Packet Scheduling with Window Service Constraints

This paper considers the scheduling problem that minimizes the average response time of two jobs subject to window constraints. By window constraints, we mean that within a fixed time interval, the server can serve at mostW packets from one job, where W is called the window size of the job. This paper investigates the effects of the window constraints in detail, and derives the optimal policy. The results shows that both the job lengths (which correspond to the remaining processing times in traditional optimization problems without window constraints) and the window sizes are essential to the optimal policy. Moreover, instead of changing priority of jobs at different times, in most cases the optimal policy gives full priority to one job. The paper also gives the following suboptimal policy: if both window sizes are greater than one half of the time interval, give full priority to the shorter job; Otherwise, give full priority to the job with the smaller window size. The difference between the optimal cost and the cost of this suboptimal policy is less than the maximum of the two window sizes.