On the multi-phase M/G/1 queueing system with random feedback |
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Authors: | M R Salehirad A Badamchizadeh |
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Institution: | (1) Department of Statistics, Allameh Tabataba’i University, Tehran, Iran |
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Abstract: | In this paper we consider an M/G/1 queue with k phases of heterogeneous services and random feedback, where the arrival is Poisson and service times has general
distribution. After the completion of the i-th phase, with probability θ
i
the (i + 1)-th phase starts, with probability p
i
the customer feedback to the tail of the queue and with probability 1 − θ
i
− p
i
= q
i
departs the system if service be successful, for i = 1, 2 , . . . , k. Finally in kth phase with probability p
k
feedback to the tail of the queue and with probability 1 − p
k
departs the system. We derive the steady-state equations, and PGF’s of the system is obtained. By using them the mean queue
size at departure epoch is obtained. |
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Keywords: | M/G/1 queue k-phase of heterogeneous service Random feedback Effective measures |
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