CONSECUTIVE CUSTOMER LOSS PHENOMENON DUE TO BUFFER OVERFLOW IN FINITE BUFFER QUEUING SYSTEM

In this paper, we will clarify the problem of consecutively lost customer due to buffer overflow in an IPP, M/M/1/K queueing system including an M1, M2/M/1/K queueing system as a special case. We define a length of a consecutive loss as the number of customers consecutively lost due to buffer overflow. And, we obtain individual distributions of the lengths of consecutive losses for the IPP- and Markov-sources. From analytical and numerical results, it is shown that either they are geometrical or they can be approximated by a geometric distribution. Also, from numerical examples, we show some properties of the length of consecutive customer loss.