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

Authors: Pankaj Sharma

Addresses: Department of Mathematics, School of Sciences, Noida International University, Gautam Buddha Nagar, Grater Noida, U.P., Pin-201306, India

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.

DOI: 10.1504/IJOR.2017.083955

International Journal of Operational Research, 2017 Vol.29 No.2, pp.183 - 196

Received: 11 Jul 2014
Accepted: 26 Sep 2014

Published online: 26 Apr 2017 *

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