Job Arrival Rate Research Articles

Particle Swarm Optimization for a redundant repairable machining system with working vacations and impatience in a multi-phase random environment

With the increasing reliance on cloud computing as the foundational manufacturing systems with intricate dynamics, featuring multiple service areas, varying job arrival rates, diverse service requirements, and the interplay of failures and impatience, significant analytical challenges arise. Queueing networks offer a powerful stochastic modeling framework to capture such complex dynamics. This paper develops a novel, exhaustive queueing model for a finite-capacity redundant multi-server system operating in a multi-phase random environment. The proposed model uniquely integrates real-world factors, including server breakdowns and repairs, waiting servers, synchronous working vacations, and state dependent balking and reneging, into a single queueing model, representing a significant advancement in the field. Using the matrix-analytic method, we establish the steady-state solution and derive key performance metrics. Numerical experiments and sensitivity analyses elucidate the impact of system parameters on performance measures. Additionally, a cost model is formulated, enabling cost optimization analysis using direct search method and Particle Swarm Optimization (PSO) to identify efficient operating configurations.

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.

Near-Optimal Stochastic Bin-Packing in Large Service Systems with Time-Varying Item Sizes

In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule jobs with time-varying resource requirements is limited. Motivated by this gap, we propose a new setting of the stochastic bin-packing problem in service systems that allows for time-varying job resource requirements, also referred to as 'item sizes' in traditional bin-packing terms. In this setting, a job or 'item' must be dispatched to a server or 'bin' upon arrival. Its resource requirement varies over time as a Markov chain while in service. Our goal is to minimize the expected number of active servers, or 'non-empty bins', in the steady state. Under our problem formulation, we develop a job dispatch policy, named Join-Requesting-Server (JRS). We show that in the asymptotic regime where the job arrival rate scales large linearly with respect to a scaling factor r, JRS achieves an additive optimality gap of O(√r) in the objective value, where the optimal objective value is Θ(r). Our approach highlights a novel policy conversion framework that utilizes the solution of a single-server problem.

Dynamic Job and Conveyor-Based Transport Joint Scheduling in Flexible Manufacturing Systems

Efficiently managing resource utilization is critical in manufacturing systems to optimize production efficiency, especially in dynamic environments where jobs continually enter the system and machine breakdowns are potential occurrences. In fully automated environments, co-ordinating the transport system with other resources is paramount for smooth operations. Despite extensive research exploring the impact of job characteristics, such as fixed or variable task-processing times and job arrival rates, the role of the transport system has been relatively underexplored. This paper specifically addresses the utilization of a conveyor belt as the primary mode of transportation among a set of production machines. In this configuration, no input or output buffers exist at the machines, and the transport times are contingent on machine availability. In order to tackle this challenge, we introduce a randomized heuristic approach designed to swiftly identify a near-optimal joint schedule for job processing and transfer. Our solution has undergone testing on both state-of-the-art benchmarks and real-world instances, showcasing its ability to accurately predict the overall processing time of a production line. With respect to our previous work, we specifically consider the case of the arrival of a dynamic job, which requires a different design approach since there is a need to keep track of partially processed jobs, jobs that are waiting, and newly arrived jobs. We adopt a total rescheduling strategy and, in order to show its performance, we consider a clairvoyant scheduling approach, in which job arrivals are known in advance. We show that the total rescheduling strategy yields a scheduling solution that is close to optimal.

Near-Optimal Stochastic Bin-Packing in Large Service Systems with Time-Varying Item Sizes

In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule jobs with time-varying resource requirements is limited. Motivated by this gap, we propose a new setting of the stochastic bin-packing problem in service systems that allows for time-varying job resource requirements, also referred to as 'item sizes' in traditional bin-packing terms. In this setting, a job or 'item' must be dispatched to a server or 'bin' upon arrival. Its resource requirement may vary over time while in service, following a Markovian assumption. Once the job's service is complete, it departs from the system. Our goal is to minimize the expected number of active servers, or 'non-empty bins', in steady state. Under our problem formulation, we develop a job dispatch policy, named Join-Reqesting-Server (JRS). Broadly, JRS lets each server independently evaluate its current job configuration and decide whether to accept additional jobs, balancing the competing objectives of maximizing throughput and minimizing the risk of resource capacity overruns. The JRS dispatcher then utilizes these individual evaluations to decide which server to dispatch each arriving job to. The theoretical performance guarantee of JRS is in the asymptotic regime where the job arrival rate scales large linearly with respect to a scaling factor r. We show that JRS achieves an additive optimality gap of O(√r) in the objective value, where the optimal objective value is Θ(r). When specialized to constant job resource requirements, our result improves upon the state-of-the-art o(r) optimality gap. Our technical approach highlights a novel policy conversion framework that reduces the policy design problem into a single-server problem.

Wasserstein Adversarial Transformer for Cloud Workload Prediction

Predictive VM (Virtual Machine) auto-scaling is a promising technique to optimize cloud applications’ operating costs and performance. Understanding the job arrival rate is crucial for accurately predicting future changes in cloud workloads and proactively provisioning and de-provisioning VMs for hosting the applications. However, developing a model that accurately predicts cloud workload changes is extremely challenging due to the dynamic nature of cloud workloads. Long- Short-Term-Memory (LSTM) models have been developed for cloud workload prediction. Unfortunately, the state-of-the-art LSTM model leverages recurrences to predict, which naturally adds complexity and increases the inference overhead as input sequences grow longer. To develop a cloud workload prediction model with high accuracy and low inference overhead, this work presents a novel time-series forecasting model called WGAN-gp Transformer, inspired by the Transformer network and improved Wasserstein-GANs. The proposed method adopts a Transformer network as a generator and a multi-layer perceptron as a critic. The extensive evaluations with real-world workload traces show WGAN- gp Transformer achieves 5× faster inference time with up to 5.1% higher prediction accuracy against the state-of-the-art. We also apply WGAN-gp Transformer to auto-scaling mechanisms on Google cloud platforms, and the WGAN-gp Transformer-based auto-scaling mechanism outperforms the LSTM-based mechanism by significantly reducing VM over-provisioning and under-provisioning rates.

Intermediate data placement and cache replacement strategy under Spark platform

Spark is widely used due to its high performance caching mechanism and high scalability, which still causes uneven workloads and produces useless intermediate caching results when faced with data-intensive applications. A data placement strategy based on an improved reservoir sampling algorithm is proposed to solve the problem of intermediate data tilt in the shuffle stage of Spark. Compared with the traditional sampling algorithm, the amount of intermediate data is accumulated while sampling. The data skew measurement model is used to classify data into skewed data, and non-skewed and coarse-grained, and fine-grained placement algorithms are designed. To further improve Spark's system memory utilization and cache hit rate, an adaptive cache replacement algorithm is proposed to maximize cache gain. We analyze the operational dependencies and propose a cache gain model. Compared with the traditional method, the two known and unknown job arrival rates are considered separately to obtain an online adaptive cache replacement strategy that maximizes cache gain. Experimental results show that our data placement strategy effectively reduces Spark applications' execution time and improves the load balance of reduce tasks. Meanwhile, the proposed adaptive cache replacement strategy effectively reduces Spark's average completion time and improves the memory utilization and cache hit rate.

An Analytical Performance Evaluation of MapReduce Model Using Transient Queuing Model

Today the MapReduce frameworks become the standard distributed computing mechanisms to store, process, analyze, query and transform the Bigdata. While processing the Bigdata, evaluating the performance of the MapReduce framework is essential, to understand the process dependencies and to tune the hyper-parameters. Unfortunately, the scope of the MapReduce framework in-built functions is limited to evaluate the performance till some extent. A reliable analytical performance model is required in this area to evaluate the performance of the MapReduce frameworks. The main objective of this paper is to investigate the performance effect of the MapReduce computing models under various configurations. To accomplish this job, we proposed an analytical transient queuing model, which evaluates the MapReduce model performance for different job arrival rates at mappers and various job completion times of mappers as well as the reducers too. In our transient queuing model, we appointed an efficient multi-server queuing model M/M/C for optimal waiting queue management. To conduct the experiments on proposed analytics model, we selected the Bigdata applications with three mappers and two reducers, under various configurations. As part of the experiments, the transient differential equations, average queue lengths, mappers blocking probability, shuffle waiting probabilities and transient states are evaluated. MATLAB based numerical simulations presented the analytical results for various combinations of the input parameters like λ, µ1 and µ2 and their effect on queue length.

Predictive Data Center Selection Scheme for Response Time Optimization in Cloud Computing

The quality of cloud computing services is evaluated based on various performance metrics out of which response time (RT) is most important. Nearly all cloud users demand its application's RT as minimum as possible, so to minimize overall system RT, the authors have proposed request response time prediction-based data center (DC) selection algorithm in this work. Proposed DC selection algorithm uses results of optimization function for DC selection formulated based on M/M/m queuing theory, as present cloud scenario roughly obeys M/M/m queuing model. In cloud environment, DC selection algorithms are assessed based on their performance in practice, rather than how they are supposed to be used. Hence, explained DC selection algorithm with various forecasting models is evaluated for minimum user application RT and RT prediction accuracy on various job arrival rates, real parallel workload types, and forecasting model training set length. Finally, performance of proposed DC selection algorithm with optimal forecasting model is compared with other DC selection algorithms on various cloud configurations.

Performance estimation of a passing-crane automated storage and retrieval system

Storage and retrieval automation has progressed rapidly. One such popular storage and retrieval system deploys two passing aisle-bound cranes. Each crane can access every location in the rack. To pass the other crane and prevent collision, each crane has to timely move the platform to an appropriate level and simultaneously rotate it. We develop a queuing model with preemptive-resume interrupted service to estimate the system response time (and hence throughput capacity) while considering two I/O point positions, random storage, and a crane assignment policy where all requests are shared between the cranes. The analytical models are validated with simulation based on the data from real cases. We find that a design with I/O points located in the middle of the rack will increase the interference, but it has a high relative throughput because of the reduced expected travel time. Compared with a system with one crane, a two-crane system has interference, but it can improve the system efficiency, especially in large systems with high job arrival rates. The model can be extended to other systems where multiple cranes are used in a single travel aisle with crane interference, e.g. passing cranes operating in a container stack lane.

Dynamic Pricing for Smart Mobile Edge Computing: A Reinforcement Learning Approach

This letter studies the revenue maximization problem for the mobile edge computing (MEC) system, where an access point (AP) is equipped with an MEC server, providing job offloading service for multiple resource-hungry users and charging users a service fee for it. Usually, the information about users' personal demand is unknown and users' job arrival rate is time-varying, which make pricing highly challenging. As such, we develop a policy gradient (PG)-based reinforcement learning (RL) algorithm. In specific, a deep neural network (DNN) is adopted as the policy network to design price policy, and a baseline neural network (BNN) is used to reduce the inherent high variance of the gradient obtained using PG. The proposed PG-based algorithm enables continuous pricing, thus constituting an advancement over the conventional Q-learning algorithm that has provided only discrete action space. Simulation results show that our proposed method converges to the optimal revenue performance, while the Q-learning algorithm suffers 44% revenue loss.

Testing the independence of job arrival rates and wage offers

Is the arrival rate of a job independent of the wage that it pays? We answer this question by testing whether unemployment insurance alters the job finding rate differentially across the wage distribution. To do this, we use a Mixed Proportional Hazard Competing Risk Model in which we classify quantiles of the wage distribution as competing risks faced by searching unemployed workers. Allowing for flexible unobserved heterogeneity across spells, we find that unemployment insurance increases the likelihood that a searcher matches to higher paying jobs relative to low or medium paying jobs, rejecting the notion that wage offers and job arrival rates are independent. We show that dependence between wages and job offer arrival rates explains 9% of the increase in the duration of unemployment associated with unemployment insurance.

Optimal Capacity Planning for Cloud Service Providers with Periodic, Time-Varying Demand

Problem Definition: We determine the jointly optimal service capacity and retrial intervals between unsuccessful service attempts for a major provider of cloud computing services. Allocating sufficient capacity to cloud services is a challenging task because demand is time-varying. Thus, most firms have been expanding their capacity with little regard to the consequences associated with idle resources, such as excessive energy consumption and excess costs. Academic/Practical Relevance: We model the system as a multi-station queueing network where the arrival rate of jobs is time-varying and the servers represent CPU cores. Jobs are infinitely impatient and those that are not immediately serviced may retry several times before permanently abandoning the system. We introduce an offered load approximation that allows us to construct a recursive representation of the offered load function which describes the fluid dynamics of the system. Methodology: We develop a calculus-of-variation approach to minimize the total functional variation of the constructed offered load function. We show that an optimal policy can be efficiently obtained and prove that it is similar to maximizing the penalized system throughput. Results: Using a data set of cloud computing requests over a representative 24-hour period from a typical service of our partner organization, we show that our optimal policy results in a 10% reduction in capacity. We also demonstrate that small changes to their service-level agreements may elicit additional savings. Managerial Implications: Our model can help reduce idle capacity and has implications for managing more sustainable and environmentally friendly cloud computing services. It may also help to explain why so much global cloud capacity is typically idle. That is, in order to satisfy service level agreements encouraging retrial jobs to be processed during off-peak periods while also ensuring that they have short wait times, providers must provision large amounts of capacity.

The incompatibility of local economic prosperity and migrants\u2019 social integration: evidence from the Netherlands

This paper investigates the effects of the conditions of local labour markets on the social networks of immigrants, with an emphasis on co-ethnic contact and contact with people native to the locality. This study focuses on the case of immigrants in the Netherlands. For this case, I derived and empirically tested a job and residential search model. I found that a high job arrival rate and large wage differences between the ethnic labour market and the host labour market both correlate with immigrants developing stronger co-ethnic networks and weaker native networks as well as with immigrants choosing to live in more ethnically concentrated areas. These findings suggest that local economic prosperity does not necessarily beget social integration: in this case study, immigrants spontaneously assimilated less into the host society during a good economic period.

Dynamic load balancing with tokens

Efficiently exploiting the resources of data centers is a complex task that requires efficient and reliable load balancing and resource allocation algorithms. The former are in charge of assigning jobs to servers upon their arrival in the system, while the latter are responsible for sharing the server resources between their assigned jobs. These algorithms should adapt to various constraints, such as data locality, that restrict the feasible job assignments. In this paper, we propose a token-based algorithm that efficiently balances the load between the servers without requiring any knowledge on the job arrival rates and the server capacities. Assuming a balanced fair sharing of the server resources, we show that the resulting dynamic load balancing is insensitive to the job size distribution. Its performance is compared to that obtained under the best static load balancing and in an ideal system that would constantly optimize the resource utilization. We also make the connection with other token-based algorithms such as Join-Idle-Queue.

Dynamic thermal characterization of raised floor plenum data centers: Experiments and CFD

World over, power consumption by “server farms” or data centers is a growing concern. With time dependent job arrival rates at the servers, the power dissipation, and concomitantly the cooling requirements are dynamic. However, due to the lack of more efficient control algorithms, cooling systems are set to conservatively pre-determined set points, which result in sub-optimal energy consumption. An important step in the development of smarter control algorithms is detailed knowledge about the dynamic behavior of the data center system, which is missing in the open literature. In this paper, we have conducted transient experiments and CFD modeling to understand data center behavior for a broad range of time-varying input parameters such as CPU utilization, cooling air temperature and flow rates. Experiments at the server, rack, and facility level of raised floor plenum data centers were designed to record system responses to these input variable perturbations. The output responses were rack inlet-outlet air temperatures & CPU temperatures. A transient CFD model was validated with experiments. We foresee that these experimental results and the validated CFD model can be used in designing smarter control algorithms as a next step.

Load Balance Based Job Scheduling in Geo-Distributed Clouds

In the wake of rapid development of Internet, more and more people could access it from any places in the world, which leads to the characteristic of geographical distribution of the data. Only one single cloud cannot deal with such data efficiently due to high delay and transmission cost. The geo-distributed clouds can alleviate it. However, because of the varied locations of geo-distributed clouds, how to balance the workloads of geo-distributed clouds is a crucial problem. In this paper, an efficient load balance based job scheduling in geo-distributed clouds is proposed in order to minimize the average waiting time, average response time of jobs and improve the system throughput. First, the clouds are divided into idle or busy state to get the job execution time in each cloud by Logistic regression. Then, the job scheduling problem is modeled as a $$ M/M/C $$ queue in each cloud. In addition, Lagrange Multiplier is given to derive the optimal job arrival rate of each cloud. Finally, the experimental results show that our proposed algorithm in this paper can decrease the average waiting time, average execution time and average response time of jobs, and improve system throughput.

Deadline Scheduling as Restless Bandits

The problem of stochastic deadline scheduling is considered. A constrained Markov decision process model is introduced in which jobs arrive randomly at a service center with stochastic job sizes, rewards, and completion deadlines. The service provider faces random processing costs, convex non-completion penalties, and a capacity constraint that limits the simultaneous processing of jobs. Formulated as a restless multi-armed bandit problem, the stochastic deadline scheduling problem is shown to be indexable. A closed-form expression of the Whittle's index is obtained for the case when the processing costs are constant. An upper bound on the gap-to-optimality for the Whittle's index policy is obtained, and it is shown that the bound converges to zero as the job arrival rate and the number of available processors increase simultaneously to infinity.

Resource-aware virtual machine migration in IoT cloud

Internet of Things (IoT) is a promising paradigm enabling many applications to network together through the internet. A huge volume of data is generated by such IoT applications for computation, storage, and analytics through the infrastructure and platform as service offered by cloud computing. Placement and execution of IoT applications in the cloud is a challenging task. In cloud-based IOT application, sudden changes in the sensing environment cause spikes of data flowing into the cloud. This causes resource starvation in the virtual machine and initiates migration of virtual machine from one physical server to other. However, unplanned migration causes a severe performance degradation to the application running on the cloud. Selection of suitable destination server for the virtual machine during migration is an important concern. This paper proposes a resource-aware virtual machine migration technique. Any sudden change in the sensing environment is observed by clustering the servers. The suitable target server is selected based on the resource utilization and job arrival rate of the destination server. The proposed technique is implemented in cloud platform running analytics on smart agriculture application. The evaluation results show that the proposed method outperforms the state of art techniques in terms of the number of migrations, energy utilization and migration time.

Wages and Employment: The Role of Occupational Skills

How skills acquired in vocational education and training (VET) affect wages and employment is not clear. We develop and estimate a search and matching model for workers with a VET degree. Workers differ in interpersonal, cognitive and manual skills, while firms require and value different combinations of these skills. Assuming that match productivity exhibits worker-job complementarity, we estimate how interpersonal, cognitive and manual skills map into job offers, unemployment and wages. We find that firms value cognitive skills on average almost twice as much as interpersonal and manual skills, and they prize complementarity in cognitive and interpersonal skills. The average return to VET skills in hourly wages is 9%, similar to the returns to schooling. Furthermore, VET appears to improve labour market opportunities through higher job arrival rate and lower job destruction. Workers thus have large benefits from acquiring a VET degree.