Abstract
An M/M/1 queueing system with an unreliable device is considered in the study. The device fails in an exponentially distributed time during which it is in the working condition and serves a demand. The device recovers during an exponentially distributed time according to the threshold policy specified by threshold level q ≥ 1. After a successive failure, the device does not recover until the number of demands exceeds level q. In the study, the system operating in the stationary regime is analyzed and the problem of optimal recovery control aimed at the minimization of the mean cost for a given penalty structure is solved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Efrosinin, Controlled Queueing Systems with Heterogeneous Servers. Dynamic Optimization and Monotonicity Properties (VDM Verlag, Saarbrücken, 2008).
O. V. Semenova and A. N. Dudin, “An M/M/N Queueing System with Controlled Service Regime and with Casualties,” Avtom. Vychislit. Tekhn., (2007).
K.-H. Wang, “Optimal Control of a Removable and Non-Reliable Server in An M/M/1 Queueing System with Exponential Startup Time,” Math. Methods Oper. Res. 58, 29–39 (2003).
D. P. Heyman and M. J. Sobel, Stochastic Models in Operations Research,” Vol. II: Stochastic Optimization (McGraw-Hill, New York, 1984).
E. Pakes, “Some Conditions for Egodicity and Recurrence of Markov Chains,” Oper. Res. 17, 1058–1061 (1969).
Additional information
Original Russian Text © D.V. Efrosinin, O.V. Semenova, 2009, published in Informatsionnye Protsessy, 209, Vol. 9, No. 4, pp. 293–300.
Rights and permissions
About this article
Cite this article
Efrosinin, D.V., Semenova, O.V. An M/M/1 system with an unreliable device and a threshold recovery policy. J. Commun. Technol. Electron. 55, 1526–1531 (2010). https://doi.org/10.1134/S1064226910120260
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064226910120260