Wiener-Hopf analysis of an M/G/1 queue with negative customers and of a related class of random walks |
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Authors: | N Bayer O J Boxma |
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Institution: | (1) CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands |
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Abstract: | Two variants of an M/G/1 queue with negative customers lead to the study of a random walkX
n+1=X
n
+
n
]+ where the integer-valued
n
are not bounded from below or from above, and are distributed differently in the interior of the state-space and on the boundary. Their generating functions are assumed to be rational. We give a simple closed-form formula for
, corresponding to a representation of the data which is suitable for the queueing model. Alternative representations and derivations are discussed. With this formula, we calculate the queue length generating function of an M/G/1 queue with negative customers, in which the negative customers can remove ordinary customers only at the end of a service. If the service is exponential, the arbitrarytime queue length distribution is a mixture of two geometrical distributions.Supported by the European grant BRA-QMIPS of CEC DG XIII. |
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Keywords: | M/G/1 queue negative customers queue length Wiener-Hopf technique |
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