Transient analysis of interdependent M/M( a,d,b )/1 queue with discouragement and controllable arrival rate

Pankaj Sharma

International Journal of Operational Research, 2017, vol. 29, issue 2, 183-196

Abstract: This paper deals with the state dependent single server queue having a general batch service rule where the arrival and service are assumed to be correlated and follow the bivariate Poisson processes. According to general bulk service rule, the service starts only when a specified number of customers, say 'a', is present in the queue and the maximum service capacity of a batch service is 'b'. Due to accessible batch, the late arriving customers are allowed to join the batch during ongoing service, if the size of the batch served is less than some fixed integer 'd' (a < d < b). When the batch size reaches the threshold limit d, no further customers are allowed to join the batch which is called non-accessible batch. To demonstrate the validity of the analytical results, numerical illustration has been taken into consideration. The sensitivity has been analysed by examining the effect of system parameters on the average queue length.

Keywords: bulk service; bivariate poisson processes; general bulk service; queue length; busy period; state dependent rates; discouragement. (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ids:ijores:v:29:y:2017:i:2:p:183-196

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