Volume 51, Number 2, April-June 2017
|Page(s)||417 - 432|
|Published online||30 March 2017|
Priority queue with batch arrival, balking, threshold recovery, unreliable server and optimal service
Department of Mathematics, IIT Roorkee, Roorkee, India
Received: 16 October 2014
Accepted: 17 September 2015
The threshold policy for the restoration of an unreliable server in a service system with bulk input and balking is investigated. The arriving customers in the queueing system are classified into two categories i.e. priority and ordinary customers. The priority customers are assumed to join the system in groups according to Poisson process. The ordinary customers join the system singly and require the essential service as well as optional service on demand and only a limited number of customers can wait in the queue when the server is busy. The service times of both types of customers and life time as well as repair time of the server are governed by the exponential distribution. When the server fails during the service of the ordinary customer, the repair is done following a threshold recovery rule according to which the repair of the failed server is started only when at least q ordinary customers are accumulated in the system. In case of failure while rendering the service to the priority customers, the server is immediately sent for the repair. The matrix geometric method (MGM) has been used to establish the queue size distribution and other performance indices. To validate the suggested MGM approach, numerical simulation is carried out by taking an illustration.
Mathematics Subject Classification: 60K25 / 60K30 / 68M20 / 90B22 / 90B25
Key words: Bulk queue / priority / unreliable server / threshold recovery / balking function / optional service / matrix geometric method / queue size
© EDP Sciences, ROADEF, SMAI 2017
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