In many modern computer-communication systems, a job may be processed in several phases, or a job may generate new tasks. Such phenomena can be modeled by service systems with feedback. In the queueing literature, attention has been mainly devoted to single-service queues with so-called Bernoulli feedback: when a customer (task) completes his service, he departs from the system with probability l-p and is fed back with probability p. In the present study a more general feedback mechanism is allowed: when a customer completes his i-th service, he departs from the system with probability l-p(i) and is fed back with probability p(i). We mainly restrict ourselves to the case of a Poisson external arrival process and identically, negative exponentially, distributed service times at each service. The resulting queueing model has the property that the joint queue-length distribution of type-i customers, i=1,2,⋯, is of product-form type. This property is exploited to analyse the sojourn-time process.
|Title of host publication||Operations Research Proceedings 1987 (Papers of the 16th Annual Meeting of DGOR, in cooperation with NSOR, Veldhoven, The Netherlands, September 23-25, 1987)|
|Editors||H. Schellhaas, P. Beek, van, H. Isermann, R. Schmidt, M. Zijlstra|
|Place of Publication||Berlin|
|Publication status||Published - 1988|