Abstract
Synoptic This paper analyzes a single server Markovian queuing system with the added complexity of customers who are prone to giving up whenever its waiting time is larger than a random threshold - his patience time. I assume that these individual patience times are independent and identically distributed exponential random variables. Application of such queuing systems can be found in hospital emergency rooms handling critical patients, inventory systems with storage of perishable goods, call centres and the like. In this paper, reneging till beginning of service is considered. Under this framework, a detailed and lucid derivation of the distribution of virtual waiting time in queue and in system is presented. Additionally, such reneging systems also have some interesting performance measures such as reneging rate, fraction of customers who renege, mean waiting times. Expressions for the same are presented.
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