Single parameter analysis of power of preemption on two and three uniform machines

We consider scheduling problems on two and three uniform parallel machines. In the case of three machines we focus on the instances in which two machines have the same speed. For these models, we analyze the power of preemption defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. We derive tight upper bounds on the power of preemption expressed as piecewise functions of a single parameter, which is the speed of the fastest machine.