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

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.