PERFORMANCE ANALYSIS OF A TELEPHONE SYSTEM WITH BOTH PATIENT AND IMPATIENT CUSTOMERS

In this paper, the performance of a telephone system in which there ar e both patient and impatient customers is studied. Depending on the wa iting time in the buffer, a customer may become impatient and therefor e the call is incomplete. An impatient customer still consumes real pr ocessing time. The impact of impatient customers on the system is much more remarkable than people would expect. We formulate this model as a queueing system with a finite buffer. The status of a customer, i.e. whether patient or impatient, depends on the waiting time in the buff er and the service time is different for the different type of custome rs. The joint distribution of the numbers of patient and impatient cus tomers in the system is obtained for the system in equilibrium. Expres sions of many performance measures, including the average number of pa tient customers or impatient customers in the system, the average leng th of the service time, the average arrivals during a service period, and the proportion of the ''useful'' service time contributing towards patient customers' service, can be expressed in terms of the joint pr obabilities. The waiting time probabilities and the average waiting ti me of a customer in the buffer and the probability that a customer wil l be served as a patient customer are also obtained. Numerical example s are presented.