Abstract
In this paper, we consider an M/M/1 queuing system with customer reneging for an unreliable sever. Customer reneging is assumed to occur due to the absence of the server during vacations. Detailed analysis for both single and multiple vacation models during different states of the server such as busy, breakdown and delayed repair periods is presented. Steady state probabilities for single and multiple vacation policies are obtained. Closed form expressions for various performance measures such as average number of customers in the system, proportion of customers served and reneged per unit time during single and multiple vacations are obtained.
Highlights
The customer reneging phenomena has been treated by many researchers under different assumptions
For the queuing models with impatient customers during vacations and for the impatient behavior of the customers during server breakdown and repair period readers may refer [2,4,5,6,7 and 8].Altman and Yechiali[1]analyzed the M/M/1,M/M/C,M/G/1,M/G/∞ queuing models with impatient customers during single and multiple vacation cases and proved that the number of customers abandoned during single vacation is smaller than multiple vacation
They analyzed both multiple and single vacation scenarios and derived the probability generating functions of the number of customers in the system when the server is on vacation period and busy period
Summary
The customer reneging phenomena has been treated by many researchers under different assumptions. Dequan Yue et al[3] analyzed customers‟ impatience in an M/M/1 queuing system under server vacations, where the assumption is that the “impatience timers” of customers depend on the servers‟ states. They analyzed both multiple and single vacation scenarios and derived the probability generating functions of the number of customers in the system when the server is on vacation period and busy period. We consider M/M/1 queuing system with reneging during the server vacations (single and multiple).While serving the customers the server may not be available due to breakdown or delay in repair. If customers are waiting for service in queue it starts busy period until the queue line exhaust
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