An M/M/1-Type queue with an individual deterministic retrial rate

Yair Y. Shaki; Moshe Haviv; Uri Yechieli

doi:10.1109/SMRLO.2016.111

An M/M/1-Type queue with an individual deterministic retrial rate

Yair Y. Shaki, Moshe Haviv, Uri Yechieli

Department of Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Consider a system where customers arrive to a single-server queue according to a Poisson process with rate λ. The service times are independent and exponential distributed with rate μ. A customer who arrives when the server is busy is blocked and goes to orbit. Each orbit customer then every T units of time to re-enter the system. If he is blocked again, he will keep trying every T units of time. Balking is not allowed. In this paper, we consider retrial policy with deterministic T and we calculate the expected number of customers in orbit (without using balance equations).

Original language	English
Title of host publication	Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016
Editors	Anatoly Lisnianski, Ilia Frenkel
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	630-632
Number of pages	3
ISBN (Electronic)	9781467399418
DOIs	https://doi.org/10.1109/SMRLO.2016.111
State	Published - 11 Mar 2016
Event	2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016 - Beer Sheva, Israel Duration: 15 Feb 2016 → 18 Feb 2016

Publication series

Name	Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016

Conference

Conference	2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016
Country/Territory	Israel
City	Beer Sheva
Period	15/02/16 → 18/02/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Keywords

Deterministic retrial rate
Queueing system

Access to Document

10.1109/SMRLO.2016.111

Cite this

Shaki, Y. Y., Haviv, M., & Yechieli, U. (2016). An M/M/1-Type queue with an individual deterministic retrial rate. In A. Lisnianski, & I. Frenkel (Eds.), Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016 (pp. 630-632). Article 7433186 (Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SMRLO.2016.111

Shaki, Yair Y. ; Haviv, Moshe ; Yechieli, Uri. / An M/M/1-Type queue with an individual deterministic retrial rate. Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016. editor / Anatoly Lisnianski ; Ilia Frenkel. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 630-632 (Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016).

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abstract = "Consider a system where customers arrive to a single-server queue according to a Poisson process with rate λ. The service times are independent and exponential distributed with rate μ. A customer who arrives when the server is busy is blocked and goes to orbit. Each orbit customer then every T units of time to re-enter the system. If he is blocked again, he will keep trying every T units of time. Balking is not allowed. In this paper, we consider retrial policy with deterministic T and we calculate the expected number of customers in orbit (without using balance equations).",

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Shaki, YY, Haviv, M & Yechieli, U 2016, An M/M/1-Type queue with an individual deterministic retrial rate. in A Lisnianski & I Frenkel (eds), Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016., 7433186, Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016, Institute of Electrical and Electronics Engineers Inc., pp. 630-632, 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016, Beer Sheva, Israel, 15/02/16. https://doi.org/10.1109/SMRLO.2016.111

An M/M/1-Type queue with an individual deterministic retrial rate. / Shaki, Yair Y.; Haviv, Moshe; Yechieli, Uri.
Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016. ed. / Anatoly Lisnianski; Ilia Frenkel. Institute of Electrical and Electronics Engineers Inc., 2016. p. 630-632 7433186 (Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Shaki YY, Haviv M, Yechieli U. An M/M/1-Type queue with an individual deterministic retrial rate. In Lisnianski A, Frenkel I, editors, Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 630-632. 7433186. (Proceedings - 2nd International Symposium on Stochastic Models in Reliability Engineering, Life Science, and Operations Management, SMRLO 2016). doi: 10.1109/SMRLO.2016.111

An M/M/1-Type queue with an individual deterministic retrial rate

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Keywords

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