On a certain type of network of queues

Abstract

The paper studies a network of queues in which units arrive singly in a Poisson stream at a service channel S from which they branch out into k parallel channels S₁, S₂, …, S_k. After having been serviced at S₁, S₂, … S_k, the units converge again into a single channel S′. The service times of units at each of the channels are assumed to be exponential. Units finally serviced at S’ may leave the system or may again join S. This has been considered by taking two models denoted as Model A and Model B. Steady-state probabilities giving the number of units present in the system have been obtained explicitly for both the models. The expressions for mean queue lengths have also been arrived at.