Scheduling to Minimize General Functions of the Mean and Variance of Sojourn Times in Queueing Systems

The optimality of shortest remaining processing time (SRPT) and its variants with respect to minimizing mean sojourn times are well known. Some recent studies have further argued that SRPT does not unfairly penalize large customers in order to benefit small customers, and thus have proposed the use of SRPT to improve performance in computer systems under various applications such as Web sites and databases. On the other hand, the variance of customer sojourn times is another important property of performance in these systems. We therefore consider alternative approaches to scheduling customers in queueing systems with the goal of providing mean sojourn times relatively close to those obtained under SRPT while also providing better variance properties. Our analysis includes deriving expressions for the mean and variance of customer sojourn times in these queueing systems, as well as for the parameters of the alternative scheduling policies. These results illustrate and quantify a fundamental performance tradeoff between decreasing the mean sojourn time and increasing the sojourn time variance, and vice versa. Our mathematical framework is then exploited to determine scheduling policies and their control parameters in order to optimize general functions of the mean and variance of sojourn times in queueing systems.