Title: Ant colony optimisation for impatient customer queue under N-policy and Bernoulli schedule vacation interruption

Authors: P. Vijaya Laxmi; S. Indira

Addresses: Department of Applied Mathematics, Andhra University, Visakhapatnam – 530003, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam – 530003, India

Abstract: This paper analyses a finite buffer multiple working vacations queue with balking, reneging and Bernoulli schedule vacation interruption under N-policy. Arriving customer decide either to join the system or to balk. After joining the queue, the customer may renege. The server leaves for working vacation after serving the queue exhaustively. At a service completion instant during working vacation, the server continue the vacation with probability q or if there are at least N customers in the queue the server interrupts the vacation and resumes regular service with probability 1 − q. The inter-arrival times of customers are assumed to be arbitrarily distributed. Service times during a regular service period, during a working vacation period and vacation times are assumed to be exponentially distributed and are mutually independent. Using recursive technique, the steady state system length distributions at various epochs are obtained. Some performance measures of the model and cost analysis using ant colony optimisation are presented. Finally, numerical results showing the effect of model parameters on key performance measures are presented.

Keywords: balking; reneging; multiple working vacation queues; Bernoulli schedule vacation interruption; BS-VI; N-policy; ant colony optimisation; ACO; impatient customers; service times; performance measures; cost analysis.

DOI: 10.1504/IJMOR.2017.081923

International Journal of Mathematics in Operational Research, 2017 Vol.10 No.2, pp.167 - 189

Received: 21 Feb 2015
Accepted: 02 May 2015
Published online: 31 Jan 2017 *

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