This article presents a transform-free approximation for the system size of M/G/c queueing systems. When thenumber of customers in the system is less than or equal to the number of server, its distribution is derived utilizingthe Markovian service time model and a new parameter. To obtain the probability of the number of customer beinggreater than the number of server, a queue is regarded as a set of each separate waiting space rather than the wholeentire queue and types of load on each waiting space are classified. The efficiency and effectiveness of theapproximation are discussed through simulation experiments.
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