Some Queuing Problems with Balking and Reneging—II

This is the second of two papers in which balking (refusing to join the queue) and reneging (leaving the queue after joining) are considered. The new element here is that the balking behavior is drastically altered The model assumes (1) Customers arrive from a single infinite source in a Poisson stream (2) Arriving customers join the system if it is empty or balk with probability 1 − β/n, n = 1, 2, … where n is the number in system. Thus β is a measure of customer willingness to join the queue (3) Joining customers renege if service does not begin within a certain time. This time is a, random variable whose density function is negative exponential with parameter α (4) A single-service facility operates on a first-come, first-served basis with negative exponential service time distribution. For the steady state, the following are obtained the state probabilities, mean number in queue and system, the probability of R or more in system, the probabilities of balking, waiting, reneging, and acquiring service, the customer loss rate, the distribution and mean value of time in queue for customers who acquire service, and the corresponding results for those who renege. All of these results are also obtained for a pure balking system (no reneging) by setting the reneging parameter a equal to zero.