Abstract
Typical queueing problems of general arrival and general service systems are solved by an approximation method. That is, approximate formulae are given for the mean customer number in the G/G/1 (∞) system, the mean customer number in the the G/G/1 (m) system and the mean queue length in the G/G/s(∞) system_ The routine of the proposed method is as follows. The sequences of arrival and departure of customers are approximately replaced by normal stochastic processes. That is, the sequences are characterized by mean and variance only. Next, the diffusion equation is constructed as to the probability distribution of the customer number in the system. Using the solution of the equation, the aimed statistical value for the queue is calculated. Finally, the calculated value may be revised to agree with the exact solution on the area where it is known.
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