Abstract
We study a two stage queuing model where the server provides two stages of service one by one in succession. We consider reneging to occur when the server is unavailable during the system breakdown or vacation periods. We concentrate on deriving the steady state solutions by using supplementary variable technique and calculate the mean queue length and mean waiting time. Further some special cases are also discussed and numerical examples are presented.
Highlights
Queues with impatient customers have attracted the attention of many researchers and we see significant contribution by numerous researchers in this area
Another early work on markovian reneging with markovian and arrival and service pattern was by Ancker and Gafarian [4], Haghighi et al [5] studied a markovian multiserver queuing system with balking and reneging
An M/G/1 queue with deterministic reneging was studied by Bae et al [6]
Summary
Queues with impatient customers have attracted the attention of many researchers and we see significant contribution by numerous researchers in this area. Customers may renege (leave the queue after joining) during server breakdowns or during the time when the server takes vacation due to impatience. This is a very realistic assumption and often we come across such queuing situations in the real world. Let μ j ( x) be the conditional probability of stage j service during the period We assume the vacation time to be a random variable following general probability law with distribution function given by W (v) and density function by w (v). D) In addition, customers arriving for service may become impatient and renege (leave the queue) after joining during vacations and breakdown periods. Let the conditional probability of completion of the repair process is β(x)dx such that β
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