We consider an online scheduling problem, motivated by the issues present at the joints of networks using ATM and TCP IP. Namely, IP packets have to broken down to small ATM cells and sent out before their deadlines, but cells corresponding to different packets can be interwoven. More formally, we consider the online scheduling problem with preemptions, where each job j is revealed at release time r_j, has processing time p_j, deadline d_j and weight w_j. A preempted job can be resumed at any time. The goal is to maximize the total weight of all jobs completed on time. Our main result are as follows: we prove that if all jobs have processing time exactly k, the deterministic competitive ratio is between 2.598 and 5, and when the processing times are at most k, the deterministic competitive ratio is Theta(k log k).
We consider the problem of maximizing the number of jobs completed by their deadline in an online single processor system where the jobs are preemptable and have release times. So in the standard three field scheduling notation, this is the online version of the problem 1 |ri; pmtn| Σ(1 - Ui). We present a deterministic algorithm Lax, and show that for every instance I, it is the case that either Lax, or the well-known deterministic algorithm SRPT (Shortest Remaining Processing Time), is constant competitive on I. An immediate consequence of this result is a constant competitive randomized algorithm for this problem. It is known that no constant competitive deterministic algorithm exists for this problem. The problem of uniprocessor scheduling under conditions of overload is investigated. The system objective is to maximize the number of tasks that complete by their deadlines. For this performance metric it is shown that, in general, any on-line algorithm may perform arbitrarily poorly as compared to a clairvoyant scheduler. Restricted instances of the general problem for which on-line schedulers ran provide a guaranteed level of performance are identified, and on-line algorithms presented for these special cases. > 