Temperature aware online algorithms for scheduling equal length jobs

We study the online scheduling problem of maximising job completion subject to temperature constraints. In our setting, jobs are of equal length and have deadlines and heat contributions. The algorithm tries to complete as many jobs as possible before their deadlines while keeping the temperature of the system within an acceptable limit. We give an optimal algorithm for the case where preemption is not allowed. Then we consider the case of preemption and prove a number of lower bounds, showing that for many combination of system parameters, preemption (with restart) is not helpful in improving the competitiveness.