Sensitivity Analysis of Tree Scheduling on Two Machines with Communication Delays

This paper presents a sensitivity analysis for the problem of scheduling UET trees with communication delays on two identical processors, to minimize the makepan. Indeed, actual communication delays may not be precisely known before the execution. The paper compares the optimal makespans with and without communication delays. This is used to get sensitivity bounds for algorithms optimal in the UECT case, that is when execution and communication times are fixed to one. Processor ordered schedules are introduced: all communications are oriented from one processor to the other. We show that these schedules are dominant for unit delays, for zero delays, but not for less than or equal to one delays. We establish that an algorithm, optimal in the UECT case and building processor ordered schedules, admits an absolute sensitivity bound equal to the difference between the maximum and the minimum communication delays: w - w* c