Equilibrium balking strategies in renewal input batch arrival queues with multiple and single working vacation

This paper investigates equilibrium threshold balking strategies of customers in a renewal input batch arrival queue with multiple and single working vacation of the server. The vacation period, service period during normal service and vacation period are considered to be independent and exponentially distributed. Upon arriving, the customers decide whether to join or balk the queue based on observation of the system-length and status of the server. The waiting time in the system is associated with a linear cost–reward structure for estimating the net benefit if a customer wishes to participate in the system. Equilibrium customer strategy is studied under four cases: fully observable, almost observable, almost unobservable and fully unobservable. Using embedded Markov chain approach and system cost analysis, we obtain the equilibrium threshold. The analysis of unobservable cases is based on the roots of the characteristics equations formed using the probability generating function of embedded pre-arrival epoch probabilities. Equilibrium balking strategy may be useful in quality of service for EPON (ethernet passive optical network) as a multiple working vacation model and accounting through gatekeeper based H.323 protocols as a single working vacation model.