We consider a single-server queuing system with a finite number of sources, where customers are not allowed to queue; instead of that, they make repeated attempts, or retrials, in order to enter service after some time. This queuing system and its variants are widely used to model disk memory systems, star-like local area networks, and other communication systems. The article extends previous works on this topic and deals with the number of retrials, produced by a tagged customer, until he finds the server available. An algorithm for determination of all moments of this number is obtained, and the results of numerical experiments are presented.
The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.
This article considers a finite-source queueing model of M/G/1 type in which a customer, arriving at a moment of a busy server, is not allowed either to queue or to do repetitions. Instead, for an exponentially distributed time interval he is blocked in the orbit of inactive customers. We carry out a steady state analysis of the system and compare it with the corresponding system with retrials. Optimization problems are considered and formulas for the Laplace-Stieltjes transform of the busy period length are obtained.
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