On the competitiveness of on-line real-time task scheduling

With respect to on-line scheduling algorithms that must direct the service of sporadic task requests we quantify the benefit of clairvoyancy, i.e., the power of possessing knowledge of various task parameters of future events. Specifically, we consider the problem of preemptively sheduling sporadic task requests in both uni- and multi-processor environments. If a task request is successfuly scheduled to completion, a value equal to the task's execution time is obtained; otherwise no value is obtained. We prove that no on-line scheduling algorithm can guarantee a cumulative value greater than 1/4th the value obtainable by a clairvoyant scheduler; i.e., we prove a 1/4th upper bound on the competitive factor of on-line real-time schedulers. We present an online uniprocessor scheduling algorithm TD₁ that actually has a competitive factor of 1/4; this bound is thus shown to be tight. We further consider the effect of restricting the amount of overloading permitted (the loading factor), and quantify the relationship between the loading factor and the upper bound on the competitive factor. Other results of a similar nature deal with the effect of value densities (measuring the importance of type of a task). Generalizations to dual-processor on-line scheduling are also considered. For the dual-processor case, we prove an upper bound of 1/2 on the competitive factor. This bound is shown to be tight in the special case when all the tasks have the same density and zero laxity.