Some Theorems on a Single-Server Queue with Balking

Ronald Stewart Dick
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Ronald Stewart Dick: Social Security Administration, Baltimore, Maryland

Operations Research, 1970, vol. 18, issue 6, 1193-1206

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.

Date: 1970
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