Exact solution of a simple finite infinite source interaction model (Q1105367)

Networks of queues with finite and infinite source customers have been used to study the interaction between the batch jobs and interactive jobs in computer systems. Earlier \textit{J. S. Kaufman} [in ``Performance '84'', North-Holland (1984; Zbl 0572.68006), pp. 345-348], developed accurate approximations for a simple non-product form network of this type. In this paper we offer exact solutions for the same model with one finite source customer. We study both FIFO and LIFO disciplines at the contention node. The results are derived for the case where the finite source think time and service time distributions are generalized hyperexponential.