Job Sizes Research Articles

Algorithm Design for an Online Berth Allocation Problem

In this paper, we investigate an online berth allocation problem, where vessels arrive one by one and their information is revealed upon arrival. Our objective is to design online algorithms to minimize the maximum load of all berths (makespan). We first demonstrate that the widely used Greedy algorithm has a very poor theoretical guarantee; specifically, the competitive ratio of the Greedy algorithm for this problem is lower bounded by Ω(log⁡m/log⁡log⁡m), which increases with the number of berths m. On account of this, we borrow an idea from algorithms for the online strip packing problem and provide a comprehensive theoretical analysis of the Revised Shelf (RS) algorithm as applied to our berth allocation problem. We prove that the competitive ratio of RS for our problem is 5, improving on the original competitive ratio of 6.66 for the online strip packing problem. Through numerical studies, we examine the RS algorithm and Greedy algorithm in an average case. The numerical simulation of competitive ratios reveals distinct advantages for different algorithms depending on job size. For smaller job sizes, the Greedy algorithm emerges as the most efficient, while for medium-sized jobs, the RS algorithm proves to be the most effective.

On the performance evaluation of distributed join-idle-queue load balancing with and without token withdrawals

Distributed Join-Idle-Queue load balancing is known to achieve vanishing waiting times in the large-scale limit provided that the number of dispatchers remains fixed, while the number of servers tends to infinity. When the number of dispatchers m scales to infinity together with the number of servers n, such that r=n/m remains fixed, the large-scale performance of Join-Idle-Queue load balancing is less clear as waiting times no longer vanish.In this paper we first discuss some existing mean field models for distributed Join-Idle-Queue load balancing with r=n/m fixed and explain why the well-known model introduced in Lu et al. (2011) is not exact in the large-scale limit. The inexactness is caused by mixing two variants of distributed Join-Idle-Queue load balancing: a variant with and one without token withdrawals. Next we introduce mean field models for Join-Idle-Queue load balancing with and without token withdrawals, where an idle server places a token at a dispatcher with the shortest among d randomly chosen dispatchers.The introduced mean field models in case of token withdrawals imply that for phase type distributed service times and a total job arrival rate of λn<n, the response time of a job corresponds to that in a standard M/PH/1 queue with load λq0. The value of q0 can be determined numerically and depends on λ,r and d, but not on the job size distribution (apart from its mean). This simple behavior is lost if token withdrawals do not take place. For the models without withdrawals we develop fast numerical algorithms to determine the performance. We present simulation experiments that suggest that the unique fixed point of the introduced mean field models provides exact results in the large-scale limit.

Strongly Tail-Optimal Scheduling in the Light-Tailed M/G/1

We study the problem of scheduling jobs in a queueing system, specifically an M/G/1 with light-tailed job sizes, to asymptotically optimize the response time tail. This means scheduling to make \mathbfP [T &gt; t], the chance a job's response time exceeds t, decay as quickly as possible in the t → ∞ limit. For some time, the best known policy was First-Come First-Served (FCFS), which has an asymptotically exponential tail: P [T &gt; t] ∼ C e -γ t . FCFS achieves the optimal decay rate ~γ, but its tail constant C is suboptimal. We derive a closed-form expression for the optimal tail constant, and we introduce γ-Boost, a new policy that achieves this optimal tail constant. We also show via simulation that γ-Boost has excellent practical performance. This abstract summarizes our full paper.

Approximations to Study the Impact of the Service Discipline in Systems with Redundancy

In this paper we develop the first methods to approximate the queue length distribution in a queueing system with redundancy under various service disciplines. We focus on a system with exponential job sizes, i.i.d. copies, and a large number of servers. In the case of Processor Sharing, we provide a pair and a triplet approximation. We also develop a pair approximation for First-Come-First-Served, Limited Processor Sharing and Last-Come-First-Served servers. We present numerical evidence that shows that all the approximations presented in the paper are highly accurate, but that none of them are asymptotically exact (as the number of servers goes to infinity).

Mixed batch scheduling with non-identical job sizes to minimize makespan

Mixed batch scheduling with non-identical job sizes to minimize makespan

Strongly Tail-Optimal Scheduling in the Light-Tailed M/G/1

We study the problem of scheduling jobs in a queueing system, specifically an M/G/1 with light-tailed job sizes, to asymptotically optimize the response time tail. This means scheduling to make \mathbfP [T &gt; t], the chance a job's response time exceeds t, decay as quickly as possible in the t \to \infty limit. For some time, the best known policy was First-Come First-Served (FCFS), which has an asymptotically exponential tail: \mathbfP [T &gt; t] \sim C e^-γ t . FCFS achieves the optimal *decay rate* γ, but its *tail constant* C is suboptimal. Only recently have policies that improve upon FCFS's tail constant been discovered. But it is unknown what the optimal tail constant is, let alone what policy might achieve it. In this paper, we derive a closed-form expression for the optimal tail constant C, and we introduce *γ-Boost*, a new policy that achieves this optimal tail constant. Roughly speaking, γ-Boost operates similarly to FCFS, but it pretends that small jobs arrive earlier than their true arrival times. This significantly reduces the response time of small jobs without unduly delaying large jobs, improving upon FCFS's tail constant by up to 50% with only moderate job size variability, with even larger improvements for higher variability. While these results are for systems with full job size information, we also introduce and analyze a version of γ-Boost that works in settings with partial job size information, showing it too achieves significant gains over FCFS. Finally, we show via simulation that γ-Boost has excellent practical performance.

Semi-Online Algorithms for the Hierarchical Extensible Bin-Packing Problem and Early Work Problem

In this paper, we consider two types of semi-online problems with hierarchies. In the extensible bin-packing problem with two hierarchical bins, one bin can pack all items, while the other bin can only pack some items. The initial size of the bin can be expanded, and the goal is to minimize the total size of the two bins. When the largest item size is given in advance, we provide some lower bounds and propose online algorithms. When the total item size is given in advance, we provide some lower bounds and propose online algorithms. In addition, we also consider the relevant early-work-maximization problem on two hierarchical machines; one machine can process any job, while the other machine can only process some jobs. Each job shares a common due date, and the goal is to maximize the total early work. When the largest job size is known, we provide some lower bounds and propose two online algorithms whose competitive ratios are close to the lower bounds.

Performance of the Gittins Policy in the G/G/1 and G/G/k, With and Without Setup Times

We consider the classic problem of preemptively scheduling jobs in a queue to minimize mean number-in-system, or equivalently mean response time. Even in single-server queueing models, this can be a nontrivial problem whose answer depends on the information available to the scheduler. The simplest case is when the scheduler knows each job's size, for which the optimal policy is Shortest Remaining Processing Time (SRPT) [9]. In the more realistic case of scheduling with unknown or partially known job sizes, people consider the Gittins policy [1-3, 12]. Roughly speaking, Gittins assigns each job a scalar rank based on an estimate of its remaining work, then serves the job of least rank.

Approximations to Study the Impact of the Service Discipline in Systems with Redundancy

As job redundancy has been recognized as an effective means to improve performance of large-scale computer systems, queueing systems with redundancy have been studied by various authors. Existing results include methods to compute the queue length distribution and response time but only when the service discipline is First-Come-First-Served (FCFS). For other service disciplines, such as Processor Sharing (PS), or Last-Come-First-Served (LCFS), only the stability conditions are known. In this paper we develop the first methods to approximate the queue length distribution in a queueing system with redundancy under various service disciplines. We focus on a system with exponential job sizes, i.i.d. copies, and a large number of servers. We first derive a mean field approximation that is independent of the scheduling policy. In order to study the impact of service discipline, we then derive refinements of this approximation to specific scheduling policies. In the case of Processor Sharing, we provide a pair and a triplet approximation. The pair approximation can be regarded as a refinement of the classic mean field approximation and takes the service discipline into account, while the triplet approximation further refines the pair approximation. We also develop a pair approximation for three other service disciplines: First-Come-First-Served, Limited Processor Sharing and Last-Come-First-Served. We present numerical evidence that shows that all the approximations presented in the paper are highly accurate, but that none of them are asymptotically exact (as the number of servers goes to infinity). This makes these approximations suitable to study the impact of the service discipline on the queue length distribution. Our results show that FCFS yields the shortest queue length, and that the differences are more substantial at higher loads.

대졸 청년층의 정부고용정책 참여 여부에 따른 노동시장 성과분석

Objectives The purpose of this study is to analyze the performance of the labor market according to whether col-lege graduates participate in government employment policies. In this study, the government's employment poli-cy is Korea’s Training Credit Programs and the Youth Job-Seeking Activity Subsidy. The labor market performance consisted of employment status, employment type, job size, wages, and job satisfaction through a review of pre-vious studies.&#x0D; Methods The population of the study is college graduates between the ages of 26 and 34. However, since there is a limit to conducting research on the entire population, this study utilized 2019GOMS among the data of the College Graduates Occupational Mobility Survey(GOMS) provided by the Korea Employment Information Service. Excluding missing values, the final targets were 948 people with the Korea’s Training Credit Programs and 964 people with Youth Job-Seeking Activity Subsidy. For data analysis, logistic regression analysis and least squares regression analysis, including propensity score matching, were conducted using the Stata 17.0 program. At this time, individual characteristic factors(gender, age), employment activity factors(linguistic training, certificate), and school characteristic factors(university type, university location, major) were dummized and put into control variables.&#x0D; Results As a result of the analysis, it was confirmed that neither policy(Korea’s Training Credit Programs, Youth Job-Seeking Activity Subsidy) had a positive effect on labor market performance according to participation.&#x0D; Conclusions Therefore, in this paper, I would like to review the results of the government's employment policy that did not have a positive effect on labor market performance, and to identify and present the causes. This is ex-pected to play an important role in future employment policy operation and research.

Performance-driven scheduling for malleable workloads

The development of adaptive scheduling algorithms that take advantage of malleability has become a crucial area of research in many large-scale projects. Malleable workloads can improve the system’s performance but, at the same time, provide an extra dimension to the scheduling problem. This paper proposes an adaptive, performance-based job scheduling method that emphasizes the backfilling concept with malleability. The proposed method performs the malleability operations only when the estimated execution time of the involved applications is better than or equal to the execution time on the allocated resources without reconfiguration. The reconfiguration feasibility is determined by performance models considering the application scalability and reconfiguration overheads. Different policies for implementing malleability are presented, each targeting a specific workload in terms of job size and scalability. The comprehensive evaluation shows an improvement in the slowdown up to 49% compared to the non-adaptive baseline scheduling algorithm.

Mathematical Models and Optimal Algorithms for Lot Scheduling Considering Job Splitting and Due Dates in Green Logistics

Lot scheduling is a promising manufacturing mode in green logistics that can efficiently save energy and reduce production costs. It has been widely applied to integrate circuit tests in semiconductor factories, textile processing in garment workshops, etc. Each processing lot is of a fixed capacity and identical processing time, and completes more than one job simultaneously. Jobs with sizes and due dates are allowed to be arbitrarily split and processed in consecutive lots. They are delivered immediately upon completion. To the best of our knowledge, in the domain of lot scheduling, there exist no mathematical programming models that describe the above features simultaneously. In this work, we focus on the single machine environment and mainly consider two lot scheduling problems with the objectives of minimizing the maximum lateness and the total tardiness, respectively. For the problems, we first propose new mixed integer linear programming models (solved by commercial solvers), which enable a systematic understanding of the studied problems and serve as a mathematical programming basis for more complicated problems. We then prove that the Earliest Due-Date (EDD) first rule and the Shortest Processing Time (SPT) first rule can optimally solve the two problems, respectively, provided that the due dates and job sizes are agreeable, i.e., a later due date indicates a larger size of job. Experimental results show the efficiency of our methods and managerial insights are drawn.

A heuristic approach to minimizing the waiting time of jobs in two-stage flow shop scheduling

The paper presents the influence of the waiting time of jobs in a 2 machine k- job Flow Shop Scheduling (FSS) problem. The main intention of the study is to find a sequence of jobs that delivers the least sum of the time of waiting for jobs. A heuristic approach has been adopted to achieve the desired objective. The experiments are conducted for more than 2000 problems of various sizes for the problems with special structures and problems with random times of processing. The weighted mean absolute error (WMAE) for the average of the sum of the waiting times of jobs is computed for both kind of problems after comparing with the optimal solutions. WMAE has been obtained less than 0.0075 for problems with special structures and less than 0.087 for problems with random times of processing. The WMAE is also reducing significantly with the increase in job size. The results demonstrate that the presented step-by-step procedure of the heuristic delivers significantly close to optimal solutions.

TSAR-ILP: Tile-Based, Synchronization-AwaRe ILP Allocating Heterogeneous Platforms for Streaming Applications

Automatic design space exploration (DSE) is key in hardware-software (HW/SW) co-design. To cope with the large design space, explorations are often heuristic-based and/or approximate yielding potentially locally optimal solutions. Without knowing the globally optimal solution, strong assertions about performance upper / lower bounds cannot be made. In contrast, integer linear programming (ILP) formulations can produce exact (optimal) solutions. Previous ILP-based formulations, however, lack support for tile-based architectures and realistic synchronization models, limiting their DSE capabilities. This work introduces a tile-based, synchronization-aware ILP (TSAR-ILP) formulation that overcomes previous limitations. With TSAR-ILP, the allocation / binding problems are introduced and formalized, attaining optimal solutions for mapping streaming applications onto template platforms. Using TSAR-ILP, this work explores a hardware acceleratorrich (HWACC-rich) platform with direct HWACC-to-HWACC communication under HW area constraints for 40 OpenVX applications. To illustrate design opportunities given by (a) the ILP formulation and (b) direct HWACC-to-HWACC communication, this paper analyzes the impact of job size. Results show that selecting smaller job sizes yields performance improvements and less area usage at the cost of slightly increased synchronization overhead. A job size reduction from 1 kB to 256 bytes gives 3.51x average performance increase across 40 applications. Finally, DSE with TSAR-ILP is shown not to be prohibitive through scalability analysis using a set of 5000 synthetic applications with varying size (10-125 nodes), with 94.3% of applications successfully achieving optimal solutions under 60 seconds.

Performance of the Gittins Policy in the G/G/1 and G/G/k, With and Without Setup Times

We consider the classic problem of preemptively scheduling jobs of unknown size (a.k.a. service time) in a queue to minimize mean number-in-system, or equivalently mean response time (a.k.a. sojourn time). We know how to solve this problem in an M/G/1, provided the job size distribution is known to the scheduler. In this case, the optimal policy is the Gittins policy (a.k.a. Gittins index policy) [1].

A Review of Women Employees' Work-Life Balance Satisfaction with Reference to AP State Higher Academic Institutions

Purpose: The primary goal of this study is to assess how satisfied women employees in institutes of higher learning are with their balance between work and personal life. To better understand women employees' work-life balance satisfaction, this study looked at an array of aspects, including demographics, family-related factors, and other organizational and work-related procedures. Theoretical framework: There is a wealth of empirical research available to assess the work-life balance satisfaction of female employees in academic institutions. Higher education has seen several advancements, such as the introduction of online learning systems, but more research is needed. Design/Methodology/Approach: An evaluation of the exhaustive survey of the literature that was employed in the research design. A data collection tool, such as a questionnaire, is employed, as well as a non-probability sampling technique, such as the Snow ball sampling technique. A standard questionnaire is used to collect data. The information was gathered from respondents in the Indian state of Andhra Pradesh. Findings: In order to analyze the data, various statistical techniques such as Anova, Regression, and the Cronbach's alpha test are used. Employees' delight with their work-life balance is influenced by their age, marital status, experience, career, and family size. The income and classification level of employees have an adverse effect on their work-life balance enjoyment. Research, Practical &amp;social implication: This study evaluated the work-life balance of female employees at higher education institutions from a number of perspectives. Originality/Value: The objective of this research is to find and evaluate the impact of different viewpoints on female employees' work-life balance. A female employee's age as well as income level. Marital status, family size, designation, occupation and level of experience, job and family-related concerns, and working hours are all examined.

Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine

We investigate a general single-batch-processing machine scheduling problem of minimizing the total costs of all jobs with general convex piecewise linear cost functions, where the processing time, due dates, and sizes of jobs are non-uniform. Since the studied problem is NP-hard and the objective is irregular, we adopt a practical 3-step method that starts from a specific job sequence, finds the optimal and near-optimal schedules of the given job sequence, and then iteratively improves the schedules. For the restricted problem where the job sequence is given, we propose a dynamic programming algorithm to obtain the optimal schedule. To further reduce the running time, we also devise a span-limit tree search (SLTS) approach to find the near-optimal schedule. We then design a local search method to improve the solutions solved by SLTS. Finally, we design a branch and bound algorithm with a lower bound method for small-sized instances. All proposed methods are based on our analysis of the mathematical properties of the scheduling problem, and extensive numerical experiments are conducted to demonstrate their effectiveness and efficiency.

Study of Permian Basin Provides Insight Into Parent-/Child-Well Interactions

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 211899, “Results From a Collaborative Parent/Child Industry Study: Permian Basin,” by Mark McClure, SPE, ResFrac; Magdalene Albrecht, SM Energy; and Carl Bernet, Ovintiv, et al. The paper has not been peer reviewed. _ The complete paper summarizes results from a collaborative industry study involving seven operators and 10 pad-scale data sets across four different shale plays. The paper specifically focuses on a subset of the data sets from the Midland and Delaware Basins. The project had three main objectives: compare and contrast observations between data sets and basins, develop general insights into parent- and child-well interactions, and provide customized economic optimization recommendations for each individual operator and data set. The simulations reveal that economic performance can be optimized with customized selection of well spacing, job size, and landing depth based on each company’s objectives and price deck. Methods Modeling Approach. The simulations were performed with a fully integrated hydraulic fracturing, wellbore, geomechanics, and reservoir simulator. The entire life cycle of the wells is captured in a single continuous simulation. The fractures are meshed as true cracks, with apertures on the order of microns to millimeters. Constitutive relations are used to capture transitions from being mechanically open to mechanically closed and vice versa. The simulations are fully 3D, and the equations are solved with a fully coupled scheme. For efficiency, the simulations include only one or a few stages along the wells. Fracture geometry is assumed to be planar, with no more than one dominant hydraulic fracture strand propagating per cluster. The modeling approach is based on the industry’s emerging recognition that hydraulic fractures in shale are planar at large scale, while being rough and complex at small scale. In the simulator, constitutive relations are used to account for the effect of small-scale complexity on processes such as proppant transport, fluid leakoff, and fracture propagation. Modeling Work Flow. For each data set, the modeling process consisted of the following steps: 1. Gather and organize data. 2. Create an initial model based on this data. 3. Create a list of key observations from the data set that constitute the objectives for the history-matching process. 4. Present the initial model and the list of key observations to stakeholders to obtain feedback and check communication. 5. Vary simulation input parameters to match the key observations while frequently communicating with stakeholders. 6. After finalizing the history match, perform a set of sensitivity analysis simulations, varying parameters such as well spacing and parent-well age. 7. Set up an economics model and perform a quantitative optimization of net present value (NPV)/section or discounted return on investment [DROI; defined as time-discounted revenue minus time-discounted operating expense divided by time-discounted capital expenditure (CAPEX)]. The steps of this work flow are detailed in the complete paper.

Performance of Load Balancers With Bounded Maximum Queue Length in Case of Non-Exponential Job Sizes

In large-scale distributed systems, balancing the load in an efficient way is crucial in order to achieve low latency. Recently, some load balancing policies have been suggested which are able to achieve a bounded maximum queue length in the large-scale limit. However, these policies have thus far only been studied in case of exponential job sizes. As job sizes are more variable in real systems, we investigate how the performance of these policies (and in particular the value of these bounds) is impacted by the job size distribution. We present a unified analysis which can be used to compute the bound on the queue length in case of phase-type distributed job sizes for four load balancing policies. We find that in most cases, the bound on the maximum queue length can be expressed in closed form. In addition, we obtain job size (in)dependent bounds on the expected response time. Our methodology relies on the use of the cavity process. That is, we conjecture that the cavity process captures the behaviour of the real system as the system size grows large. For each policy, we illustrate the accuracy of the cavity process by means of simulation.

Improved multi-objective artificial bee colony algorithm for parallel machine lot-streaming scheduling problem with limited and unequal sub-lots

Job splitting is a full-time effective measure used to improve corporate competitiveness, especially when the lot size of jobs is considerably large. This work investigates a parallel machine lot-streaming scheduling problem, where unequal sub-lot is considered and the number of sub-lots is strictly limited by that of cutters. Focus on this problem, a mixed-integer linear programming model is formulated to minimize makespan and due time deviation simultaneously, to scrutinize the coupling relationship among decision variables, i.e., the number and size of sub-lots, the machine allocation, and the processing order of all sub-lots. Then, an improved multi-objective artificial bee colony algorithm (IMOABC) with two categories of improvements is developed to obtain high-quality Pareto front solutions. Specifically, a semi-random initialization is proposed to balance the workload as evenly as possible, which includes a half-normal distribution strategy for determining the number of utilized sub-lots, an equal-probability lot-splitting strategy for determining the size of each sub-lots, and a machine allocation strategy to synchronize the completion time of all machines. Besides, a multipoint preservative crossover is designed to enhance diversity in the employed bee phase, a sub-lot adjustment operator is proposed to implement objective-oriented local search in the onlooker bee phase, and an individual restart mechanism is adopted to avoid being trapped in local optimum in the scout bee phase. Extensive experiment results demonstrate that IMOABC significantly outperforms the other six state-of-the-art algorithms in terms of diversity and convergence.