Job Arrivals Research Articles

Replication-Based Load Balancing

Load balancing of large distributed server systems is a complex optimization problem of critical importance in cloud systems and data centers. Existing schedulers often incur a high communication overhead when collecting the data required to make scheduling decisions, hence delaying job requests on their way to the executing servers. We propose a novel scheme that incurs no communication overhead between the users and the servers upon job arrival, thus removing any scheduling overhead from the job's critical path. Our approach is based on creating several replicas of each job and sending each replica to a different server. Upon the arrival of a replica to the head of the queue at its server, the latter signals the servers holding replicas of that job, so as to remove them from their queues. We show, through analysis and simulations, that this scheme significantly improves the expected queuing overhead over traditional schemes under various load conditions and different job length distributions. In addition, we show that our scheme remains efficient even when the inter-server signal propagation delay is significant (relative to the job's execution time). We provide a heuristic solution to the performance degradation that occurs in such cases and show, by simulations, that it efficiently mitigates the detrimental effect of propagation delays.

Dynamic Agent-based Bi-objective Robustness for Tardiness and Energy in a Dynamic Flexible Job Shop

Nowadays, manufacturing systems are shifting rapidly with the significant change in technology, business, and industry to become more complex and involved in more difficult issues, customised products, variant services and products, unavailable machines, and rush jobs. In the current practices, there are limited models or approaches that are dealing with these complexities. Most of the scheduling models in literature are proposed as centralised approaches. Researchers recently started to pay attention to reduce energy consumption in manufacturing due to the rising cost and the environmental impact. The energy consumption factor has been lately introduced into scheduling research among other traditional objectives such as time, cost and quality. Although reducing energy in manufacturing systems is very important, few researchers have considered energy consumption factor into scheduling in dynamic flexible manufacturing systems. This paper proposes an agent-based dynamic bio-objective robustness for energy and time in a job shop. Two types of agent are introduced which are machine agent and product agent. A new decision making and negotiation model for multi-agent systems is developed. Two types of dynamic unexpected events in the shop floor are introduced: dynamic job arrival and machines breakdown. A case study is provided in order to verify the result.

Distributionally Robust Appointment Scheduling with Random No-Shows and Service Durations

We consider a single-server scheduling problem given a fixed sequence of job arrivals with random no-shows and service durations. The joint probability distribution of the uncertain parameters is assumed to be ambiguous and only the support and first moments are known. We formulate a class of distributionally robust optimization models that incorporate the worst-case expected cost and the worst-case conditional Value-at-Risk (CVaR) of appointment waiting, server idleness, and overtime as the objective or constraints. Our models flexibly adapt to different prior beliefs of no-show probabilities. We obtain exact mixed-integer nonlinear programming (MINLP) reformulations that facilitate decomposition algorithms, and derive valid inequalities to strengthen the reformulations. In particular, we derive the convex hulls for special cases of no-show beliefs, yielding polynomial-size linear programming reformulations for the least and the most conservative supports of no shows. We test various instances to demonstrate the computational efficacy of our approaches and provide insights for appointment scheduling under distributional ambiguity of multiple uncertainties.

Interdatacenter Job Routing and Scheduling With Variable Costs and Deadlines

To reduce their operational costs, datacenter (DC) operators can schedule large jobs at DCs in different geographical locations with time- and location-varying electricity and bandwidth prices. We introduce a framework and algorithms to do so that minimize electricity and bandwidth cost subject to job indivisibility, deadlines, priorities, and DC resource constraints. In doing so, we provide a way for DC operators to predict their operational costs for different DC placements and capacities, and thus make informed decisions about how to expand their DC network. Our distributed algorithm uses estimated job arrivals and day-ahead electricity prices to optimize over sliding time windows. We demonstrate its effectiveness on a Google DC trace and investigate the effects of different cost and performance criteria. The algorithm leverages heterogeneous job resource requirements and routing and scheduling flexibility: even deadline and indivisibility constraints yield little cost increase, though they significantly improve job completion times and localization at only one DC, respectively. We show that our algorithm reduces the cost much more than optimizing only electricity, only bandwidth, or a combination of resource costs and job completion times.

Energy-efficient dynamic scheduling for a flexible flow shop using an improved particle swarm optimization

Due to increasing energy requirements and associated environmental impacts, nowadays manufacturing companies are facing the emergent challenges to meet the demand of sustainable manufacturing. Most existing research on reducing energy consumption in production scheduling problems has focused on static scheduling models. However, there exist many unexpected disruptions like new job arrivals and machine breakdown in a real-world production scheduling. In this paper, it is proposed an approach to address the dynamic scheduling problem reducing energy consumption and makespan for a flexible flow shop scheduling. Since the problem is strongly NP-hard, a novel algorithm based on an improved particle swarm optimization is adopted to search for the Pareto optimal solution in dynamic flexible flow shop scheduling problems. Finally, numerical experiments are carried out to evaluate the performance and efficiency of the proposed approach.

Online Preemptive Hierarchical Scheduling on Two Uniform Machines with Rejection

This paper studies the online hierarchical scheduling problem on two uniform machines with rejection. Two uniform machines M1, M2run at the speeds of s ∈ (0, +∞), 1 separately; and they are provided with different capabilities. Each machine has a certain GOS level 1 or 2 and every job is also associated with a hierarchy 1 or 2. The job can only be assigned to the machine whose GOS level does not exceed the job's hierarchy. Preemption is permitted but idle is not introduced. Jobs come one by one over list. When a job arrives, it can be accepted and scheduled on some machine or rejected by paying its penalty. The objective is to minimize the sum of makespan yielded by accepted jobs and total penalties of all rejected jobs. For this problem, we propose a family of several online algorithms according to the range of s and the related lower bound is also obtained. These algorithms achieve optimal competitive ratio when s ∈ (0, 1) ∪ [1.618, +∞), but have a small gap between upper bound and lower bound in interval [1, 1.618).

Scheduling Storms and Streams in the Cloud

Motivated by emerging big streaming data processing paradigms (e.g., Twitter Storm, Streaming MapReduce), we investigate the problem of scheduling graphs over a large cluster of servers. Each graph is a job, where nodes represent compute tasks and edges indicate data-flows between these compute tasks. Jobs (graphs) arrive randomly over time, and upon completion, leave the system. When a job arrives, the scheduler needs to partition the graph and distribute it over the servers to satisfy load balancing and cost considerations. Specifically, neighboring compute tasks in the graph that are mapped to different servers incur load on the network; thus a mapping of the jobs among the servers incurs a cost that is proportional to the number of "broken edges''. We propose a low complexity randomized scheduling algorithm that, without service preemptions, stabilizes the system with graph arrivals/departures; more importantly, it allows a smooth trade-off between minimizing average partitioning cost and average queue lengths. Interestingly, to avoid service preemptions, our approach does not rely on a Gibbs sampler; instead, we show that the corresponding limiting invariant measure has an interpretation stemming from a loss system.

A two-stage artificial bee colony algorithm scheduling flexible job-shop scheduling problem with new job insertion

This study addresses the scheduling problem in remanufacturing engineering. The purpose of this paper is to model effectively to solve remanufacturing scheduling problem. The problem is modeled as flexible job-shop scheduling problem (FJSP) and is divided into two stages: scheduling and re-scheduling when new job arrives. The uncertainty in timing of returns in remanufacturing is modeled as new job inserting constraint in FJSP. A two-stage artificial bee colony (TABC) algorithm is proposed for scheduling and re-scheduling with new job(s) inserting. The objective is to minimize makespan (maximum complete time). A new rule is proposed to initialize bee colony population. An ensemble local search is proposed to improve algorithm performance. Three re-scheduling strategies are proposed and compared. Extensive computational experiments are carried out using fifteen well-known benchmark instances with eight instances from remanufacturing. For scheduling performance, TABC is compared to five existing algorithms. For re-scheduling performance, TABC is compared to six simple heuristics and proposed hybrid heuristics. The results and comparisons show that TABC is effective in both scheduling stage and rescheduling stage.

Schedulability analysis of a graph-based task model for mixed-criticality systems

We present a new graph-based real-time task model that can specify complex job arrival patterns and global state-based mode switching. The mode switching is of a mixed-criticality style, meaning that it allows immediate changes to the parameters of active jobs upon mode switches. The resulting task model generalizes previously proposed task graph models as well as mixed-criticality (sporadic) task models; the merging of these mutually incomparable modeling paradigms allows formulation of new types of tasks. A sufficient schedulability analysis for EDF on preemptive uniprocessors is developed for the proposed model.

Integrated rescheduling and preventive maintenance for arrival of new jobs through evolutionary multi-objective optimization

In this paper, we study a rescheduling problem in response to arrival of new jobs in single machine layout, where preventive maintenance should be determined. Preventive maintenance together with controllable processing time could alleviate the inherent deteriorating effect in manufacturing system. Processing sequence of original and new jobs, compression of each job, and position of maintenance should be optimized simultaneously with regards to total operational cost (job's total completion times, maintenance cost and compression cost) and total completion time deviation. An improved elitist non-dominated sorting genetic algorithm (NSGA-II) has been proposed to solve the rescheduling problem. To address the key problem of balancing between exploration and exploitation, we hybridize differential evolution mutation operation with NSGA-II to enhance diversity, constitute high-quality initial solution based on assignment model for exploitation, and incorporate analytic property of non-dominated solutions for exploration. Finally computational study is designed by randomly generating various instances with regards to the problem size from given distributions. By use of existing performance indicators for convergence and diversity of Pareto fronts, we illustrate the effectiveness of the hybrid algorithm and the incorporation of domain knowledge into evolutionary optimization in rescheduling.

Scheduling jobs on a single serial-batching machine with dynamic job arrivals and multiple job types

This paper investigates a scheduling model with certain co-existing features of serial-batching, dynamic job arrival, multi-types of job, and setup time. In this proposed model, the jobs of all typ...

A dynamic model and an algorithm for short-term supply chain scheduling in the smart factory industry 4.0

Smart factories Industry 4.0 on the basis of collaborative cyber-physical systems represents a future form of industrial networks. Supply chains in such networks have dynamic structures which evolve over time. In these settings, short-term supply chain scheduling in smart factories Industry 4.0 is challenged by temporal machine structures, different processing speed at parallel machines and dynamic job arrivals. In this study, for the first time, a dynamic model and algorithm for short-term supply chain scheduling in smart factories Industry 4.0 is presented. The peculiarity of the considered problem is the simultaneous consideration of both machine structure selection and job assignments. The scheduling approach is based on a dynamic non-stationary interpretation of the execution of the jobs and a temporal decomposition of the scheduling problem. The algorithmic realisation is based on a modified form of the continuous maximum principle blended with mathematical optimisation. A detailed theoretical analysis of the temporal decomposition and computational complexity is performed. The optimality conditions as well as the structural properties of the model and the algorithm are investigated. Advantages and limitations of the proposed approach are discussed.

Explaining the Gender Wage Gap: Estimates from a Dynamic Model of Job Changes and Hours Changes

I address the causes of the gender wage gap with a new dynamic model of wage, hours, and job changes that permits me to decompose the gap into a portion due to gender differences in preferences for hours of work and in constraints. The dynamic model allows the differences in constraints to reflect possible gender differences in job arrival rates, job destruction rates, the mean and variance of the wage offer distribution, and the wage cost of part-time work. The model is estimated using the 1996 panel of the Survey of Income and Program Participation. I find that the preference for part-time work increases with marriage and number of children among women but not among men. These demographic factors explain a sizable fraction of the gender gap in employment, but they explain no more than 6 percent of the gender wage gap. Differences in constraints, mainly in the form of the mean offered wages and rates of job arrival and destruction, explain most of the gender wage gap. Policy simulation results suggest that, relative to reducing the wage cost of part-time work, providing additional employment protection to part-time jobs is more effective in reducing the gender wage gap.

Minimising the total weighted tardiness and instability for the parallel machine re-scheduling problem with deadlines and ready times

The parallel machine rescheduling problem (PMRP) assumes that the jobs have different ready times and due date-to-deadline windows. PMRP can be defined as updating the existing schedule after being disrupted by job-related events including the arrival of new jobs, departure of an existing job, and changes to job priority. In PMRP, bi-criteria objective function is considered to simultaneously minimise both the total weighted tardiness (schedule quality) and schedule instability. We first formulate the PMRP by revising and extending the mixed integer linear programming (MILP) model of the scheduling problem in Kaplan and Rabadi (2012). Five heuristic algorithms, namely MetaRE, BestINSERT, SEPRE, LSHIFT and SHUFFLE, are introduced to handle the bi-objective PMRP using the developed algorithms by Kaplan and Rabadi (2012, 2013). Experiments have been conducted for small size (12 jobs) and large size (60 size) problems for different types of disruptions.

A honey-bees optimization algorithm for a two-agent single-machine scheduling problem with ready times

In this paper we consider two agents that compete on the use of a common processor. Each of the agents has a set of jobs that have to be processed on the same machine without preemption. Each of the agents wants to minimize an objective function that depends on the completion time of its own jobs. In addition, each job has different release dates. In the presence of unequal release dates, it is sometimes advantageous to form a non-full batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. The objective is to find a schedule that performs well with respect to the objectives of both agents. To solve this difficulty problem, we construct a branch-and-bound solution scheme incorporating these bounds and some dominance rules for the optimal solution. In view of the advantage of combining local and global searches in the honey-bees optimization algorithm, we attempt to use a marriage in honey-bees optimization algorithm (MBO) to find near-optimal solutions. We conduct extensive computational experiments to evaluate the performance of the algorithms.

A discrete teaching-learning-based optimisation algorithm for realistic flowshop rescheduling problems

In this study, we proposed a discrete teaching-learning-based optimisation (DTLBO) for solving the flowshop rescheduling problem. Five types of disruption events, namely machine breakdown, new job arrival, cancellation of jobs, job processing variation and job release variation, are considered simultaneously. The proposed algorithm aims to minimise two objectives, i.e., the maximal completion time and the instability performance. Four discretisation operators are developed for the teaching phase and learning phase to enable the TLBO algorithm to solve rescheduling problems. In addition, a modified iterated greedy (IG)-based local search is embedded to enhance the searching ability of the proposed algorithm. Furthermore, four types of DTLBO algorithms are developed to make detailed comparisons with different parameters. Experimental comparisons on 90 realistic flowshop rescheduling instances with other efficient algorithms indicate that the proposed algorithm is competitive in terms of its searching quality, robustness, and efficiency.

Optimal Semi-Online Algorithm for Scheduling on Two Parallel Batch Processing Machines

Batch processing machine scheduling in uncertain environment attracts more and more attention in the last decade. This paper deals with semi-online scheduling on two parallel batch processing machines with non-decreasing processing time of job. Jobs arrive over time in the online paradigm, and the processing time of any batch is equal to the length of the last arrival job in the batch. We study the unbounded model where each processing batch may contain an unlimited number of jobs, and the objective is to minimize the makespan. Given any job Jj together with its following job Jj+1, it is assumed that their processing times satisfy pj+1 ≥ αpj where α ≥ 1 is a constant. That is, jobs arrive in a non-decreasing order of processing times. We mainly propose an optimal ϕ-competitive online algorithm where ϕ ≥ 1 is a solution of equation ϕ3 + (α-1)ϕ2 + (α2 - α - 1)ϕ - α2 = 0.

Minimization of makespan for the single batch-processing machine scheduling problem with considering aging effect and multi-maintenance activities

This paper considers the single batch-processing machine scheduling problem with aging effect and multi-maintenance activity concept. Real processing time of jobs increases due to machine’s aging effect. Maintenance time is constant and the machine returns to its initial condition after each maintenance activity and the aging effect starts anew. Our scheduling problem is under assumptions: non identical job sizes and dynamic job arrivals. We have to determine jointly (1) the maintenance frequencies, (2) the position of the maintenance activities on the machine, (3) the grouping of the jobs into the batches, and (4) the sequence of the batches on the machine, to minimize makespan. At first, we formulate the problem as a mathematical model. Since this problem has been proved to be NP-hard; therefore, a heuristic and two meta-heuristic algorithms are offered for the real-sized problems. The performance of the proposed algorithms is analyzed on the various test problems based on the considered measures.

Light traffic performance under the power of two load balancing strategy

We consider the power-of-two policy with d = 2, Poisson job arrivals, heterogeneous servers and a general job requirement distribution. With the help of the first two light traffic derivatives for the average job response time, we point to interesting structural features associated with server heterogeneity in light traffic.

Parallel Workload Modeling with Realistic Characteristics

Workload modeling and performance evaluation play crucial roles in the study of scheduling algorithms on large-scale parallel and distributed systems. An effective design of a scheduling algorithm for these systems requires experiments with hundreds of simulations to evaluate its performance. Since each simulation needs one workload as input, only real workloads with usually a limited availability are not sufficient, and so representative workload models are needed. Several studies have shown that realistic workload characteristics such as burstiness, bag-of-tasks, etc., cause significant performance impacts on scheduling. Therefore, we argue that realistic workload models should contain as many characteristics of real workloads as possible. In practice, researchers use unrealistic workloads in their scheduling evaluations because they lack models that can help generate realistic workloads. In this article, we analyze real parallel workloads to show the presence of important characteristics including long range dependence, periodicity and temporal burstiness of job arrivals, bag-of-tasks behavior, and correlation of runtime and number of processors. Then, we present a systematic approach to create a complete model that contains all of these characteristics. Validation of our model with real world data shows that it does not only capture the above characteristics, but also can fit marginal distributions well.