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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8628443
- 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, doi:10.1007/978-3-030-27181-7_19.
- APA
- Devos, A., Fiems, D., Walraevens, J., & Bruneel, H. (2019). An approximate analysis of a bernoulli alternating service model. Queueing Theory and Network Applications, 14th International Conference, QTNA 2019, Proceedings, 11688, 314–329. https://doi.org/10.1007/978-3-030-27181-7_19
- 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. https://doi.org/10.1007/978-3-030-27181-7_19.
- 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. doi:10.1007/978-3-030-27181-7_19.
- 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://doi.org/10.1007/978-3-030-27181-7_19}}, volume = {{11688}}, year = {{2019}}, }
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