On sojourn time in Jackson networks of queues
1987 ◽
Vol 24
(02)
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pp. 495-510
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This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.
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1979 ◽
Vol 11
(02)
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pp. 422-438
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1999 ◽
Vol 12
(4)
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pp. 339-356
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2003 ◽
Vol 40
(2)
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pp. 293-304
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1991 ◽
Vol 4
(2)
◽
pp. 111-116
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1990 ◽
Vol 27
(02)
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pp. 465-468
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