Scheduling time-constrained jobs in the presence of background traffic

In this paper we study the scheduling of jobs with a constraint on the average waiting time in the presence of background jobs. The objective is to schedule to s servers such that the throughput of the background traffic is maximized while satisfying the response time constraint on the foreground traffic. The arrivals are determined by a Poisson process and the service times of the jobs are independent exponentially distributed. We consider both the situation where service requirements by both types of jobs are equal and unequal. The first situation is solved to optimality, for the second situation we find the best policy within a certain class of policies. Optimal schedules always keep part of the service capacity free for arriving foreground jobs. Applications of this model can be found in computer systems, communication networks and call centers.