Non-preemptive Scheduling Research Articles

Simulated annealing and imperialist competitive algorithm for minimising makespan in an open shop

This paper presents an imperialist competitive algorithm (ICA) and a simulated annealing (SA) algorithm in a non-preemptive open shop scheduling problem with job dependent setup times and sequence dependent transportation times to minimise the makespan (total completion time). The parameters of the algorithms are tuned by the response surface methodology (RSM). Based on classic approach, the scheduling problems are classified into small, medium and large sized problems. To evaluate the performance of the proposed ICA, its results are compared with the optimum ones obtained by GAMS for the small sized instances. Moreover, for the medium to large sized instances, the obtained solutions by the ICA are compared with the solutions of the effective method – SA algorithm – and the results are analysed.

The Exact Analysis of Limited Service Polling Systems Combined with Non-preemptive Priority Scheduling under Self-similar Traffic Input

The cyclic execution of several multi-typed queues through a unified server requires superlative tactics of polling strategies. Further, a number of traditional scheduling schemes have been put forward to provide assured Quality of Service (QoS) to the end-user. In the prior work, no effort has been put to combine the traditional scheduling schemes with polling mechanisms. Moreover, in the prior work, the researchers have utilized traditional Poisson distribution to analyze a variety of polling mechanisms to offer the standardized QoS to the end user. However, it has been proven through numerous studies that traffic carried by internet is self-similar and unfortunately, the traditional Poisson models are unable to capture the bursty nature of internet traffic. To overcome the limitations of prior work, in the present study, we combine the limited service polling model with traditional non-preemptive scheduling scheme in two different ways. We build an analytical framework considering multiple classes of self-similar traffic and analyze their behavior on the basis of G/M/1 queuing system. We construct the Markov chain for G/M/1 queuing system and present the closed form expressions of packet latencies for related traffic classes. Simulated experiments in C++ were performed to test our proposed analytical framework for evaluating the QoS parameters and Markov chain transformation. This study clearly indicates that the combination of traditional polling mechanism with common scheduling scheme such as priority can offer a differential treatment to facilitate the required QoS for latest 4G wireless network applications according to their requirement.

Robust Scheduling of Task Graphs under Execution Time Uncertainty

Effective multicore computing requires to make efficient usage of the computational resources on a chip. Offline mapping and scheduling can be applied to improve the performance, but classical approaches require considerable a priori knowledge of the target application. In a practical setting, precise information is often unavailable; one can then resort to approximate time and resource usage figures, but this usually requires to make conservative assumptions. The issue is further stressed if real-time guarantees must be provided. We tackle predictable and efficient nonpreemptive scheduling of multitask applications in the presence of duration uncertainty. Hard real-time guarantees are provided with limited idle time insertion, by exploiting a hybrid offline/online technique known as Precedence Constraint Posting (PCP). Our approach does not require probability distributions to be specified, relying instead on simple and cheaper-to-obtain information (bounds, average values). The method has been tested on synthetic applications/platforms and compared with an offline optimized Fixed Priority Scheduling (FPS) approach and a pure online FIFO scheduler; the results are very promising, as the PCP schedules exhibit good stability and improved average execution time (14 percent on average, up to 30 percent versus FPS and up to 40 percent versus the FIFO scheduler).

The fast algorithm for founding nonpreemptive schedule with some on-time jobs in minimal processing time.

The fast algorithm for founding nonpreemptive schedule with some on-time jobs in minimal processing time.

Research of Hybrid Scheduling Based on Network Calculus in Coal Mine Ethernet

According to the characteristics of data in coalmine industrial Ethernet ring networks and in order to guarantee the demand of the real-time data in it, a hybrid scheduling method with non-preemptive priority and EDF scheduling method based on the IEEE802.1p protocol is proposed in the switch. We calculate the maximum transmitting delay of the real-time data using network calculus theory. The result shows that EDF decreases transmission delay for non-periodic data better than FCFS by theoretical computation and simulation.

Tight approximation algorithms for scheduling with fixed jobs and nonavailability

We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, for example, in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt et al. [1999]; for scheduling with nonavailability we provide the same lower bound. We use dual approximation, creation of a gap structure, and a PTAS for the multiple subset sum problem, combined with a postprocessing step to assign large jobs.

Online scheduling with one rearrangement at the end: Revisited

In this paper, we consider an online non-preemptive scheduling problem on two related machines, with only one rearrangement at the end, called Online scheduling with one rearrangement at the end (OSORE). We proposed an improved algorithm for 1⩽s⩽2, where s is the speed ratio between the fast machine and slow machine. The upper bounds are 2(s+1)s+2 for 1⩽s⩽2 and s+2s+1 for 2<s⩽2, which are better than previous results, i.e. (s+1)2s+2 for 1⩽s⩽2 and s+1s for 2<s⩽2 (Liu et al., 2009 [7]).

Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width

We study the problems of non-preemptively scheduling and packing malleable and parallel tasks with precedence constraints to minimize the makespan. In the scheduling variant, we allow the free choice of processors; in packing, each task must be assigned to a contiguous subset. Malleable tasks can be processed on different numbers of processors with varying processing times, while parallel tasks require a fixed number of processors. For precedence constraints of bounded width, we resolve the complexity status of the problem with any number of processors and any width bound. We present an FPTAS based on Dilworth's decomposition theorem for the NP-hard problem variants, and exact efficient algorithms for all remaining special cases. For our positive results, we do not require the otherwise common monotonous penalty assumption on the processing times of malleable tasks, whereas our hardness results hold even when assuming this restriction. We complement our results by showing that these problems are all strongly NP-hard under precedence constraints which form a tree.

A Dynamic Resource Allocation Method for Parallel DataProcessing in Cloud Computing

Problem statement: One of the Cloud Services, Infrastructure as a Service (IaaS) provides a Compute resourses for demand in various applications like Parallel Data processing. The computer resources offered in the cloud are extremely dynamic and probably heterogeneous. Nephele is the first data processing framework to explicitly exploit the dynamic resource allocation offered by today’s IaaS clouds for both, task scheduling and execution. Particular tasks of processing a job can be assigned to different types of virtual machines which are automatically instantiated and terminated during the job execution. However, the current algorithms does not consider the resource overload or underutilization during the job execution. In this study, we have focussed on increasing the efficacy of the scheduling algorithm for the real time Cloud Computing services. Approach: Our Algorithm utilizes the Turnaround time Utility effieciently by differentiating it into a gain function and a loss function for a single task. The algorithm also assigns high priority for task of early completion and less priority for abortions/deadlines issues of real time tasks. Results: The algorithm has been implemented on both preemptive and Non-premptive methods. The experimental results shows that it outperfoms the existing utility based scheduling algorithms and also compare its performance with both preemptive and Non-preemptive scheduling methods. Conculsion: Hence, a novel Turnaround time utility scheduling approach which focuses on both high priority and the low priority tasks that arrives for scheduling is proposed.

On Preemptive Multi-wavelength Scheduling in Hybrid WDM/TDM Passive Optical Networks

In this paper, we investigate the wavelength scheduling problem in hybrid wavelength division multiplexing/time division multiplexing passive optical networks (WDM/TDM PONs), which can be mapped into multiprocessor scheduling problems with wavelengths and optical network unit (ONU) requests being considered as machines and jobs, respectively. To achieve high bandwidth utilization, guarantee low delay, and ensure short-term fairness, we try to construct a schedule with the minimum latest job completion time. First, we investigate the non-preemptive scheduling problem, which was shown to be NP-hard, and hence requires heuristic algorithms to approximate the optimal solution. The approximation ratio of the best heuristic algorithm is as large as 2-1/m, where m is the number of wavelengths. Motivated to achieve a smaller latest job completion time, we then investigate the preemptive scheduling problem. Preemption allows jobs to be scheduled more flexibly, and thus may yield a smaller makespan. However, with preemption, jobs may be split into subjobs and scheduled in discontinuous time durations at the expense of more guard time. We show that, with the consideration of guard time, the preemptive scheduling with the objective of minimizing the latest job completion time is NP-hard. To address the problem, we propose an approach by using linear programming with guard time supplement. It is shown that the proposed algorithm can ensure that the latest job completion time is no greater than the optimal value plus (m-1)g/m, where g is the guard time between the scheduling of two ONUs. When the network is highly loaded, the approximation ratio is around 1.00061 and 1.002056 for hybrid WDM/TDM Ethernet PON (EPON) and Gigabit-capable PON (GPON), respectively.

Shop and batch scheduling with constraints

This is a summary of the PhD thesis defended by the author in September 2011 at the Ecole des Mines de Nantes (EMNantes). The thesis was advised by Narendra Jussien (EMNantes) and co-advised by Louis-Martin Rousseau (Ecole Polytechnique de Montreal—Poly), Christelle Gueret (EMNantes) and Andre Langevin (Poly). The manuscript is written in French and can be obtained from http://tel.archives-ouvertes. fr/tel-00630122/fr/ or by email from arnaud.malapert@unice.fr. The focus of the dissertation is to study the resolution of shop and batch scheduling problems derived from real-world applications using constraint programming. The remainder of this abstract summarizes the results of the dissertation. In shop problems, n jobs, consisting each of m tasks, must be processed on m machines. The processing orders of tasks which belong to a job can vary: global order (flow shop); order per job (job shop); no order (open shop). We consider the construction of non-preemptive schedules of minimal makespan, which is NP-Hard for m ≥ 3. The study and classification of models and search algorithms show that one of the major challenge of solving optimally these problems is to provide good solutions as quick as the metaheuristics. Therefore, we introduce a new algorithm characterized by its: simplicity, most of its components are available in constraint solvers; flexibility, two constraint models offer different trade-offs among propagation strength, speed and simplicity; genericity, it is applicable to any disjunctive scheduling problem. The algorithm relies on recent constraint filtering algorithm and (randomized) branching techniques with new upper bound heuristics. The algorithm starts with a randomized constructive heuristic (without propagation) which initializes the upper bound so that the selection and propagation of initial choices are improved. During the search, the filtering is based on the disjunctive graph model and disjunctive global constraints, whereas the branching is conducted by adding precedences to the disjunctive graph with the profile strategy. Besides, randomized restart policies combined with nogood recording allow to search diversification and learning from restarts. Indeed, nogoods

Efficient approximation algorithms for the routing open shop problem

We consider the routing open shop problem being a generalization of two classical discrete optimization problems: the open shop scheduling problem and the metric traveling salesman problem. The jobs are located at nodes of some transportation network, and the machines travel on the network to execute the jobs in the open shop environment. The machines are initially located at the same node (depot) and must return to the depot after completing all the jobs. It is required to find a non-preemptive schedule with the minimum makespan. The problem is NP-hard even on the two-node network with two machines. We present new polynomial-time approximation algorithms with worst-case performance guarantees.

Algorithm for Cost Non-preemptive Scheduling of Partial k-Trees

Let G be a graph, in which each vertex (job) v has a positive integer weight (processing time) p(v) and eachedge (u,v) represented that the pair of jobs u and v cannot be processed in the same slot. In this paper we assume that every job is non-preemptive. Let C={1,2,...} be a color set. A multicoloring (scheduling) F of G is to assign each job v a set of p(v) consecutive positive integers (processing consecutive time slots) in C so that any pair of adjacent vertices receive disjoint sets. Such a multicoloring is called a non-preemptive scheduling. The cost non-preemptive scheduling problem is to find an optimal multicoloring of G.

Single-facility scheduling by logic-based Benders decomposition

Logic-based Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size scales up. We solve single-facility non-preemptive scheduling problems with time windows and long time horizons. The Benders master problem assigns jobs to predefined segments of the time horizon, where the subproblem schedules them. In one version of the problem, jobs may not overlap the segment boundaries (which represent shutdown times, such as weekends), and in another version, there is no such restriction. The objective is to find feasible solutions, minimize makespan, or minimize total tardiness.

A Note on “A Genetic Algorithm for the Preemptive and Non-Preemptive Multi-Mode Resource-Constrained Project Scheduling Problem

Peteghem et al. [1] considered resource-constrained project scheduling problem (RCPSP) with preemptive activities. However, some points should be made clear. How and when an activity is divided? How many parts an activity should be splitted? Whether the preemptive-based scenario is correctly performed to further improve the total makespan of a project? The first two questions are not very clearly presented. As for the last question, the answer is “no exactly” after careful examination..

Scheduling Hybrid WDM/TDM Passive Optical Networks With Nonzero Laser Tuning Time

Owing to the high bandwidth provisioning, hybrid wavelength division multiplexing/time division multiplexing (WDM/TDM) passive optical network (PON) is becoming an attractive future-proof access network solution. In hybrid WDM/TDM PON, tunable lasers are potential candidate light sources attributed to their multiwavelength provisioning capability and color-free property. Currently, the laser tuning time ranges from a few tens of nanoseconds to seconds, or even minutes, depending on the adopted technology. Different laser tuning time may introduce different network performance. To achieve small packet delay and ensure fairness, the schedule length for given optical network unit (ONU) requests is desired to be as short as possible. This paper illustrates contributions in four main aspects. First, we show that both preemptive and nonpreemptive scheduling problems with the objective of minimizing the schedule length are NP-hard when the laser tuning time is nonzero. Second, we present a heuristic preemptive scheduling algorithm with an approximation factor of at most 2 and a heuristic nonpreemptive scheduling algorithm with an approximation factor of at most 2-1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> is the number of wavelengths. Third, extensive simulations have been conducted, and simulation results show that our proposed algorithms, which consider laser tuning time, achieve significantly better performances as compared to algorithms that are directly derived from existing algorithms without considering laser tuning time. Fourth, since the scheduling in one cycle is related to that in the last cycle, we provide some discussions on the scheduling in multiple cycles.

Optimal algorithms for online scheduling with bounded rearrangement at the end

In this paper, we consider an online non-preemptive scheduling problem on two related machines, where at most K jobs are allowed to be rearranged, but only after all jobs have been revealed and (temporarily) scheduled. We minimize the makespan, and we call the problem as Online scheduling with bounded rearrangement at the end (BRE), which is a semi-online problem. Jobs arrive one by one over list. After all the jobs have been arrived and scheduled, we are informed that the input sequence is over; then at most K already scheduled jobs can be reassigned. With respect to the worst case ratio, we close the gap between the lower bound and upper bound, improving the previous result as well.Especially, for the lower bound, (i) for s≥2 an improved lower bound s+2s+1 is obtained, which is better than (s+1)2s2+s+1 (Liu et al. (2009) [9]); (ii) for 1+52≤s<2, an improved lower bound s2s2−s+1 is obtained, which is better than (s+1)2s2+s+1 (Liu et al. (2009) [9]). For the upper bound, (i) for s≥2 and K=1, a new upper bound s+2s+1 is obtained, which is optimal and better than the one s+1s in Liu et al. (2009) [9]; (ii) for 1+52≤s<2 and K=2, an upper bound s2s2−s+1 is proposed, which is optimal and better than the previous one s+1s in Liu et al. (2009) [9]; (iii) for s<1+52 and K=2, an upper bound (s+1)2s2+s+1 is obtained, which is also optimal and better than the previous one min{s+1s,(s+1)2s+2} in Liu et al. (2009) [9].

Comparing the minimum completion times of two longest-first scheduling-heuristics

For the basic problem of non-preemptively scheduling n independent jobs on m identical parallel machines so that the minimum (or earliest) machine completion time is maximized, we compare the performance relationship between two well-known longest-first heuristics—the LPT- (longest processing time) and the RLPT-heuristic (restricted LPT). We provide insights into the solution structure of these two sequencing heuristics and prove that the minimum completion time of the LPT-schedule is at least as long as the minimum completion time of the RLPT-schedule. Furthermore, we show that the minimum completion time of the RLPT-heuristic always remains within a factor of 1/m of the optimal minimum completion time. The paper finishes with a comprehensive experimental study of the probabilistic behavior of RLPT-schedules compared to LPT-schedules in the two-machine case.

Robust scheduling on a single machine using time buffers

This article studies the scheduling of buffer times in a single-machine environment. A buffer time is a machine idle time in between two consecutive jobs and is a common tool to protect a schedule against disruptions such as machine failures. This article introduces new classes of robust machine scheduling problems. For an arbitrary non-preemptive scheduling problem 1|β|γ, three corresponding robustness problems are obtained: (i) maximize overall (weighted) buffer time while ensuring a given schedule's performance (with regard to the objective function γ); (ii) optimize the schedule's performance (with regard to γ) while ensuring a given minimum overall (weighted) buffer time; and (iii) find the trade-off curve regarding both objectives. The relationships between the different classes of problems and the corresponding underlying problems are outlined. Furthermore, the robust counterparts of three very basic single-machine scheduling problems are analyzed.

Optimizing Distributed Real-Time Embedded System Handling Dependence and Several Strict Periodicity Constraints

This paper focuses on real-time nonpreemptive multiprocessor scheduling with precedence and strict periodicity constraints. Since this problem is NP-hard, there exist several approaches to resolve it. In addition, because of periodicity constraints our problem stands for a decision problem which consists in determining if, a solution exists or not. Therefore, the first criterion on which the proposed heuristic is evaluated is its schedulability. Then, the second criterion on which the proposed heuristic is evaluated is its execution time. Hence, we performed a schedulability analysis which leads to a necessary and sufficient schedulability condition for determining whether a task satisfies its precedence and periodicity constraints on a processor where others tasks have already been scheduled. We also present two multiperiodic applications.