Arbitrary Release Times Research Articles

Provably Efficient Online Nonclairvoyant Adaptive Scheduling

Multiprocessor scheduling in a shared multiprogramming environment can be structured in two levels, where a kernel-level job scheduler allots processors to jobs and a user-level thread scheduler maps the ready threads of a job onto the allotted processors. We present two provably-efficient two-level scheduling schemes called G-RAD and S-RAD respectively. Both schemes use the same job scheduler RAD for the processor allotments that ensures fair allocation under all levels of workload. In G-RAD, RAD is combined with a greedy thread scheduler suitable for centralized scheduling; in S-RAD, RAD is combined with a work-stealing thread scheduler more suitable for distributed settings. Both G-RAD and S-RAD are non-clairvoyant. Moreover, they provide effective control over the scheduling overhead and ensure efficient utilization of processors. We also analyze the competitiveness of both G-RAD and S-RAD with respect to an optimal clairvoyant scheduler. In terms of makespan, both schemes can achieve O(1)-competitiveness for any set of jobs with arbitrary release time. In terms of mean response time, both schemes are O(1)-competitive for arbitrary batched jobs. To the best of our knowledge, G-RAD and S-RAD are the first non-clairvoyant scheduling algorithms that guarantee provable efficiency, fairness and minimal overhead.

Online bin packing with arbitrary release times

We study a new variant of the online bin-packing problem, in which each item a i is associated with a size a i and also a release time r i so that it must be placed at least r i above the bottom of a bin. Items arrive in turn and must be assigned without any knowledge of subsequent items. The goal is to pack all items into unit-size bins using the minimum number of bins. We study the problem with all items have equal size. First, we show that the ANY FIT algorithm cannot be approximated within any constant. Then we present a best possible online algorithm with asymptotic competitive ratio of two.

List scheduling for jobs with arbitrary release times and similar lengths

This paper considers the problem of on-line scheduling a list of independent jobs in which each job has an arbitrary release time and length in [1,r] with r?1 on m parallel identical machines. For the list scheduling algorithm, we give an upper bound of the competitive ratio for any m?1 and show that the upper bound is tight when m=1. When m=2, we present a tight bound for r?4. For r<4, we give a lower bound and show that 2 provides an upper bound.

Improved algorithm for a generalized on-line scheduling problem on identical machines

This paper considers the problem of on-line scheduling a list of independent jobs in which each job has an arbitrary release time on m parallel identical machines. In this problem, jobs arrive in form of order before its release time and decisions have to be made whenever an order is placed and the orders arrive according to any sequence. A heuristic algorithm, NMLS, better than MLS is given for any m ⩾ 2. The competitive ratio is improved from 2.93920 to 2.78436.

On-line Scheduling for Jobs with Arbitrary Release Times

This paper considers the problem of on-line scheduling a list of independent jobs in which each job has an arbitrary release time on m parallel identical machines. A tight bound is given for List Scheduling(LS) algorithm and a better algorithm is given for m≥2.

Scheduling divisible loads on heterogeneous linear daisy chain networks with arbitrary processor release times

The problem of distributing and processing a divisible load in a heterogeneous linear network of processors with arbitrary processors release times is considered. A divisible load is very large in size and has computationally intensive CPU requirements. Further, it has the property that the load can be partitioned arbitrarily into any number of portions and can be scheduled onto processors independently for computation. The load is assumed to arrive at one of the farthest end processors, referred to as boundary processors, for processing. The processors in the network are assumed to have nonzero release times, i.e., the time instants from which the processors are available for processing the divisible load. Our objective is to design a load distribution strategy by taking into account the release times of the processors in such a way that the entire processing time of the load is a minimum. We consider two generic cases in which all processors have identical release times and when all processors have arbitrary release times. We adopt both the single and multiinstallment strategies proposed in the divisible load scheduling literature in our design of load distribution strategies, wherever necessary, to achieve a minimum processing time. Finally, when optimal strategies cannot be realized, we propose two heuristic strategies, one for the identical case, and the other for nonidentical release times case, respectively. Several conditions are derived to determine whether or not optimal load distribution exists and illustrative examples are provided for the ease of understanding.

Experimental Analysis of Timing Validation Methods for Distributed Real-Time Systems

Scheduling jobs dynamically on processors is likely to achieve better performance in multiprocessor and distributed real-time systems. Exhaustive methods for determining whether all jobs complete by their deadlines, in systems that use modern priority-driven scheduling strategies, are often infeasible or unreliable since the execution time of each job may vary. We previously published research results on finding worst-case bounds and efficient algorithms for validating systems in which independent jobs have arbitrary release times and deadlines, and are scheduled on processors dynamically in a priority-driven manner. An efficient method has been proposed to determine how late the completion times of jobs can be in dynamic systems where the jobs are preemptable and nonmigratable. This paper further presents the performance characteristics of the proposed methods, and shows its soundness by providing extensive simulation results. The worst-case completion times of jobs obtained with the proposed methods are compared with the values by simulations under different workload characteristics. The simulation results show that the proposed algorithm performs considerably well for diverse workloads. Considering the previous work showed the unlikelihood of finding tighter bounds than the one given in the paper, the simulation results indicate that the proposed methods effectively constitute a theoretical basis needed for a comprehensive validation strategy that is capable of dealing with dynamic distributed real-time systems.

The complexity of scheduling starting time dependent tasks with release times

We consider a family of problems of scheduling a set of starting time dependent tasks with release times and linearly increasing/decreasing processing rates on a single machine to minimize the makespan. We first present an equivalence relationship between several pairs of problems. Based on this relationship, we show that the makespan problem with arbitrary release times and identical increasing processing rates is strongly NP-complete and the corresponding case with only one non-zero release time is at least NP-complete in the ordinary sense. On the other hand, the makespan problem with arbitrary release times and identical decreasing processing rates is solvable in O( n 6 log n) time by a dynamic programming algorithm. Using a different approach, we also show that, when the normal processing times are identical, the makespan problem with arbitrary release times and increasing/decreasing processing rates is strongly NP-complete and the corresponding case with only one non-zero release time is at least NP-complete in the ordinary sense.

Bounding completion times of jobs with arbitrary release times, variable execution times and resource sharing

The workload of many real time systems can be characterized as a set of preemptable jobs with linear precedence constraints. Typically their execution times are only known to lie within a range of values. In addition, jobs share resources and access to the resources must be synchronized to ensure the integrity of the system. The paper is concerned with the schedulability of such jobs when scheduled on a priority driven basis. It describes three algorithms for computing upper bounds on the completion times of jobs that have arbitrary release times and priorities. The first two are simple but do not yield sufficiently tight bounds, while the last one yields the tightest bounds but has the greatest complexity.

Predictable distributed dynamic scheduling in RTDOS

Future dynamic distributed hard real-time systems may control unpredictable environments, and will need predictable and flexible runtime systems that can handle unknown and changing task populations. In this extreme case not only is task scheduling dynamic, but the system topology and architecture might be adapted to unforeseen configurations. The paper addresses the difficult problem of dynamic distributed task scheduling. A new predictable dynamic deadline guarantee scheme has been designed and implemented in the authors' real-time distributed operating system (RTDOS). The algorithms have been proven to guarantee task deadlines even during transient overloads. RTDOS is designed to tackle unpredictable and highly dynamic environments; therefore its task model is quite unrestrictive, supporting periodic and aperiodic tasks both with arbitrary release times and deadlines. The authors place no restriction on the inter-arrival times between successive aperiodic task instances. Moreover, their resource scheduling considers precedence constraints, device allocation and communication requirements. As a consequence, the results can be generalised and applied to many real-time domains. Furthermore, the complexity of the authors' schedulability test has been proved to be O(n). A domain-wide scheduler is described, which maintains its predicted maximum response time even when local nodes are under heavy load. Experimental results confirm the proven expectations of our scheduling scheme.

An NC Algorithm for Scheduling Unit-Time Jobs with Arbitrary Release Times and Deadlines

The problem of scheduling $n$ unit-time jobs with real-valued release times and deadlines is shown to be in NC. The solution is based on characterizations of a canonical schedule and best subset of jobs to be scheduled in a given time interval. The algorithm runs on a CREW PRAM in $O((\log n)^2)$ time and uses $O(n^4/ \log n)$ processors.

Multiprocessor Scheduling of Unit-Time Jobs with Arbitrary Release Times and Deadlines

We present a polynomial time algorithm for constructing an optimal schedule, if a feasible schedule exists, for tthe following multimachine scheduling problem. There are n unit-time jobs, with arbitrary release times and deadlines, and m identical parallel machines. A feasible schedule is one in which no job is started before it is released, each job is completed by its deadline, and no job is interrupted once it begins to run.

Scheduling Unit–Time Tasks with Arbitrary Release Times and Deadlines

The basic problem considered is that of scheduling n unit-time tasks, with arbitrary release times and deadlines, so as to minimize the maximum task completion time. Previous work has shown that this problem can be solved rather easily when all release times are integers. We are concerned with the general case in which noninteger release times are allowed, a generalization that considerably increases the difficulty of the problem even for only a single processor. Our results are for the one-processor case, where we provide an $O(n\log n)$ algorithm based on the concept of “forbidden regions”.