IJERT-Steady State Analysis Of A Non-Markovian Bulk Queueing Model With Multiple Vacation , Accessible Batches, Setup Times With N-Policy And Closedown Times (original) (raw)

2013, International Journal of Engineering Research and Technology (IJERT)

https://www.ijert.org/steady-state-analysis-of-a-non-markovian-bulk-queueing-model-with-multiple-vacation-accessible-batches-setup-times-with-n-policy-and-closedown-times https://www.ijert.org/research/steady-state-analysis-of-a-non-markovian-bulk-queueing-model-with-multiple-vacation-accessible-batches-setup-times-with-n-policy-and-closedown-times-IJERTV2IS70255.pdf In this paper, a generalized non-Markovian bulk arrival service queueing system is considered with multiple vacations, setup times and closedown time. The service starts only if minimum of 'a' customers are available in the queue. At the service completion epoch, if the number of customers is  ,where a≤  ≤d-1 (d≤b) then the server takes the entire queue for batch service and admits the subsequent arrivals for service till the service of the current batch is over, or the accessible limit d is reached, whichever occurs first. At the service initiation epoch, if the number of customers waiting in the queue '  ' is atleast 'd' (a≤d≤b), then the server takes min( ,b) customers for service and does not allow further arrival into the batch. On completion of a service, if the queue length is less than 'a', then the server performs a closedown work such as, shutting down the machine, removing the tools etc. Following closedown work, the server leaves for a vacation of random length irrespective of queue length. When the server returns for a vacation and if the queue length is still less than 'a', he leaves for another vacation and so on until he finds atleast 'a' customers waiting for service in the queue. That is, if the server finds atleast 'N' customers waiting for service, then he requires a setup time 'R' to start the service. After the setup he serves a batch of 'b' customers, where b≥a. Various characteristics of queueing system and a cost model are presented.