Abstract
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.
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References
Van den Berg, J.L., Boxma, O.J., Groenenduk, W.P. (1987) Sojourn times in the M/G/l queue with deterministic feedback, Report OS-R8708, Centre for Mathematics and Computer Science, Amsterdam.
Van den Berg, J.L., Boxma, O.J. (1987) Sojourn times in feedback queues, Report OS-R8710, Centre for Mathematics and Computer Science, Amsterdam.
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© 1988 Springer-Verlag Berlin Heidelberg
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van den Berg, J.L., Boxma, O.J. (1988). Sojourn Times in Feedback Queues. In: Schellhaas, H., van Beek, P., Isermann, H., Schmidt, R., Zijlstra, M. (eds) DGOR/NSOR. Operations Research Proceedings, vol 1987. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73778-7_119
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DOI: https://doi.org/10.1007/978-3-642-73778-7_119
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