Abstract
ABSTRACT The quality control services provided to customers play an important role in increasing an organization’s economic benefit. Under the quality control process, we present a novel iterative algorithm to obtain the transient probability of the feedback M/M/1/N queue with balking and retention of reneged customers. Based on the Laplace transform, we obtain the exponential matrix corresponding to the proposed system consequently, obtaining the exact solution of the probability dynamical system of differential equations of customers in the system. Also, an efficient algorithm has been introduced. The Laplace transform and the proposed algorithm enable us to obtain the exact solutions of the transient-states of queuing systems with different capacities. Several numerical examples are given to illustrate the behavior of probabilities as functions in time, the expected number of units in the system, queue and the optimization of the model. A transient solution for some important queuing systems is driven as a special case.
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