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A review ofL=λW and extensions

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Abstract

A fundamental principle of queueing theory isL=λW (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=λG and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=λW relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=λG and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.

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  1. AT&T Bell Laboratories, Room2C-178, 07974-0636, Murray Hill, NJ, USA

    Ward Whitt

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This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.

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Whitt, W. A review ofL=λW and extensions. Queueing Syst 9, 235–268 (1991). https://doi.org/10.1007/BF01158466

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  • DOI: https://doi.org/10.1007/BF01158466

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