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Transient queue size distribution solution of Geom/G/1 queue with feedback – a recursive method. (English) Zbl 1300.90011
Summary: This paper considers the Geom/G/1 queueing model with feedback according to a late arrival system with delayed access (LASDA). Using recursive method, this paper studies the transient property of the queue size from the initial state \(N(0^{+}) = i\). Some new results about the recursive expression of the transient queue size distribution at any epoch \(n^{+}\) and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch \(n^{-}\), and \(n\) are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered (being different from the relations given in M/G/1 queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer network.

MSC:
90B22 Queues and service in operations research
93C55 Discrete-time control/observation systems
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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