Online Algorithms for Temperature Aware Job Scheduling Problems

Temperature is an important consideration when designing microprocessors. When exposed to high temperatures component reliability can be reduced, while some components completely fail over certain temperatures. We consider the design and analysis of online algorithms; in particular algorithms that use knowledge of the amount of heat a job will generate. We consider algorithms with two main objectives. The first is maximising job throughput. We show upper and lower bounds for the case where jobs are unit length, both when jobs are weighted and unweighted. Many of these bounds are matching for all cooling factors in the single and multiple machine case. We extend this to consider the single machine case where jobs have longer than unit length. When all jobs are equal length we show matching bounds for the case without preemption. We also show that both models of pre-emption enable at most a slight reduction in the competitive ratio of algorithms. We then consider when jobs have variable lengths. We analyse both the models of unweighted jobs and the jobs with weights proportional to their length. We show bounds that match within constant factors, in the non-preemptive and both preemptive models. The second objective we consider is minimising flow time. We consider the objective of minimising the total flow time of a schedule. We show NP-hardness and inapproximability results for the offline case, as well as giving an approximation algorithm for the case where all release times are equal. For the online case we give some negative results for the case where maximum job heats are bounded. We also give some results for a resource augmentation model that include a 1-competitive algorithm when the extra power for the online algorithm is high enough. Finally we consider the objective of minimising the maximum flow time of any job in a schedule.