Markovian queueing system with random balking

An M/M/1queueing system with the customer impatience in the form of random balking is considered in this paper. Effecting in the model a system size-based balking according to which a new customer will join the queue with probability q k if he finds k(≥0) customers in the system on his arrival, we obtained the stationary distribution of the system size, its mean and variance. Further the stationary characteristics of the system for various balking probability functions are investigated. The maximum likelihood estimate of the balking parameter is also discussed. The models we treated here find practical application in helping the management of any enterprises to provide adequate service for its customers with tolerable waiting, whenever, customer impatience becomes sufficiently strong and customers leave before being served.