Parallel machine scheduling with flexible resources

Parallel machine flexible resource scheduling (PMFRS) problems consider an additional flexible resource (e.g. operators), which can be freely allocated to any jobs and/or any machines and may speed-up the process in proportion to its amount. If job–machine assignment is unspecified, the problem is referred to as unspecified PMFRS (UPMFRS). This paper reviews the mathematical models of both PMFRS and UPMFRS problems in the literature and not only gives some extensions to the model of dynamic PMFRS problem but also presents integer programming (IP) models for static and dynamic UPMFRS problems with the objective of minimizing makespan. To solve large-sized dynamic PMFRS and UPMFRS problems, a relaxed IP based constraint programming (CP) approach is also proposed. All IP models and the proposed IP/CP approach are tested with an extensive computational study. The results of the computational experiments are discussed with respect to the major parameters of the problem and conclusions are drawn.     

Parallel machine match-up scheduling with manufacturing cost considerations

Many scheduling problems in practice involve rescheduling of disrupted schedules. In this study, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules considering the manufacturing cost implications in response to disruptions. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain manufacturing cost, which is a convex function of the compression on the processing time. In rescheduling it is highly desirable to catch up the original schedule as soon as possible by reassigning the jobs to the machines and compressing their processing times. On the other hand, one must also keep the manufacturing cost due to compression of the jobs low. Thus, one is faced with a tradeoff between match-up time and manufacturing cost criteria. We introduce alternative match-up scheduling problems for finding schedules on the efficient frontier of this time/cost tradeoff. We employ the recent advances in conic mixed-integer programming to model these problems effectively. We further provide a fast heuristic algorithm driven by dual prices of convex subproblems for generating approximate efficient schedules.     

Parallel machine scheduling with precedence constraints and setup times

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. These problems are strongly NP-hard and it is even conjectured that no list scheduling algorithm can be defined without explicitly considering jointly scheduling and resource allocation. We propose dominance conditions based on the analysis of the problem structure and an extension to setup times of the energetic reasoning constraint propagation algorithm. An exact branch-and-bound procedure and a climbing discrepancy search (CDS) heuristic based on these components are defined. We show how the proposed dominance rules can still be valid in the CDS scheme. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases.     

Parallel machine scheduling problems using memetic algorithms

In this paper, we investigate how to apply the hybrid genetic algorithms (the memetic algorithms) to solve the parallel machine scheduling problem. There are two essential issues to be dealt with for all kinds of parallel machine scheduling problems: job partition among machines and job sequence within each machine. The basic idea of the proposed method is that (a) use the genetic algorithms to evolve the job partition and then (b) apply a local optimizer to adjust the job permutation to push each chromosome climb to his local optima. Preliminary computational experiments demonstrate that the hybrid genetic algorithm outperforms the genetic algorithms and the conventional heuristics.     

Scheduling with multiple servers

In this paper, we consider the problem of scheduling a set of jobs on a set of identical parallel machines. Before the processing of a job can start, a setup is required which has to be performed by a given set of servers. We consider the complexity of such problems for the minimization of the makespan. For the problem with equal processing times and equal setup times we give a polynomial algorithm. For the problem with unit setup times, m machines and m − 1 servers, we give a pseudopolynomial algorithm. However, the problem with fixed number of machines and servers in the case of minimizing maximum lateness is proven to be unary NP-hard. In addition, recent algorithms for some parallel machine scheduling problems with constant precessing times are generalized to the corresponding server problems for the case of constant setup times. Moreover, we perform a worst case analysis of two list scheduling algorithms for makespan minimization.     

Single machine scheduling with job delivery to multiple customers

We investigate a single machine scheduling problem with job delivery to multiple customers. In this problem, each job needs to be processed on the single machine, and then delivered by a single vehicle to its customer, where the job has a physical size representing the fraction of space it occupies on the vehicle. The vehicle delivers a shipment from the machine to a customer and has to return back to the machine for delivering the next shipment. It takes different constant time for the round trips between the machine and the different customers. The goal is to minimize the makespan, by that time all the jobs are processed and delivered to their respective customers, and the vehicle returns back to the machine. We propose a 2-approximation algorithm for the general case; when there are only two customers, we present an improved 5/3-approximation algorithm. The design and performance analysis of these two algorithms integrate several known results and techniques for the single machine scheduling problem, the bin-packing problem, and the knapsack problem.     

Parallel machine total tardiness scheduling with a new hybrid metaheuristic approach

This work proposes a hybrid metaheuristic (HMH) approach which integrates several features from tabu search (TS), simulated annealing (SA) and variable neighbourhood search (VNS) in a new configurable scheduling algorithm. In particular, either a deterministic or a random candidate list strategy can be used to generate the neighbourhood of a solution, both a tabu list mechanism and the SA probabilistic rule can be adopted to accept solutions, and the dimension of the explored neighbourhood can be dynamically modified. The considered class of scheduling problems is characterized by a set of independent jobs to be executed on a set of parallel machines with non-zero ready times and sequence dependent setups. In particular, the NP-hard generalized parallel machine total tardiness problem (GPMTP) recently defined by Bilge et al. [A tabu search algorithm for parallel machine total tardiness problem. Computers & Operations Research 2004;31:397–414], is faced. Several alternative configurations of the HMH have been tested on the same benchmark set used by Bilge et al. The results obtained highlight the appropriateness of the proposed approach.     

Parallel machine scheduling with splitting jobs by a hybrid differential evolution algorithm

The problem of parallel machine scheduling for minimizing the makespan is an open scheduling problem with extensive practical relevance. It has been proved to be non-deterministic polynomial hard. Considering a job’s batch size greater than one in the real manufacturing environment, this paper investigates into the parallel machine scheduling with splitting jobs. Differential evolution is employed as a solution approach due to its distinctive feature, and a new crossover method and a new mutation method are brought forward in the global search procedure, according to the job splitting constraint. A specific local search method is further designed to gain a better performance, based on the analytical result from the single product problem. Numerical experiments on the performance of the proposed hybrid DE on parallel machine scheduling problems with splitting jobs covering identical and unrelated machine kinds and a realistic problem are performed, and the results indicate that the algorithm is feasible and efficient.     

Multi-stage resource-aware scheduling for data centers with heterogeneous servers

This paper presents a three-stage algorithm for resource-aware scheduling of computational jobs in a large-scale heterogeneous data center. The algorithm aims to allocate job classes to machine configurations to attain an efficient mapping between job resource request profiles and machine resource capacity profiles. The first stage uses a queueing model that treats the system in an aggregated manner with pooled machines and jobs represented as a fluid flow. The latter two stages use combinatorial optimization techniques to solve a shorter-term, more accurate representation of the problem using the first-stage, long-term solution for heuristic guidance. In the second stage, jobs and machines are discretized. A linear programming model is used to obtain a solution to the discrete problem that maximizes the system capacity given a restriction on the job class and machine configuration pairings based on the solution of the first stage. The final stage is a scheduling policy that uses the solution from the second stage to guide the dispatching of arriving jobs to machines. We present experimental results of our algorithm on both Google workload trace data and generated data and show that it outperforms existing schedulers. These results illustrate the importance of considering heterogeneity of both job and machine configuration profiles in making effective scheduling decisions.     

解不同交货期并行机调度问题的并行遗传算法

为有效地解决不同交货期窗口下的非等同并行多机提前/拖后调度问题,设计了一种分段编码的混合遗传算法。此编码方式能反映工件的分配序列,并利用调度优先级规则和最好适应值规则相结合的启发式算法对其顺序进行了调整,加快了收敛速度。同时为了更好地适应调度实时性和解大规模此类问题的需要,基于遗传算法自然并行性特点的基础上,实现了主从式控制网络模式下并行混合遗传算法。计算结果表明,此算法是有效的,优于遗传算法,有着较高的并行性,并能适用于大规模不同交货期窗口下非等同并行多机提前/拖后调度问题。     

Parallel machine scheduling with fuzzy processing times using a robust genetic algorithm and simulation

This paper addresses parallel machine scheduling problems with fuzzy processing times. A robust genetic algorithm (GA) approach embedded in a simulation model is proposed to minimize the maximum completion time (makespan). The results are compared with those obtained by using the “longest processing time” rule (LPT), which is known as the most appropriate dispatching rule for such problems. This application illustrates the need for efficient and effective heuristics to solve such fuzzy parallel machine scheduling problems (FPMSPs). The proposed GA approach yields good results quickly and several times in one run. Moreover, because it is a search algorithm, it can explore alternative schedules providing the same results. Thanks to the simulation model, several robustness tests are conducted using different random number sets, and the robustness of the proposed approach is demonstrated.     

Aperiodic servers in a deadline scheduling environment

A real-time system may have tasks with soft deadlines, as well as hard deadlines. While earliest-deadline-first scheduling is effective for hard-deadline tasks, applying it to soft-deadline tasks may waste schedulable processor capacity or sacrifice average response time. Better average response time may be obtained, while still guaranteeing hard deadlines, with an aperiodic server. Three scheduling algorithms for aperiodic servers are described, and schedulability tests are derived for them. A simulation provides performance data for these three algorithms on random aperiodic tasks. The performances of the deadline aperiodic servers are compared with those of several alternatives, including background service, a deadline polling server, and rate-monotonic servers, and with estimates based on the M/M/1 queueing model. This adds to the evidence in support of deadline scheduling,versus fixed priority scheduling.     

Priority scheduling service for E-commerce web servers

Service scheduling is one of the crucial issues in E-commerce environment. E-commerce web servers often get overloaded as they have to deal with a large number of customers’ requests—for example, browse, search, and pay, in order to make purchases or to get product information from E-commerce web sites. In this paper, we propose a new approach in order to effectively handle high traffic load and to improve web server’s performance. Our solution is to exploit networking techniques and to classify customers’ requests into different classes such that some requests are prioritised over others. We contend that such classification is financially beneficial to E-commerce services as in these services some requests are more valuable than others. For instance, the processing of “browse” request should get less priority than “payment” request as the latter is considered to be more valuable to the service provider. Our approach analyses the arrival process of distinct requests and employs a priority scheduling service at the network nodes that gives preferential treatment to high priority requests. The proposed approach is tested through various experiments which show significant decrease in the response time of high priority requests. This also reduces the probability of dropping high priority requests by a web server and thus enabling service providers to generate more revenue.     

Caching and scheduling in NAD-based multimedia servers

Multimedia-on-demand (MOD) applications have grown dramatically in popularity, especially in the domains of education, business, and entertainment. Current MOD servers waste precious resources in performing store-and-forward copying. This excessive overhead increases cost and severely limits the scalability of these servers. In this paper, we propose using the network-attached disk (NAD) architecture to design highly scalable and cost-effective MOD servers. In order to ensure enhanced performance, we propose a scheme, called distributed interval caching (DIG), which utilizes the on-disk buffers for caching intervals between successive streams. We also propose another scheme, called multiobjective scheduling (MOS), which increases the degrees of resource sharing by scheduling the waiting requests for service intelligently. We then integrate the two schemes and study the overall performance benefits through extensive simulation. The results demonstrate that the integrated policy works very well in increasing the number of customers that can be serviced concurrently while decreasing their waiting times for service. The performance benefits vary with several architectural, system workload, and scheduling parameters. We conclude this study by developing an analytical model for ideal DIG in order to estimate the performance limits which may be achieved through various optimizations.     

A buffer-inventory-based dynamic scheduling algorithm for multimedia-on-demand servers

We present a producer-consumer model of multimedia-on-demand (MOD) servers. The producer retrieves media data from a disk and places it into a set of buffers, while the consumer sends out the data in the buffers to the users. We develop for the producer a buffer-inventory-based dynamic scheduling (BIDS) algorithm that guarantees non-zero inventory and non-overflow of data in the buffers to meet the continuity requirement and no-loss of data for each media stream. The algorithm can deal with heterogeneous me dia streams as well as the transient circumstances upon service completions and arrivals of new requests. To smooth out the impact of bursty data of variable-bit-rate media streams and therefore increase the maximum admissible load of requests, we also introduce into the scheduling scheme a time-scale-dependent peak consumption rate and a virtual cycle time. Based on BIDS, an effective admission control mechanism can be easily established by checking two simple conditions respectively on the overall system load and buffer size. Our algorithm is very easy to implement. Experiments carried out with an actual disk system and real video stream data verify that it is more robust compared to static scheduling algorithms previously proposed in the literature, especially when handling variable-bit-rate media streams.     

Approximate analysis of multiqueue systems with multiple cyclic servers

In this paper we consider an approximate model of a system of multiple queues served cyclically by a number of identical servers, which is an extension of the Kuehn model for the single server multiqueueing system. The arrival process of customers is Poissonian, walking and service times are general, servers work in the repeated mode, and they serve at most one customer per visit at a queue (node) in a cycle. Applications in the performance evaluation of the existent network of processors of the Brazilian switching system TRÓPICO are considered. The approximation is validated by means of computer simulations.     

Maximum entropy two-station cyclic queues with multiple general servers

Summary The efficient implementation and extension of various approximate methods for general queueing networks require the study of two-station cyclic queues. In this paper maximum entropy formalism is used to analyse two-station cyclic queues with multiple general servers and a fixed number of jobs. New robust one step recursions for the queue length distribution are derived and asymptotic connections to infinite capacity queues are established. Links with Birth-Death and global balance solutions are determined and extensions to load dependent servers with Bernoulli feedback are presented. Numerical examples provide useful information on how critically system behaviour is affected by the distributional form of service times and simple bounds for typical performance measures such as throughout and mean queue length are defined. Moreover, the utility of the work as a building block for the approximate analysis of a general central server model is demonstrated.Some of the material included in this paper has been orally presented to the International Workshop on Computer Performance Evaluation, 28–30 April 1986, Sophia-Antipolis (INRIA), France [1]This work is jointly supported by Science and Engineering Research Council (SERC), UK and Metron Technology Ltd., UK, under grants GR/D/12422 and GR/AA/772, respectively     

Proxy-assisted periodic broadcast for video streaming with multiple servers

Large scale video streaming over the Internet requires a large amount of resources such as server I/O bandwidth and network bandwidth. A number of video delivery techniques can be used to lower these requirements. Periodic broadcast by a central server combined with proxy caching offers a significant reduction of the aggregate network and server I/O bandwidth usage. However, the resources available to a single server are still limited. In this paper we propose a system with multiple geographically distributed servers. The problem of multiple servers for periodic broadcast is quite different from the problem of object location for multiple web servers. Multiple servers offer increased amount of resources and service availability and may potentially allow a further reduction of network bandwidth usage. On the other hand, the benefit of periodic broadcast mostly comes from high demand videos. With multiple servers holding a video, the demand of the video at each server is reduced. Therefore, it is a challenge to use multiple servers efficiently. We first analyze the dependence of the resource requirements on the number and locations of the servers. Based on the character of the function describing such a dependence, we formulate and solve the problem of video location and delivery, in a way that minimizes resource usage. We explore a trade-off between network and I/O bandwidth requirements. We evaluate our proposed solutions through a number of tests.

Parallel failure recovery techniques in cluster-based media servers

For large-scale video-on-demand (VOD) service, cluster servers are highlighted due to their high performance and low cost. A cluster server consists of a front-end node and multiple backend nodes. Though the increase in backend nodes provides more quality of service (QoS) streams, the possibility of backend node failure is proportionally increased. The failure causes not only the cessation of streaming services but also the loss of current playing positions. In this paper, when a backend node fails, recovery mechanisms are studied to support the streaming service continuously. Without considering the characteristics of cluster-based servers and MPEG media, the basic redundant array of independent disks (RAID) techniques cause a network bottleneck in the internal network path and demonstrate inefficient CPU usage in backend nodes. To address these problems, a new failure recovery mechanism is proposed based on the pipeline computing concept. The proposed method not only distributes the internal network traffic generated from the recovery operations but also utilizes the CPU time available in the backend nodes. In the experiments, even if a backend node fails, the proposed method provides continuous streaming media services within a short MTTR value as well as more QoS streams than the existing method.