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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*The research of the fourth author was funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office. This work is supported by Russian Foundation for Basic research, projects No 15–07–02341 A, 15–07–02354 A,15–07–02360 A. The work of the first author is partially supported by EU COST ACROSS action No IC-1304.
Proceedings of the XXXII International Seminar on Stability Problems for Stochastic Models, Trondheim, Norway, June 16–21, 2014.
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Avrachenkov, K., Morozov, E.V., Nekrasova, R.S. et al. Stability of Constant Retrial Rate Systems with NBU Input*. J Math Sci 214, 22–33 (2016). https://doi.org/10.1007/s10958-016-2755-8
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DOI: https://doi.org/10.1007/s10958-016-2755-8