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In this paper, we study a single server queuing model with retention of reneging customers. The transient solution of the model is derived using probability generating function technique. The time-dependent mean and variance of the model are also obtained. Some important special cases of the model are derived and discussed. Finally, based on the numerical example, the transient performance analysis of the model is performed.

In this paper, we study an infinite capacity multi-server Markovian queuing system with balking and retention of reneging customers. The transient analysis of the model is performed. The probability generating function technique along with Bessel function properties is used to derive the time-dependent state probabilities explicitly. [ABSTRACT FROM PUBLISHER]

In this paper, a finite capacity Markovian single-server queuing system with discouraged arrivals, reneging, and retention of reneging customers is studied. The time-dependent probabilities of the queuing system are obtained by using a computational technique based on the 4th order Runge-Kutta method. With the help of the time-dependent probabilities, we develop some important measures of performance of the system, such as expected system size, expected reneging rate, and expected retention rate. The time-dependent behavior of the system size probabilities and the expected system size is also studied. Further, the variations in the expected system size, the expected reneging rate, and the expected retention rate with respect to the probability of retaining a reneging customer are also studied. Finally, the effect of discouragement in the same model is analyzed. [ABSTRACT FROM AUTHOR]