Extremal scheduling of parallel processing with and without real-time constraints
Journal of the ACM (JACM)
Operations Research Letters
Dynamic priority protocols for packet voice
IEEE Journal on Selected Areas in Communications
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In this paper we study the extremal properties of the stationary customer lag times in tandem G/GI/1 networks under different service disciplines in terms of convex and increasing convex orderings. Each customer carries a reference time with it and the lag time is defined to be the difference between the time that the customer departs from the system and its reference time. We show that among the class of work conserving non-preemptive service disciplines that are service time independent, the service discipline that schedules customers with the smallest reference times (SR) and the service discipline that schedules the customer with the largest reference time (LR) provide the minima and maxima respectively. If we restrict ourselves to the subset of these disciplines that do not use reference times but do use arrival times in making scheduling decisions, then the first in first out (FIFO) and last come first serve (LCFS) service disciplines provide the minima and maxima respectively. We also present similar results for G/M/1 queue when preemptions are allowed and for the class of service disciplines that are not work conserving.