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# Stability of retrial queueing system with constant retrial rate

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Organization
Abstract
We study the stability of a single-server retrial queueing system with constant retrial rate and general input and service processes. In such system the external (primary) arrivals follow a renewal input with rate $\lambda$. The system also has service times with rate $\mu$. If a new customer finds all servers busy and the buffer full, it joins an infinite-capacity virtual buffer (or \textit{orbit}). An orbital (secondary) customer attempts to rejoin the primary queue after an exponentially distributed time with rate $\mu_0$.
Keywords
stability condition, constant retrial rate, multi-class system, approach, regenerative, retrial system

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## Citation

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Chicago
Avrachenkov, Konstantin, Evsey Morozov, Ruslana Nekrasova, and Bart Steyaert. 2014. “Stability of Retrial Queueing System with Constant Retrial Rate.” In XXXII International Seminar on Stability Problems for Stochastic Models, Abstracts, 116–117.
APA
Avrachenkov, K., Morozov, E., Nekrasova, R., & Steyaert, B. (2014). Stability of retrial queueing system with constant retrial rate. XXXII International Seminar on Stability Problems for Stochastic Models, Abstracts (pp. 116–117). Presented at the XXXII International Seminar on Stability Problems for Stochastic Models.
Vancouver
1.
Avrachenkov K, Morozov E, Nekrasova R, Steyaert B. Stability of retrial queueing system with constant retrial rate. XXXII International Seminar on Stability Problems for Stochastic Models, Abstracts. 2014. p. 116–7.
MLA
Avrachenkov, Konstantin, Evsey Morozov, Ruslana Nekrasova, et al. “Stability of Retrial Queueing System with Constant Retrial Rate.” XXXII International Seminar on Stability Problems for Stochastic Models, Abstracts. 2014. 116–117. Print.
@inproceedings{5840185,
abstract     = {We  study the stability of a single-server retrial queueing system
with constant retrial rate and general input and service processes.
In such system the external (primary) arrivals follow a renewal input with rate \${\textbackslash}lambda\$.  The system also has  service times with rate \${\textbackslash}mu\$. If a new customer finds all  servers busy and the buffer
full, it joins an infinite-capacity virtual buffer (or {\textbackslash}textit\{orbit\}). An   orbital  (secondary) customer attempts to rejoin the primary queue after an exponentially distributed time with rate \${\textbackslash}mu\_0\$.},
author       = {Avrachenkov, Konstantin and Morozov, Evsey and Nekrasova, Ruslana and Steyaert, Bart},
booktitle    = {XXXII International Seminar on Stability Problems for Stochastic Models, Abstracts},
language     = {eng},
location     = {Trondheim, Norway},
pages        = {116--117},
title        = {Stability of retrial queueing system with constant retrial rate},
year         = {2014},
}