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).
Our model is sometimes called the , as opposed to @cite_9 , in which an interrupted job can only be processed from the very beginning. @cite_1 form another related model, in which all the job parameters are reals, the time is continuous, and uniform weights are assumed.
@cite_9 @cite_1
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We consider the following scheduling problem. The input is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a single-processor nonpreemptive schedule that maximizes the number of completed jobs. In the online version, each job arrives at its release time. We give two online algorithms with competitive ratios below @math and show several lower bounds on the competitive ratios. First, we give a barely random @math -competitive algorithm that uses only one random bit. We also show a lower bound of @math on the competitive ratio of barely random algorithms that randomly choose one of two deterministic algorithms. If the two algorithms are selected with equal probability, we can further improve the bound to @math . Second, we give a deterministic @math -competitive algorithm in the model that allows restarts, and we show that in this model the ratio @math is optimal. For randomized algorithms with restarts we show a lower bound of @math . 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. >