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A relation between stationary queue and waiting time distributions

  • Rasoul Haji (a1) and Gordon F. Newell (a1)
Abstract

A theorem is proved which, in essence, says the following. If, for any queueing system, (i) the arrival process is stationary, (ii) the queue discipline is first-in-first-out (FIFO), and (iii) the waiting time of each customer is statistically independent of the number of arrivals during any time interval after his arrival, then the stationary random queue size has the same distribution as the number of customers who arrive during a random time interval distributed as the stationary waiting time.

Copyright
COPYRIGHT: © Applied Probability Trust 1971 
References
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[1] Little, J. D. C. (1961) A proof for the queueing formula: L= ?W, Operat. Res. 9, 383–387.
[2] Jewell, W. S. (1967) A simple proof of: L = ?W. Operat. Res. 15, 1109–1116.
[3] Beutler, F. J. and Leneman, O. A. Z. (1966) The theory of stationary point processes. Acta Math. 116, 159–197.
[4] Haji, R. (1970) The variance of the number of customers in a queue. Operations Research Center Report 70–18, University of California, Berkeley.
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Journal of Applied Probability
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