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Proportionate progress: A notion of fairness in resource allocation
 Algorithmica
, 1996
"... Given a set of n tasks and m resources, where each task x has a rational weight x:w = x:e=x:p; 0 < x:w < 1, a periodic schedule is one that allocates a resource to a task x for exactly x:e time units in each interval [x:p k; x:p (k + 1)) for all k 2 N. We de ne a notion of proportionate progress, ca ..."
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Cited by 242 (25 self)
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Given a set of n tasks and m resources, where each task x has a rational weight x:w = x:e=x:p; 0 < x:w < 1, a periodic schedule is one that allocates a resource to a task x for exactly x:e time units in each interval [x:p k; x:p (k + 1)) for all k 2 N. We de ne a notion of proportionate progress, called Pfairness, and use it to design an e cient algorithm which solves the periodic scheduling problem. Keywords: Euclid's algorithm, fairness, network ow, periodic scheduling, resource allocation.
Algorithms and Complexity Concerning the Preemptive Scheduling of Periodic, RealTime Tasks on One Processor
 RealTime Systems
, 1990
"... We investigate the preemptive scheduling of periodic, realtime task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the pape ..."
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Cited by 179 (13 self)
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We investigate the preemptive scheduling of periodic, realtime task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the paper, that all parameters are indeed integers. We then give as our main lemma both necessary and sufficient conditions for a task system to be feasible on one processor. Although these conditions cannot, in general, be tested efficiently (unless P = NP), they do allow us to give efficient algorithms for deciding feasibility on one processor for certain types of periodic task systems. For example, we give a pseudopolynomial time algorithm for synchronous systems whose densities are bounded by a fixed constant less than 1. This algorithm represents an exponential improvement over the previous best algorithm. We also give a polynomialtime algorithm for systems having a fixed number of distinct typ...
Optimal TimeCritical Scheduling Via Resource Augmentation
, 1997
"... We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worstcase analysis, no good online a ..."
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Cited by 131 (4 self)
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We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worstcase analysis, no good online algorithms exist for these problems, and for some variants no good offline algorithms exist unless P = NP. We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the online algorithm is allowed more resources than the optimal offline algorithm to which it is compared. Using this approach, we establish that several wellknown online algorithms, that have poor performance from an absolute worstcase perspective, are optimal for the problems in question when allowed moderately more resources. For the optimization of average flow time, these are the first results of any sort, for any NPhard version of the problem, that indicate that...
SkipOver: Algorithms and Complexity for Overloaded Systems that Allow Skips
 In Proceedings of the 16th IEEE RealTime Systems Symposium
, 1996
"... In applications ranging from video reception to telecommunications and packet communication to aircraft control, tasks enter periodically and have fixed response time constraints, but missing a deadline is acceptable, provided most deadlines are met. We call such tasks "occasionally skippable". We l ..."
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Cited by 96 (0 self)
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In applications ranging from video reception to telecommunications and packet communication to aircraft control, tasks enter periodically and have fixed response time constraints, but missing a deadline is acceptable, provided most deadlines are met. We call such tasks "occasionally skippable". We look at the problem of uniprocessor scheduling of occasionally skippable periodic tasks in an environment having periodic tasks. We show that making optimal use of skips is NPhard. We then look at two algorithms called SkipOver Algorithms (one a variant of earliest deadline first and one of rate monotonic scheduling) that exploit skips. We give schedulability bounds for both. 1 Introduction 1.1 Basic Assumptions and Definitions We consider a uniprocessor system in which preemption is possible at any time and costs nothing. All tasks are periodic but they may enter the system at any time. A task is characterized by its computation requirements and period; the deadline of a task equals it...
Optimal Priority Assignment And Feasibility Of Static Priority Tasks With Arbitrary Start Times
, 1991
"... Within the hard realtime community, static priority preemptive scheduling is receiving increased attention. Current optimal priority assignment schemes require that at some point in the system lifetime all tasks must be released simultaneously. Two main optimal priority assignment schemes have bee ..."
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Cited by 94 (2 self)
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Within the hard realtime community, static priority preemptive scheduling is receiving increased attention. Current optimal priority assignment schemes require that at some point in the system lifetime all tasks must be released simultaneously. Two main optimal priority assignment schemes have been proposed: ratemonotonic, where task period equals deadline, and deadlinemonotonic where task deadline maybe less than period. When tasks are permitted to have arbitrary start times, a common release time between all tasks in a task set may not occur. In this eventuality, both ratemonotonic and deadlinemonotonic priority assignments cease to be optimal. This paper presents an method of determining if the tasks with arbitrary release times will ever share a common release time. This has complexity O(m log e m) in the longest task period. Also, an optimal priority assignment method is given, of complexity O(n 2 + n) in the number of tasks. Finally, an efficient feasibility test is presen...
PriorityDriven Scheduling of Periodic Task Systems on Multiprocessors
, 2001
"... The scheduling of systems of periodic tasks upon multiprocessor platforms is considered. ..."
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Cited by 91 (15 self)
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The scheduling of systems of periodic tasks upon multiprocessor platforms is considered.
A categorization of realtime multiprocessor scheduling problems and algorithms
 HANDBOOK ON SCHEDULING ALGORITHMS, METHODS, AND MODELS
, 2004
"... ..."
Feasibility Problems for Recurring Tasks on One Processor
, 1992
"... We give a comprehensive summary of our recent research on the feasibility problems for various types of hardrealtime preemptive task systems on one processor. We include results on periodic, sporadic, and hybrid task systems. While many of the results herein have appeared elsewhere, this is the fi ..."
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Cited by 39 (6 self)
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We give a comprehensive summary of our recent research on the feasibility problems for various types of hardrealtime preemptive task systems on one processor. We include results on periodic, sporadic, and hybrid task systems. While many of the results herein have appeared elsewhere, this is the first paper presenting a holistic view of the entire problem.
FixedPriority Preemptive Multiprocessor Scheduling: To Partition or not to Partition
, 2000
"... Traditional multiprocessor realtime scheduling partitions a task set and applies uniprocessor scheduling on each processor. For architectures where the penalty of migration is low, such as uniformmemory access sharedmemory multiprocessors, the nonpartitioned method becomes a viable alternative. ..."
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Cited by 37 (2 self)
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Traditional multiprocessor realtime scheduling partitions a task set and applies uniprocessor scheduling on each processor. For architectures where the penalty of migration is low, such as uniformmemory access sharedmemory multiprocessors, the nonpartitioned method becomes a viable alternative. By allowing a task to resume on another processor than the task was preempted on, some task sets can be scheduled where the partitioned method fails. We address fixedpriority scheduling of periodically arriving tasks on Ñ equally powerful processors having a nonpartitioned ready queue. We propose a new priorityassignment scheme for the nonpartitioned method. Using an extensive simulation study, we show that the priorityassignment scheme has equivalent performance to the best existing partitioning algorithms, and outperforms existing fixedpriority assignment schemes for the nonpartitioned method. We also propose a dispatcher for the nonpartitioned method which reduces the number of preemptions to levels below the best partitioning schemes.
Some Insights on FixedPriority Preemptive NonPartitioned Multiprocessor Scheduling
"... Fixedpriority preemptive scheduling of independent periodic tasks on a homogeneous multiprocessor is solved using one of two different methods based on how tasks are assigned to the processors at runtime. In the partitioned method, ..."
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Cited by 20 (2 self)
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Fixedpriority preemptive scheduling of independent periodic tasks on a homogeneous multiprocessor is solved using one of two different methods based on how tasks are assigned to the processors at runtime. In the partitioned method,