Some Theorems on a Single-Server Queue with Balking

Abstract

An M / G /1 batched-service queuing model is described for a waiting room of size m . When the waiting room is filled, the arrival rate changes from λ to λ p ; i.e., 100 (1 − p ) per cent of all arrivals balk if the waiting room is full. Since p may be zero, the model includes finite queues as special cases. The special case with m = 0 has been handled by Takács. However, in this paper the steady-state probability formulas for length of queue given by Takács are corrected, and the results extended for m ≧ 1.