Bandwidth allocation with preemption
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Hard deadline queueing system with application to unified messaging service
ACM SIGMETRICS Performance Evaluation Review - Special issue on the fifth workshop on MAthematical performance Modeling and Analysis (MAMA 2003)
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On-line scheduling in real-time environments has been studied by a number of researchers [3, 8, 6, 2, 4, 1]. If the system is not overloaded, there exist several optimal uniprocessor on-line scheduling algorithms for real-time tasks, such as Earliest-Deadline-First and Least- Laxity. First. However, it has been proven that there are no optimal multi-processor on-line scheduling algorithms for real-time tasks [3]. On the other hand, if overload is allowed, no optimal on-line scheduling algorithms exist, even for uniprocessors. Many researchers have turned to approximation algorithms [3, 8, 6, 2]. Therefore, it is important to study the behavior of approximation algorithms. A good on-line scheduling algorithm should have both good average performance and good worst case performance. If we know the performance range of an on-line scheduling algorithm, it will greatly help in designing predictable real-time systems. In this paper, we study the performance bounds for both uniprocessor and multiprocessor on-line scheduling. Specifically, we consider tasks with different values to the system and consider the perfor- mance bound to be the ratio of the value obtained by an on-line scheduling algorithm and the value obtained by an ideal optimal off-line "clairvoyant" algorithm. If all tasks have the same value density, i.e. the value per unit computation time, we show that the tight upper bound of the uniprocessor on-line scheduling problem is 1/4. More generally, if tasks have different value densities and the ratio between the high- est and the lowest value density is , we show that the upprboundfortheuniprocessoron - lineschedulingproblemis1/(+1+2).T woon-lineschedulingalgorithms, T D1andT D/, arepresented, whichcanreachthetwoupperbounds, respectively.T hegeneralizationfrom; lineschedulingisalsoconsidered.W efoundthattheupperboundforthedual-processoron-lineschedulingproblemis1/2ifalltaskshavethesamevaluedensity.Ingeneral, theupperb; processoron-lineschedulingproblemis1/2whenkisanevennumberand(1/2-1/(4k))whenkisanoddnumberunderthesameassumptions.