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Generalised Pollaczek–Khinchin formula for the Polya/G/1 queue

Generalised Pollaczek–Khinchin formula for the Polya/G/1 queue

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A generalised Pollaczek–Khinchin formula for the Polya/G/1 queue, with a Polya peaked arrival process, general distributed service times, and infinite number of waiting positions, is obtained. It is shown that the peakedness of the number of arrivals and the variance of the service time lead to a significant increase in the service delay and queue length.

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