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Article

Stability Analysis of a Multiserver model with Simultaneous Service and a Regenerative Input Flow

Afanaseva L., Bashtova E., Grishunina S.

We study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and a random service time is identical at all occupied servers. The service time has an exponential or a phase-type distribution. We de fine an auxiliary service process that is the number of served customers under assumption that always there are customers at the system. Then we construct the sequence of common regeneration points for the regenerative input flow and the auxiliary service process. Basing on relation between the real and auxiliary service processes we obtain the upper and lower estimates for the mean of the really served customers during the common regeneration period. It allows us to deduce the stability criterion of the model under consideration. It turns out that the stability condition does not depend on the structure of the input flow, only the rate of this process plays a role. Nevertheless the distribution of the service time is a very important factor. We give an example which shows that the stability condition can not be expressed in terms of the mean of the service time.