Job Sizes Research Articles

Optimal Multiserver Scheduling with Unknown Job Sizes in Heavy Traffic

We consider scheduling to minimize mean response time of the M/G/k queue with unknown job sizes. In the singleserver k = 1 case, the optimal policy is the Gittins policy, but it is not known whether Gittins or any other policy is optimal in the multiserver case. Exactly analyzing the M/G/k under any scheduling policy is intractable, and Gittins is a particularly complicated policy that is hard to analyze even in the single-server case.

A Self-Adaptive Differential Evolution Algorithm for Scheduling a Single Batch-Processing Machine With Arbitrary Job Sizes and Release Times.

Batch-processing machines (BPMs) can process a number of jobs at a time, which can be found in many industrial systems. This article considers a single BPM scheduling problem with unequal release times and job sizes. The goal is to assign jobs into batches without breaking the machine capacity constraint and then sort the batches to minimize the makespan. A self-adaptive differential evolution algorithm is developed for addressing the problem. In our proposed algorithm, mutation operators are adaptively chosen based on their historical performances. Also, control parameter values are adaptively determined based on their historical performances. Our proposed algorithm is compared to CPLEX, existing metaheuristics for this problem and conventional differential evolution algorithms through comprehensive experiments. The experimental results demonstrate that our proposed self-adaptive algorithm is more effective than other algorithms for this scheduling problem.

Stability and tail behavior of redundancy systems with processor sharing

We investigate the stability condition for redundancy-d systems where each of the servers follows a processor-sharing (PS) discipline. We allow for generally distributed job sizes, with possible dependence among the d replica sizes being governed by an arbitrary joint distribution. We establish that for homogeneous servers the stability condition for the associated fluid-limit model is characterized by the expectation of the minimum of d replica sizes being less than the mean interarrival time per server. In the special case of identical replicas, the stability condition is insensitive to the job size distribution given its mean, and the stability threshold is inversely proportional to the number of replicas. In the special case of i.i.d. replicas, the stability threshold decreases (increases) in the number of replicas for job size distributions that are NBU (NWU). We also discuss the extension to heterogeneous servers.For heavy-tailed job sizes we characterize the tail behavior of the response time distribution. In particular, for regularly varying job sizes with tail index −ν it is shown that the tail index of the response time equals −ν and −dν for identical and i.i.d. replicas, respectively.

Lunar cycle inspired PSO for single machine total weighted tardiness scheduling problem

In the large scale Single machine total weighted tardiness scheduling problem (SMTWTSP) is a group of not-interrelated tasks having different parameters to be executed on one machine. The problem’s objective is to identify the minimum total weighted tardiness using a newly developed variant of the particle swarm optimization (PSO) algorithm. In the past, the PSO algorithm has proved itself as an efficient swarm intelligence based strategy to solve complex combinatorial problems. Here, in this article, the lunar cycle inspired local search technique is assimilated into PSO, and the designed PSO variant is termed as lunar cycle inspired PSO (LCPSO). The performance of the designed LCPSO is tested over 25 large SMTWTSP instances of job size 1000. The reported results show that the designed LCPSO is a competitive PSO variant that can be applied to provide an effective solution for the SMTWTSP type combinatorial optimization problem.

Social participation and mortality according to company size of the longest-held job among older men in Japan: A 6-year follow-up study from the JAGES.

ObjectivesThe purpose of this study was to examine the relationship between social participation (type/pattern) and mortality according to company size of the longest‐held job among older men in Japan who have worked in the company.MethodsLongitudinal data from the Japan Gerontological Evaluation Study were used in this study. Functionally independent individuals aged 65 years and older in Japan were surveyed. Work and community organizations (local community, hobbies, and sports) were used as social participation. A Cox proportional hazards model was used to calculate mortality hazard ratios.ResultsAnalysis was carried out on 19 260 participants. A total of 2870 deaths occurred during the 6‐year follow‐up period. Those in companies with 49 or fewer employees had the highest prevalence of work participation and the lowest participation in any community organization. Regardless of company size, the mortality risk was significantly lower for participants in any social participation (eg, the hazard ratio for participation in a hobby organization among those with a company size of 49 employees or fewer was 0.74, 95% CI: 0.65‐0.85) compared to nonparticipants whose company size was 49 or fewer employees.ConclusionsIn Japan, although older men who have worked for small companies may have fewer benefits, their social participation may reduce their mortality risks. To avoid increasing health inequalities, it is necessary to create an environment in which they are more likely to participate in social activities.

Deep Learning Based Resource Availability Prediction for Local Mobile Crowd Computing

Mobile crowd computing (MCC) that utilizes public-owned (crowd’s) smart mobile devices (SMDs) collectively can give adequate computing power without any additional financial and ecological cost. However, the major challenge is to cope with the mobility (or availability) issue of SMDs. User’s unpredicted mobility makes the SMDs really unstable resources. Selecting such erratic resources for job schedule would result in frequent job offloading and, in the worst case, job loss, which would affect the overall performance and the quality of service of MCC. In a Local MCC, generally, a set of users are available for a certain period regularly. Based on this information, the chances of a user being available for a certain duration from a given point of time can be predicted. In this paper, we provide an effective model to predict the availability of the users (i.e., their SMDs) in such an MCC environment. We argue that before submitting a job to an SMD, the stability of it is to be assessed for the duration of execution of the job to be assigned. If the predicted availability period is greater than the job size, then only the job should be assigned to the SMD. An accurate prediction will minimize the unnecessary job offloading or job loss due to the early departure of the designated SMD. We propose an advanced convolutional feature extraction mechanism that is applied to LSTM and GRU-based time-series prediction models for predicting SMD availability. To collect user mobility data, we considered a research lab scenario, where real mobility traces were recorded with respect to a Wi-Fi access point. We compared the prediction performances of convolutional LSTM and GRU with the basic LSTM and GRU and ARIMA in terms of MAE, RMSE, R2, accuracy, and perplexity. In all the measurements, the proposed convolutional LSTM exhibited considerably better prediction performance.

Integrated Scheduling Problem on a Single Bounded Batch Machine with an Unavailability Constraint

We consider a scheduling problem where a set of jobs are first processed on a machine with an unavailability interval and, then, delivered to the customer directly. We focus on an integrated schedule of production and distribution such that the sum of the maximum delivery time and total delivery cost is optimized. We study two classes of processing machines in the production part. In the first class, the serial-batch machine, the processing time of a batch is the sum of the processing times of its jobs. In the second class, the parallel-batch machine, the processing time of a batch is the maximum processing time of the jobs contained in the batch. The machine has a fixed capacity, and the jobs are processed in batches under the condition that the total size of the jobs in a batch cannot exceed the machine capacity. Two patterns of job’s processing, i.e., resumable and non-resumable, are considered if it is interrupted by the unavailability interval on the machine. In the distribution part, there are sufficient vehicles with a fixed capacity to deliver the completed jobs. The total size of the completed jobs in one delivery cannot exceed the vehicle capacity. We show that these four problems are NP-hard in the strong sense in which the jobs have the same processing times and arbitrary sizes, and we propose an approximation algorithm for solving these four problems. Moreover, we show that the performance ratio of the algorithm is 2 for the serial-batch machine setting, and the error bound is 71/99 for the parallel-batch machine setting. We also evaluate the performance of the approximation algorithm by the computational results.

The Proactive Component of Organisational Behaviour and Prospects

Research designs that incorporate environmental variation are often indicated as desirable, but few procedures have been developed to do so. Efforts to implement studies of the concept of "organizational climate" provide several methods for assessing organizational behavior, environmental diversity, and provide relevant information about hypotheses about the relationship between individuals and contexts.Field research, assessments of participant perceptions, measurements of objective indicators, and experimental control of organisational variables are all techniques for studying climatic variability. By establishing stimuli, restricting response options, and rewarding and punishing behaviour, conditions can affect behaviour. 55 Descriptive organizational characteristics such as size, structure, complexity of systems, leadership style, and goal orientations deserve further study. Selected bibliography 104 titles indicate studies of how organizations function in both person and variance climate variables. This course investigates the connection between workplace deviations and employee organisational responses. We expect that men exhibit a variety of workplace behaviours that differ considerably from those of their female counterparts, based on organisational environment and workplace diversity research. Similarly, there is a strong positive correlation between organisational responses from employees and various facets of deviant conduct in the workplace. Affective phenomenology theory, agency theory, and classification of aberrant behaviour theory are all included in this study. Six hundred and ninety-six workers responded to the survey. Our theories were confirmed by the findings. First, male participants showed significantly lower productivity, interpersonal violence, political activity, and asset allocation, as compared to female participants. In particular, women were more likely than men to experience reductions in productivity, interpersonal hostility, and political disengagement. A multiple regression analysis comes next.Significantly predicts different aspects of workplace variability in employee behaviour using a system that includes response factors (supervision, organisational identity, job types, job sizes, coworkers, physical working conditions, and financial rewards). Although the value has long been seen as positive, it has only recently come to dominate theory development, research, and implementation in the psychology and behaviour fields. This study looks at a few representative positive traits, including the Big Five personality, core self-evaluations, traits, and virtues, as well as positive systems (derived from positive organisational scholarship), efficacy, optimism, hope, and resilience, as well as psychological capital. It also looks at positive behaviours (organizational citizenship and bold policy action). The majority of research on organisational behaviour is done at the level of individual theory, measurement, and analysis. Group level and relative mixed level theories constitute only a small portion of these levels, although organisational behaviour as a field is frequently thought to involve individual, group, and organisational level occurrences. Because organisational citizenship behaviour (OCB) is taken into account at many levels, OCB research is complicated.

Achievable Stability in Redundancy Systems

We consider a system with N~parallel servers where incoming jobs are immediately replicated to, say, d~servers. Each of the N servers has its own queue and follows a FCFS discipline. As soon as the first job replica is completed, the remaining replicas are abandoned. We investigate the achievable stability region for a quite general workload model with different job types and heterogeneous servers, reflecting job-server affinity relations which may arise from data locality issues and soft compatibility constraints. Under the assumption that job types are known beforehand we show for New-Better-than-Used (NBU) distributed speed variations that no replication $(d=1)$ gives a strictly larger stability region than replication $(d>1)$. Strikingly, this does not depend on the underlying distribution of the intrinsic job sizes, but observing the job types is essential for this statement to hold. In case of non-observable job types we show that for New-Worse-than-Used (NWU) distributed speed variations full replication ($d=N$) gives a larger stability region than no replication $(d=1)$.

Efficient Online Scheduling for Coflow-Aware Machine Learning Clusters

Distributed machine learning (DML) is an increasingly important workload. In a DML job, each communication phase can comprise a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coflow</i> , and there are dependencies among its coflows. Thus, efficient coflow scheduling becomes critical for DML jobs. However, the majority of existing solutions focus on scheduling single-stage coflows with no dependencies. While there are a few studies schedule dependent coflows of multi-stage jobs, they suffer from either practical or theoretical issues. Motivated by this situation, we study how to schedule dependent coflows of multiple DML jobs to minimize the total JCT in a shared cluster. We present a formal mathematical formulation for this problem and prove its NP-hardness. To solve this problem without job size information, we present an online coflow-aware optimization framework called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Parrot</i> . The core idea in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Parrot</i> is to infer the job with the shortest remaining processing time (SRPT) each time and dynamically control the inferred job's bandwidth based on how confident it is an SRPT job while being mindful of not starving any other job. Specifically, in the design of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Parrot</i> , we present a least per-coflow attained service (LPCAS) policy to infer the SRPT job. We further propose a dynamic job weight assignment mechanism and a linear program (LP) based weighted bandwidth scaling strategy for sharing bandwidth among DML jobs. We have proved that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Parrot</i> algorithm has a non-trivial competitive ratio. The results from large-scale trace-driven simulations further demonstrate that our <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Parrot</i> can reduce the total JCT by up to 58.4 percent, compared to the state-of-the-art Aalo solution.

Optimal Multiserver Scheduling with Unknown Job Sizes in Heavy Traffic

We consider scheduling to minimize mean response time of the M/G/k queue with unknown job sizes. In the singleserver k = 1 case, the optimal policy is the Gittins policy, but it is not known whether Gittins or any other policy is optimal in the multiserver case. Exactly analyzing the M/G/k under any scheduling policy is intractable, and Gittins is a particularly complicated policy that is hard to analyze even in the single-server case. In this work we introduce monotonic Gittins (M-Gittins), a new variation of the Gittins policy, and show that it minimizes mean response time in the heavy-traffic M/G/k for a wide class of finite-variance job size distributions. We also show that the monotonic shortest expected remaining processing time (M-SERPT) policy, which is simpler than M-Gittins, is a 2-approximation for mean response time in the heavy traffic M/G/k under similar conditions. These results constitute the most general optimality results to date for the M/G/k with unknown job sizes. Our techniques build upon work by Grosof et al. [6], who study simple policies, such as SRPT, in the M/G/k; Bansal et al. [2], Kamphorst and Zwart [7], and Lin et al. [9], who analyze mean response time scaling of simple policies in the heavy-traffic M/G/1; and Aalto et al. [1] and Scully et al. [11, 13], who characterize and analyze the Gittins policy in the M/G/1.

Energy Consumption by Servers under Unknown Service Demand

We evaluate energy consumption under unknown service demands using three policies: task assignment based on guessing size (TAGS), the shortest queue strategy and random allocation in a homogeneous environment. We modelled these policies using performance evaluation processing algebra (PEPA) to derive numerical solutions. Our results show that servers running under TAGS consumes more energy than other policies in terms of total energy consumption. In contrast, TAGS consumes less energy than random allocation in terms of energy per job when the arrival rate is high and the job size is variable.

Optimal multiserver scheduling with unknown job sizes in heavy traffic

We consider scheduling to minimize mean response time of the M/G/k queue with unknown job sizes. In the single-server k=1 case, the optimal policy is the Gittins policy, but it is not known whether Gittins or any other policy is optimal in the multiserver case. Exactly analyzing the M/G/k under any scheduling policy is intractable, and Gittins is a particularly complicated policy that is hard to analyze even in the single-server case.In this work we introduce monotonic Gittins (M-Gittins), a new variation of the Gittins policy, and show that it minimizes mean response time in the heavy-traffic M/G/k for a wide class of finite-variance job size distributions. We also show that the monotonic shortest expected remaining processing time (M-SERPT) policy, which is simpler than M-Gittins, is a 2-approximation for mean response time in the heavy traffic M/G/k under similar conditions. These results constitute the most general optimality results to date for the M/G/k with unknown job sizes. Our techniques build upon work by Grosof et al. (2018), who study simple policies, such as SRPT, in the M/G/k; Bansal et al. (2018), Kamphorst and Zwart (2020), and Lin et al. (2010), who analyze mean response time scaling of simple policies in the heavy-traffic M/G/1; and Aalto et al. (2009,2011) and Scully et al. (2018,2020), who characterize and analyze the Gittins policy in the M/G/1.

A Two-Stage Three-Machine Flow Shop Assembly Problem Mixed with a Controllable Number and Sum-of-Processing Times-Based Learning Effect by Simulated Annealing Algorithms

The two-stage assembly scheduling problem is widely used in industrial and service industries. This study focuses on the two-stage three-machine flow shop assembly problem mixed with a controllable number and sum-of-processing times-based learning effect, in which the job processing time is considered to be a function of the control of the truncation parameters and learning based on the sum of the processing time. However, the truncation function is very limited in the two-stage flow shop assembly scheduling settings. Thus, this study explores a two-stage three-machine flow shop assembly problem with truncated learning to minimize the makespan criterion. To solve the proposed model, we derive several dominance rules, lemmas, and lower bounds applied in the branch-and-bound method. On the other hand, three simulated annealing algorithms are proposed for finding approximate solutions. In both the small and large size number of job situations, the SA algorithm is better than the JS algorithm in this study. All the experimental results of the proposed algorithm are presented on small and large job sizes, respectively.

Size-based scheduling for TCP flows: Implementation and performance evaluation

In many theoretical works, the benefits of size-based scheduling disciplines have been proved. The Foreground–Background discipline (or Least Attained Service (LAS)) and the multi-level processor sharing discipline are two examples of scheduling algorithms that provide an improvement of the expected flow completion time for heavily-tailed TCP flows with respect to the widely adopted Processor Sharing (PS) discipline.In this work, we provide an implementation of the 2-level processor sharing queue (2LPS) for a Linux kernel and we measure its performance with TCP flow sizes taken from real-world datasets. 2LPS is the simplest implementation of a size-based scheduling and is parametrised with a threshold a: at each epoch, flows which received less than a service have hard priority on those that have crossed the threshold.We give a numerical procedure to solve the 2LPS queue which allows for the computation of the optimal threshold for arbitrary job size distributions (approximated arbitrary well by generalised hyper-exponential distributions) and compare the results with those obtained by other disciplines (LAS and Shortest Remaining Processing Time (SRPT)).Finally, we measure the performance of its implementation. Our findings show that the benefits of 2LPS, although slightly lower than those predicted by the theoretical model, are still significant and that using just two levels with optimal threshold seems the best trade-off between the complexity and resource demand of the implementation of a size-based scheduler and the improvements in the expected response time.

Single machine lot scheduling with non-uniform lot capacities and processing times

In this paper, we investigate the single machine lot scheduling problem in which each lot contains one or more jobs (or part of jobs). Jobs with different sizes are splittable and should be processed in consecutive lots. Any completed (part of a) job is delivered to the customer on its completion. We generalize the problem studied in Zhang et al. (Inf Process Lett 142:46–51, 2019) such that lots may have different capacities and processing times, and the sizes of jobs are unbounded. We show that for this generalized case, the WSPT (Weighted Shortest Processing Time first) rule is still optimal for both minimizing total weighted completion time and minimizing total weighted discounted completion time.

QoS-aware simulation job scheduling algorithm in virtualized cloud environment

Cloud computing is attracting an increasing number of simulation applications running in the virtualized cloud data center. These applications are submitted to the cloud in the form of simulation jobs. Meanwhile, the management and scheduling of simulation jobs are playing an essential role to offer efficient and high productivity computational service. In this paper, we design a management and scheduling service framework for simulation jobs in two-tier virtualization-based private cloud data center, named simulation execution as a service (SimEaaS). It aims at releasing users from complex simulation running settings, while guaranteeing the QoS requirements adaptively. Furthermore, a novel job scheduling algorithm named adaptive deadline-aware job size adjustment (ADaSA) algorithm is designed to realize high job responsiveness under QoS requirement for SimEaaS. ADaSA tries to make full use of the idle fragmentation resources by tuning the number of requested processes of submitted jobs in the queue adaptively, while guaranteeing that jobs’ deadline requirements are not violated. Extensive experiments with trace-driven simulation are conducted to evaluate the performance of our ADaSA. The results show that ADaSA outperforms both cloud-based job scheduling algorithm KCEASY and traditional EASY in terms of response time (up to 90%) and bounded slow down (up to 95%), while obtains approximately equivalent deadline-missed rate. ADaSA also outperforms two representative moldable scheduling algorithms in terms of deadline-missed rate (up to 60%).

Stochastic Load Balancing on Unrelated Machines

We consider the problem of makespan minimization on unrelated machines when job sizes are stochastic. The goal is to find a fixed assignment of jobs to machines, to minimize the expected value of the maximum load over all the machines. For the identical-machines special case when the size of a job is the same across all machines, a constant-factor approximation algorithm has long been known. Our main result is the first constant-factor approximation algorithm for the general case of unrelated machines. This is achieved by (i) formulating a lower bound using an exponential-size linear program that is efficiently computable and (ii) rounding this linear program while satisfying only a specific subset of the constraints that still suffice to bound the expected makespan. We also consider two generalizations. The first is the budgeted makespan minimization problem, where the goal is to minimize the expected makespan subject to scheduling a target number (or reward) of jobs. We extend our main result to obtain a constant-factor approximation algorithm for this problem. The second problem involves q-norm objectives, where we want to minimize the expected q-norm of the machine loads. Here we give an [Formula: see text]-approximation algorithm, which is a constant-factor approximation for any fixed q.

Multiple Server SRPT With Speed Scaling Is Competitive

Can the popular shortest remaining processing time (SRPT) algorithm achieve a constant competitive ratio on multiple servers when server speeds are adjustable (speed scaling) with respect to the flow time plus energy consumption metric? This question has remained open for a while, where a negative result in the absence of speed scaling is well known. The main result of this paper is to show that multi-server SRPT with speed scaling can be constant competitive, with a competitive ratio that only depends on the power-usage function of the servers, but not on the number of jobs/servers or the job sizes (unlike when speed scaling is not allowed). When all job sizes are unity, we show that round-robin routing is optimal and can achieve the same competitive ratio as the best known algorithm for the single server problem. Finally, we show that a class of greedy dispatch policies, including policies that route to the least loaded or the shortest queue, do not admit a constant competitive ratio. When job arrivals are stochastic, with Poisson arrivals and i.i.d. job sizes, we show that random routing and a simple gated-static speed scaling algorithm achieves a constant competitive ratio.

Energy-efficient scheduling of a single batch processing machine with dynamic job arrival times

Research on manufacturing scheduling has historically emphasized production efficiency. With rising environmental consciousness, manufacturing companies are paying increasing attention to energy efficiency on the shop floor. Manufacturing consumes a large amount of electricity globally. The mismatch between electric supply and demand has been a huge problem, which even becomes worse when renewable energy becomes more popular. The time-of-use (TOU) pricing policy is a widely used demand response (DR) approach, trying to align demand to supply. This paper considers energy-efficient scheduling of a single batch processing machine with non-identical job sizes and release times under a TOU electric tariff so as to simultaneously minimize total electricity cost, a criterion of environmental and energy sustainability, and makespan, a criterion of productivity. A mathematical formulation is developed to optimize electricity cost and makespan. Due to computational complexity, a hybrid multi-objective meta-heuristic algorithm is developed to find the Pareto front. Two constructive heuristics are presented to group jobs into batches. Two different approaches are presented to improve total electricity costs. The performance of the proposed model and algorithms is evaluated through extensive numerical experiments. Production managers can use the model and algorithms provided in this work to make a trade-off between productivity and sustainability.