Abstract
In this paper, we present a batch arrival non- Markovian queuing model with second optional service. Batches arrive in Poisson stream with mean arrival rate ?, such that all customers demand the first essential service, whereas only some of them demand the second "optional" service. We consider reneging to occur when the server is unavailable during the system breakdown or vacations periods. The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly.
Highlights
The research study on queuing systems with impatient customers has become an extensive and interesting area in queuing theory literature
Sometimes customers get impatient after joining the queue and leave the system without getting service
Extensive amount of work has been done on queuing systems related to impatient customers
Summary
The research study on queuing systems with impatient customers has become an extensive and interesting area in queuing theory literature. Customers may renege (leave the queue after joining) during server breakdowns or during the time when the server takes vacation due to impatience. In real world, this is a very realistic assumption and often we come across such queuing situations. Customers arriving for service may become impatient and renege (leave the queue) after joining during vacations and breakdown times. = probability that at time 't' there are 'n' customers in the queue and the server is on vacation irrespective of the value of. (4.56) where denote the steady state probabilities that the server is providing first stage of service, second stage of service and server under repair without regard to the number of customers in the queue. Where ρ < 1 is the stability condition under which the steady states exits
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