Offline and Online Scheduling of Jobs with Service and Delay Costs

We study continuous time job scheduling and server speed scaling problems with focus on minimizing service and job waiting costs. Jobs arrive over time and are to be served by a server. Each job is characterized by its arrival time, service requirement and deadline. The processor incurs service cost, the service cost rate being an increasing convex function of the service rate. Further, the jobs also incur linear waiting cost. We first consider the offline version of the problem where arrival times, requirements and deadlines of all the jobs are known a priori. We propose job scheduling algorithms that minimize the total accrued cost. We then consider the online version of the problem and propose two heuristics. Our problem can be seen as an extension of the well studied speed scaling problem with a delay cost also included.