Exploiting the characteristics of serial queues to reduce the mean and variance of flow time using combined priority rules

This paper addresses the trade-off challenge from reducing either the mean or variance of flow time when using simple sequencing rules in balanced, multi-class, serial queues. Study results show that instead of the expected zero sum situation, a balance between the two objectives can be achieved by assigning different priority rules to different queues. The order of priority rule assignments in different queues is shown to be relevant because variability along the line creates unbalanced queue lengths for each station, depending on the characteristics of the line. Thus, it was found that a simple heuristic for reducing both the mean and the variance of flow time in non-heavy traffic environments is to assign the first queue a priority rule that reduces its mean queue length while assigning the other queues a priority rule that reduces the variance of flow time. Conversely, for very-high traffic environments, performance improvements are shown from assigning the first queue a priority rule that reduces the variance of flow time while assigning the other queues a priority rule that reduces queue length.