Abstract
This paper considers an M/M/1 queue with a very general feedback mechanism. When a customer completes his i-th service, he departs from the system with probability 1 - p(i) and he cycles back with probability p(i). The main result of the paper is a formula for the joint distribution of the successive sojourn times of a customer in the system. As a by-result, it is shown that the sojourn times in all individual cycles are identically, negative exponentially, distributed. Also, the correlation between the sojourn times of the j-th and k-th cycle of a customer is calculated; furthermore, the distribution of the total sojourn time is derived.
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© 1989 Springer-Verlag Berlin · Heidelberg
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van den Berg, J.L., Boxma, O.J. (1989). Sojourn Times in Feedback Queues. In: Pressmar, D., Jäger, K.E., Krallmann, H., Schellhaas, H., Streitferdt, L. (eds) Operations Research Proceedings 1988. Operations Research Proceedings, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74862-2_70
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DOI: https://doi.org/10.1007/978-3-642-74862-2_70
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