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Approximations for customer-viewed delays in multiprogrammed, transaction-oriented computer systems

A common method of insuring the efficient use of resources in a computer system is to limit the degree of multiprogramming, i.e., the number of jobs allowed in the system at the same time. Many systems vary the multiprogramming level dynamically, white others fix the level a priori. This paper analyzes a transaction-oriented computer system with a fixed level of multiprogramming. We are primarily concerned with the performance of such systems as viewed by the customers submitting the transactions. While the common technique of approximating such systems with a state-dependent server model is often adequate, in some situations it can lead to large errors. We introduce the concept of the mean forward recurrence time of the output process under saturation and we show that errors that occur in using a state-dependent server model are directly related to this mean forward recurrence time. We give an improved approximation technique using this quantity and show that its accuracy depends on the dominant time constant (relaxation time) of the computer system. The variability in the output process of the computer system that is implied by a large mean forward recurrence time (relative to the mean interdeparture time) can have broad implications on the analysis and design of computer systems, particularly with a fixed degree of multiprogramming. Thus, even though estimation of this mean forward recurrence time may be difficult (although readily measured) in complex systems, a knowledge of this quantity may be necessary to achieve a reasonable degree of confidence in performance models.