Abstract
In this article an M/G/1 queueing model with single server, Poisson input, k-phases of heterogeneous services and Bernoulli feedback design has been considered. For this model, we derive the steady-state probability generating function (PGF) of queue size at the random epoch and at the service completion epoch. Then, we derive the Laplace-Stieltjes Transform (LST) of the distribution of response time, the means of response time, number of customers in the system and busy period.
Highlights
The M/G/1 queueing model is one of the famous and applied models in which the distribution of service times is unknown
First we find the steady-state probability generating function (PGF) of queue size at the random epoch and at the service completion epoch
In this article we have obtained some results for an M/G/1 queue with k-phases of heterogeneous services and Bernoulli feedback design
Summary
The M/G/1 queueing model is one of the famous and applied models in which the distribution of service times is unknown. It means that the service customer is not acceptable and must go to the end of queue According to these conditions, we have considered an M/G/1 queueing model with k-Phase Optional Services and Bernoulli feedback. We have considered an M/G/1 queueing model with k-Phase Optional Services and Bernoulli feedback For this model, first we find the steady-state probability generating function (PGF) of queue size at the random epoch and at the service completion epoch. The means of response time, number of customers in the system and busy period will be derived by using the PGF and LST In relation of this model, [1,2,3,4,5,6,7,8,9,11] have derived some results.
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