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Stability of constant retrial rate systems with NBU input*

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Abstract
We study the stability of a single-server retrial queueing system with constant retrial rate, general input and service processes. First, we present a review of some relevant recent results related to the stability criteria of similar systems. Sufficient stability conditions were obtained by Avrachenkov and Morozov (2014), which hold for a rather general retrial system. However, only in the case of Poisson input is an explicit expression provided; otherwise one has to rely on simulation. On the other hand, the stability criteria derived by Lillo (1996) can be easily computed but only hold for the case of exponential service times. We present new sufficient stability conditions, which are less tight than the ones obtained by Avrachenkov and Morozov (2010), but have an analytical expression under rather general assumptions. A key assumption is that interarrival times belongs to the class of new better than used (NBU) distributions. We illustrate the accuracy of the condition based on this assumption (in comparison with known conditions when possible) for a number of non-exponential distributions.

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MLA
Avrachenkov, K., et al. “Stability of Constant Retrial Rate Systems with NBU Input*.” JOURNAL OF MATHEMATICAL SCIENCES (NEW YORK, N.Y.), vol. 214, no. 1, 2016, pp. 22–33, doi:10.1007/s10958-016-2755-8.
APA
Avrachenkov, K., Morozov, E. V., Nekrasova, R. S., & Steyaert, B. (2016). Stability of constant retrial rate systems with NBU input*. JOURNAL OF MATHEMATICAL SCIENCES (NEW YORK, N.Y.), 214(1), 22–33. https://doi.org/10.1007/s10958-016-2755-8
Chicago author-date
Avrachenkov, K., E. V. Morozov, R. S. Nekrasova, and Bart Steyaert. 2016. “Stability of Constant Retrial Rate Systems with NBU Input*.” JOURNAL OF MATHEMATICAL SCIENCES (NEW YORK, N.Y.) 214 (1): 22–33. https://doi.org/10.1007/s10958-016-2755-8.
Chicago author-date (all authors)
Avrachenkov, K., E. V. Morozov, R. S. Nekrasova, and Bart Steyaert. 2016. “Stability of Constant Retrial Rate Systems with NBU Input*.” JOURNAL OF MATHEMATICAL SCIENCES (NEW YORK, N.Y.) 214 (1): 22–33. doi:10.1007/s10958-016-2755-8.
Vancouver
1.
Avrachenkov K, Morozov EV, Nekrasova RS, Steyaert B. Stability of constant retrial rate systems with NBU input*. JOURNAL OF MATHEMATICAL SCIENCES (NEW YORK, NY). 2016;214(1):22–33.
IEEE
[1]
K. Avrachenkov, E. V. Morozov, R. S. Nekrasova, and B. Steyaert, “Stability of constant retrial rate systems with NBU input*,” JOURNAL OF MATHEMATICAL SCIENCES (NEW YORK, N.Y.), vol. 214, no. 1, pp. 22–33, 2016.
@article{8536880,
  abstract     = {{We study the stability of a single-server retrial queueing system with constant retrial rate, general input and service processes. First, we present a review of some relevant recent results related to the stability criteria of similar systems. Sufficient stability conditions were obtained by Avrachenkov and Morozov (2014), which hold for a rather general retrial system. However, only in the case of Poisson input is an explicit expression provided; otherwise one has to rely on simulation. On the other hand, the stability criteria derived by Lillo (1996) can be easily computed but only hold for the case of exponential service times. We present new sufficient stability conditions, which are less tight than the ones obtained by Avrachenkov and Morozov (2010), but have an analytical expression under rather general assumptions. A key assumption is that interarrival times belongs to the class of new better than used (NBU) distributions. We illustrate the accuracy of the condition based on this assumption (in comparison with known conditions when possible) for a number of non-exponential distributions.}},
  author       = {{Avrachenkov, K. and Morozov, E. V. and Nekrasova, R. S. and Steyaert, Bart}},
  issn         = {{1072-3374}},
  journal      = {{JOURNAL OF MATHEMATICAL SCIENCES (NEW YORK, N.Y.)}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{22--33}},
  title        = {{Stability of constant retrial rate systems with NBU input*}},
  url          = {{http://doi.org/10.1007/s10958-016-2755-8}},
  volume       = {{214}},
  year         = {{2016}},
}

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