Job Arrival Process Research Articles

Mean-field fluctuations at diffusion scale in threshold-based randomized routing for processor sharing systems and applications

In this article, we study the fluctuations of the empirical occupation measures of servers around their mean-field limit in a large system of heterogeneous processor sharing servers. It is assumed that there are M different servers grouped by their speeds and that the total number of servers is N. In particular, we study the sensitivity of the fluctuations to arrival rate parameters at the diffusion scale. The job arrival process is assumed to be Poisson with rate N ( λ − β N ) and the job lengths are assumed to be exponentially distributed with unit mean. On arrival, a finite number of servers from each group are selected and the destination server depends on the server occupancy normalized to their speeds and pre-defined thresholds, referred to as the Join-Below-Threshold scheme. We derive Functional Central Limit Theorems (FCLTs) for the fluctuations that enable us to estimate the error of the mean-field approximations to the empirical measures associated with a system with N servers. We then use these results to show mean response time for finite systems can be approximated by the response time given by the mean-field limit and the error is O ( 1 N ) for which the constants can be precisely calculated.

The Anatomy of Sorting—Evidence From Danish Data

In this paper, we formulate and estimate a flexible model of job mobility and wages with two‐sided heterogeneity. The analysis extends the finite mixture approach of Bonhomme, Lamadon, and Manresa (2019) and Abowd, McKinney, and Schmutte (2019) to develop a new Classification Expectation‐Maximization algorithm that ensures both worker and firm latent‐type identification using wage and mobility variations in the data. Workers receive job offers in worker‐type segmented labor markets. Offers are accepted according to a logit form that compares the value of the current job with that of the new job. In combination with flexibly estimated layoff and job finding rates, the analysis quantifies the four different sources of sorting: job preferences, segmentation, layoffs, and job finding. Job preferences are identified through job‐to‐job moves in a revealed preference argument. They are in the model structurally independent of the identified job wages, possibly as a reflection of the presence of amenities. We find evidence of a strong pecuniary motive in job preferences. While the correlation between preferences and current job wages is positive, the net present value of the future earnings stream given the current job correlates much more strongly with preferences for it. This is more so for short‐ than long‐tenure workers. In the analysis, we distinguish between type sorting and wage sorting. Type sorting is quantified by means of the mutual information index. Wage sorting is captured through correlation between identified wage types. While layoffs are less important than the other channels, we find all channels to contribute substantially to sorting. As workers age, job arrival processes are the key determinant of wage sorting, whereas the role of job preferences dictate type sorting. Over the life cycle, job preferences intensify, type sorting increases, and pecuniary considerations wane.

Improving the performance of batch schedulers using online job runtime classification

Job scheduling in high-performance computing platforms is a hard problem that involves uncertainties on both the job arrival process and their execution times. Users typically provide only loose upper bounds for job execution times, which are not so useful for scheduling heuristics based on processing times. Previous studies focused on applying regression techniques to obtain better execution time estimates, which worked reasonably well and improved scheduling metrics. However, these approaches require a long period of training data.In this work, we propose a simpler approach by classifying jobs as small or large and prioritizing the execution of small jobs over large ones. Indeed, small jobs are the most impacted by queuing delays, but they typically represent a light load and incur a small burden on the other jobs. The classifier operates online and learns by using data collected over the previous weeks, facilitating its deployment and enabling a fast adaptation to changes in the workload characteristics.We evaluate our approach using four scheduling policies on seven HPC platform workload traces. We show that: first, incorporating such classification reduces the average bounded slowdown of jobs in all scenarios, second, in most considered scenarios, the improvements are comparable to the ideal hypothetical situation where the scheduler would know in advance the exact running time of jobs.

Modeling arrival-to-departure sequence disorder in flow-controlled manufacturing systems

Flow control policies, such as clear the largest buffer first, have been used extensively in mediating server access between multiple job-arrival processes within manufacturing systems requiring significant set-up times between job types. Although the stability and performance characteristics of clearing policies have been studied, how these clearing policies affect the growth in arrival-to-departure sequence disorder across a machine or workcell is still an area for further research. In this paper, a closed-form model is formulated that characterises the steady-state average arrival-to-departure sequence disorder experienced by jobs processed through a stable flow controlled manufacturing system. Specifically addressed are the effects of upstream sequence disorder on the work-in-process of a downstream assembly process. A simulation study is used to validate the model’s accuracy and applicability in predicting steady-state average arrival-to-departure sequence disorder. A simulation study of an assembly process shows that by balancing upstream steady-state average sequence disorder, downstream work-in-process can be minimised while under a logical component grouping constraint.

Self‐adaptation and mutual adaptation for distributed scheduling in benevolent clouds

SUMMARYJoint service involving several clouds is an emerging form of cloud computing. In hybrid clouds, the schedulers within 1 cloud must not only self‐adapt to the job arrival processes and the workload but also mutually adapt to the scheduling polices of other schedulers. However, as a combinatorial optimization problem, scheduling is challenged by the adaptation to those dynamics and uncertain behaviors of the peers. This article studies the collaboration among benevolent clouds that are cooperative in nature and willing to accept jobs from other clouds. We take advantage of machine learning and propose a distributed scheduling mechanism to learn the knowledge of job model, resource performance, and others' policies. Without explicit modeling and prediction, machine learning guides scheduling decisions based on experiences. To examine the performance of our approach, we conducted simulation using the SP2 job workload log of the San Diego Supercomputer Center under a test bed based on agent‐based systems—SWARM. The results validate that our approach has much shorter mean response time than 5 typical dynamic scheduling algorithms—opportunistic load balancing, minimum execution time, minimum completion time, switching algorithm, and k‐percent best. A better collaboration in hybrid cloud is achieved by full adaptation.

Distributed multipliers in MWM for analyzing job arrival processes in massive HPC workload datasets

There are three distributed multipliers multifractal wavelet model (MWM) on network traffic. The β multifractal wavelet model (β MWM) recently has been introduced as a good choice to yield long range dependence (LRD) and fractal behavior for a job arrival process for parallel workload analysis. In this paper, based on the Multifractal Wavelet Model (MWM), we choose the three kinds of distributions for the multipliers, namely the symmetric β-distribution, a symmetric point-mass distribution, and a hybrid distribution, the influence which distributed multipliers had on the MWM was analyzed with the analysis and comparison between the real job arrival process and the synthesized one. We find that the choice of β-distribution wavelet multipliers Aj,k is not necessary. For the job arrival process, we can use different distributed multipliers to control the wavelet energy decay in MWM.

Manufacturing intelligence to forecast and reduce semiconductor cycle time

Semiconductor manufacturing is one of the most complicated production processes with the challenges of dynamic job arrival, job re-circulation, shifting bottlenecks, and lengthy fabrication process. Owing to the lengthy wafer fabrication process, work in process (WIP) usually affects the cycle time and throughput in the semiconductor fabrication. As the applications of semiconductor have reached the era of consumer electronics, time to market has played an increasingly critical role in maintaining a competitive advantage for a semiconductor company. Many past studies have explored how to reduce the time of scheduling and dispatching in the production cycle. Focusing on real settings, this study aims to develop a manufacturing intelligence approach by integrating Gauss-Newton regression method and back-propagation neural network as basic model to forecast the cycle time of the production line, where WIP, capacity, utilization, average layers, and throughput are rendered as input factors for indentifying effective rules to control the levels of the corresponding factors as well as reduce the cycle time. Additionally, it develops an adaptive model for rapid response to change of production line status. To evaluate the validity of this approach, we conducted an empirical study on the demand change and production dynamics in a semiconductor foundry in Hsinchu Science Park. The approach proved to be successful in improving forecast accuracy and realigning the desired levels of throughput in production lines to reduce the cycle time.

Statistical Analysis and Modeling of Jobs in a Grid Environment

The existence of good probabilistic models for the job arrival process and the delay components introduced at different stages of job processing in a Grid environment is important for the improved understanding of the Grid computing concept. In this study, we present a thorough analysis of the job arrival process in the EGEE infrastructure and of the time durations a job spends at different states in the EGEE environment. We define four delay components of the total job delay and model each component separately. We observe that the job inter-arrival times at the Grid level can be adequately modelled by a rounded exponential distribution, while the total job delay (from the time it is generated until the time it completes execution) is dominated by the computing element’s register and queuing times and the worker node’s execution times. Further, we evaluate the efficiency of the EGEE environment by comparing the job total delay performance with that of a hypothetical ideal super-cluster and conclude that we would obtain similar performance if we submitted the same workload to a super-cluster of size equal to 34% of the total average number of CPUs participating in the EGEE infrastructure. We also analyze the job inter-arrival times, the CE’s queuing times, the WN’s execution times, and the data sizes exchanged at the kallisto.hellasgrid.gr cluster, which is node in the EGEE infrastructure. In contrast to the Grid level, we find that at the cluster level the job arrival process exhibits self-similarity/long-range dependence. Finally, we propose simple and intuitive models for the job arrival process and the execution times at the cluster level.

Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures

In this paper, we study process completion time and propose an accurate approximation for the mean waiting time in queues with servers experiencing autocorrelated times to failure, which include only busy periods from a repair completion until the next failure. To do this, we employ a three-parameter renewal approximation that represents the stream of autocorrelated times to failure. The approximation gives rise to a renewal interruption process with two-state Hyper-exponential (H2) times to failure. Then we compute the mean waiting time exactly in a queue experiencing H2 times to failure when the job arrival process is Poisson. This model provides an approximation for the mean waiting time of the original queue having an autocorrelated disruption process. We also propose an accurate approximation for queues with renewal job arrival processes when the server interruption process is general.

Scalable dimensioning of optical transport networks for grid excess load handling

Grids consist of the aggregation of numerous dispersed computational and storage resources, able to satisfy even the most demanding computing jobs. An important aspect of Grid deployment is the allocation and activation of installed network capacity, needed to transfer data and jobs to and from remote resources. Due to the data-intensive nature of Grid jobs, it is expected that optical transport networks will play an important role in Grid deployment. As Grids possibly consist of high numbers of resources, and users, solving the network dimensioning problem (i.e. determining the number of wavelength channels per fiber and wavelength granularity required) using straightforward Integer Linear Programs (ILP) does not scale well with increasing number of jobs. Therefore, we propose the use of Divisible Load Theory (DLT) when modeling the OCS (with wavelength translation) dimensioning problem in this context. We compare this approach to both an exact ILP and heuristic (derived from the exact ILP) approach as a function of the job arrival process, network related parameters and the Grid job scheduling strategy on the Grid. Results show the convergence of the DLT-based and the exact ILP approach, which indicates that the DLT-based approach is of practical use in cases where the exact ILP-based problem becomes intractable. We study an excess load scenario and evaluate the network cost for varying wavelength granularity, fiber/wavelength cost models, network topology and traffic demand asymmetry under multiple Grid scheduling strategies. Results indicate the suitability of our DLT-based approach as an Optical Transport Network dimensioning tool to be used by network operators.

A robust policy for serial agile production systems

AbstractOne of the major problems in modeling production systems is how to treat the job arrival process. Restrictive assumptions such as Markovian arrivals do not represent real world systems, especially if the arrival process is generated by job departures from upstream workstations. Under these circumstances, cost‐effective policies that are robust with respect to the nature of the arrival process become of interest. In this paper, we focus on minimizing the expected total holding and setup costs in a two‐stage produce‐to‐order production system operated by a cross‐trained worker. We will show that if setup times are insignificant in comparison with processing times, then near‐optimal policies can be generated with very robust performances with respect to the arrival process. We also present conditions under which these near‐optimal policies can be obtained by using only the arrival and service rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.

Approximating the mean response time of parallel queues with JSQ policy

This paper presents an accurate model for evaluating the mean system size of parallel queues with the Join the Shortest Queue (JSQ) policy. The system considered consists of N identical queues with infinite buffers, and each of the queues has one server. The job arrival process is assumed to be Poisson. The service times are assumed to be exponentially distributed. When a job arrives at the system, it is sent to the queue with the smallest number of jobs. Ties are broken by randomly selecting one of the queues with the minimal number of jobs. Exact analysis of the system is known to be very difficult, and our model gives very accurate results. A birth-death Markov process is used to model the evolution of the number of jobs in the system. An iterative procedure is devised to estimate the state transition rates. The mean job response time can then be calculated. Extensive simulations are performed and compared with the analytical results. Our results show that this method provides very accurate estimates (within 3.5%) of the mean job response times for N up to 64.

Analysis of periodic and event-driven rescheduling policies in dynamic shops

Abstract We address the problem of rescheduling production systems in the face of dynamic job arrivals. Using simple single-and parallel-machine models to gain insight, we provide worst-case and computational analyses of periodic and event-driven rescheduling policies. Our results indicate that event-driven policies can obtain high-quality schedules with less rescheduling than continuous rescheduling policies. We also show that if structure in the job arrival process is exploited very effective periodic rescheduling policies can be designed.

The impact of a job buffer in a token-bank rate-control throttle

In this paper we study a rate-control throttle with a finite-capacity token bank and a finite-capacity job buffer. The primary purpose is to gain additional insight into the impact of the job buffer. We show that the overflow processes of jobs and tokens depend on the job-buffer and token-bank capacities only through their sum, in a very strong sense. Given two throttles with arbitrary token and job arrival processes, which differ only in their initial conditions and buffer capacities, having common total capacity, there exists a random time after which the overflow processes in these two systems coincide. For given total capacity, the job buffer smooths the stream of admitted jobs, but the reduced congestion is less than might be expected. For example, the heavy-traffic limiting behavior of a downstream infinite-capacity ^-server queue is unaffected by the job buffer in the throttle. We make a sample-path comparison of the throughputs at a downstream finite-capacity queue regulated by a token-bank rate-c...

Adaptive load sharing in heterogeneous distributed systems

In this paper, we study the performance characteristics of simple load sharing algorithms for heterogeneous distributed systems. We assume that nonnegligible delays are encountered in transferring jobs from one node to another. We analyze the effects of these delays on the performance of two threshold-based algorithms called Forward and Reverse. We formulate queuing theoretic models for each of the algorithms operating in heterogeneous systems under the assumption that the job arrival process at each node in Poisson and the service times and job transfer times are exponentially distributed. The models are solved using the Matrix-Geometric solution technique. These models are used to study the effects of different parameters and algorithm variations on the mean job response time: e.g., the effects of varying the thresholds, the impact of changing the probe limit, the impact of biasing the probing, and the optimal response times over a large range of loads and delays. Wherever relevant, the results of the models are compared with the M/M/ 1 model, representing no load balancing (hereafter referred to as NLB), and the M/M/K model, which is an achievable lower bound (hereafter referred to as LB).

A comparison of priority-based decentralized load balancing policies

Load balancing policies in distributed systems divide jobs into two classes; those processed at their of origination ( local jobs ) and those processed at some other site in the system after being transfered through a communication network ( remote jobs ). This paper considers a class of decentralized load balancing policies that use a threshold on the local job queue length at each host in making decisions for remote processing. They differ from each other according to how they assign priorities to each of these job classes, ranging from one providing favorable treatment to local jobs to one providing favorable treatment to remote jobs. Under each policy, the optimal load balancing problem is formulated as an optimization problem with respect to the threshold parameter. The optimal threshold is obtained numerically using matrix-geometric formulation and an iteration method. Last, we consider the effects that the job arrival process can have on performance. One expects that load balancing for systems operating in an environment of bursty job arrivals should be more beneficial than for an environment with random job arrivals. This fact is observed through numerical examples.