Expected Processing Time Research Articles

Deep reinforcement learning based adaptive threshold multi-tasks offloading approach in MEC

Offloading tasks and data is an important use case for Mobile Edge Computing (MEC) that benefits a wide variety of mobile applications on different platforms, including autonomous vehicles and smartphones. A moving vehicle may pass through multiple Roadside Units (RSUs) and the MEC servers located within them as it travels. On-board applications generate structured tasks and can offload them to observable servers. However, since the mobile node cannot determine the information of the global server, choosing the best server becomes a key issue. In this paper, we address the problem of the offloading threshold in traditional Optimal Stopping Theory (OST) based decision models that cannot adapt to the environment. We use Deep Q-Network (DQN) to provide the model with the optimal offloading threshold for adaptive environments and propose a DQN-based Adaptive Threshold Multi-task Offloading approach (DQN-ATMOO). This method uses the principle of OST to solve the offloading order decision problem, divides structured tasks into sub-tasks, and executes offloading in sequence, with the goal of maximizing the probability of offloading to the best server and minimizing the total offloading delay. We experimentally compare and evaluate the proposed model using simulated and real datasets. The results show that the proposed model can be effectively implemented on mobile nodes and significantly reduces the total expected processing time.

Joint parallel-machine scheduling and maintenance planning optimisation with deterioration, unexpected breakdowns, and condition-based maintenance

The joint optimisation of production scheduling and maintenance planning can significantly decrease production interruptions (or stoppages) and, simultaneously, improve production stability and enhance the reliability and availability of equipment and machines. This paper studies the joint optimisation of production schedules and CBM plans in a parallel-machine production setting. The machines are subject to deterioration, unexpected breakdowns, and deterioration-based failures. The reliability of the machines is modelled as a multi-state system in which two deterioration thresholds are introduced to initiate maintenance and prevent deterioration-based failures. An integrated optimisation model is proposed to solve this new problem. The proposed model employs Markov chains to formulate machines’ reliability and a matrix-based approach to estimate the expected processing times, energy consumption, and maintenance costs. Then, a mixed-integer programming model is proposed that jointly optimises production schedules and maintenance plans by minimising a weighted sum objective function that includes expected lateness, maintenance, and energy consumption costs. A genetic algorithm (GA) is used to solve the new problem, and extensive computational experiments are performed to test the performance of the proposed GA. The results show the superiority of the proposed GA for all the test problems compared to two well-known metaheuristics.

Elastic Resource Allocation for Coded Distributed Computing Over Heterogeneous Wireless Edge Networks

Coded distributed computing (CDC) has recently emerged to be a promising solution to address the straggling effects in conventional distributed computing systems. By assigning redundant workloads to the computing nodes, CDC can significantly enhance the performance of the whole system. However, since the core idea of CDC is to introduce redundancies to compensate for uncertainties, it may lead to a large amount of wasted energy at the edge nodes. It can be observed that the more redundant workload added, the less impact the straggling effects have on the system. However, at the same time, the more energy is needed to perform redundant tasks. In this work, we develop a novel framework, namely CERA, to elastically allocate computing resources for CDC processes. Particularly, CERA consists of two stages. In the first stage, we model a joint coding and node selection optimization problem to minimize the expected processing time for a CDC task. Since the problem is NP-hard, we propose a linearization approach and a hybrid algorithm to quickly obtain the optimal solutions. In the second stage, we develop a smart online approach based on Lyapunov optimization to dynamically turn off straggling nodes based on their actual performance. As a result, wasteful energy consumption can be significantly reduced with minimal impact on the total processing time. Simulations using real-world datasets have shown that our proposed approach can reduce the system’s total processing time by more than 200% compared to that of the state-of-the-art approach, even when the nodes’ actual performance is not known in advance. Moreover, the results have shown that CERA’s online optimization stage can reduce the energy consumption by up to 37.14% without affecting the total processing time.

Prioritized scheduling technique for healthcare tasks in cloud computing

The Internet-of-things (IoT) plays a significant role in healthcare monitoring, where the IoT Cloud integration introduces many new opportunities for real-time remote monitoring of the patient. Task scheduling is one of the major challenges in cloud environment. Solving that problem reduces delay, missed tasks, and failure rate, and increases the guarantee ratio. This paper proposes a new task scheduling and allocation technique: Prioritized Sorted Task-Based Allocation (PSTBA) for healthcare monitoring implemented in IoT cloud-based architecture. The proposed technique selects the best virtual machine to execute the health task considering multiple factors such as; the wait time of the VM and the Expected processing time (EPT) of the task as well as its criticality. An extensive simulation study is conducted using the CloudSim simulator to evaluate the performance of the proposed technique. The proposed technique is compared to the Sorted Task-Based Allocation (STBA) and FCFS techniques and it reduces the delay by 13.7% and 80.2%, the failure rate by 21% and 37.5%, and increases the guarantee ratio by 2.2% and 4.5% compared to STBA and FCFS, respectively. In analyzing the critical health tasks, the proposed PSTBA has also reduced the critical health tasks missed ratio by 15.7% and 50.9% compared to STBA and FCFS, respectively. The simulation results demonstrate that PSTBA is more effective than the STBA and FCFS techniques in terms of delay, missed critical tasks, guarantee ratio, and failure rate.

Multi-Task Offloading Based on Optimal Stopping Theory in Edge Computing Empowered Internet of Vehicles.

Vehicular edge computing is a new computing paradigm. By introducing edge computing into the Internet of Vehicles (IoV), service providers are able to serve users with low-latency services, as edge computing deploys resources (e.g., computation, storage, and bandwidth) at the side close to the IoV users. When mobile nodes are moving and generating structured tasks, they can connect with the roadside units (RSUs) and then choose a proper time and several suitable Mobile Edge Computing (MEC) servers to offload the tasks. However, how to offload tasks in sequence efficiently is challenging. In response to this problem, in this paper, we propose a time-optimized, multi-task-offloading model adopting the principles of Optimal Stopping Theory (OST) with the objective of maximizing the probability of offloading to the optimal servers. When the server utilization is close to uniformly distributed, we propose another OST-based model with the objective of minimizing the total offloading delay. The proposed models are experimentally compared and evaluated with related OST models using simulated data sets and real data sets, and sensitivity analysis is performed. The results show that the proposed offloading models can be efficiently implemented in the mobile nodes and significantly reduce the total expected processing time of the tasks.

A Hybrid Data-Driven Approach for Forecasting the Characteristics of Production Disruptions and Interruptions

Manufacturing companies sometimes suffer from unexpected production disruptions/interruptions events (DIEs), affecting the production performance and cost. Since DIEs vary in type and cause, predicting the characteristics of their corresponding production downtimes is a challenging task. Although efforts have been devoted to forecast/prevent specific types of DIEs, such as machine-related events, it is still difficult to deal with the uncertainty caused by a combination of production DIEs of various types. Moreover, the absence of a realistic scenario generator incorporating DIEs has been a challenge in production scheduling under uncertainty. This study investigates the potential use of a hybrid data-driven approach in incorporating the uncertainties of a wide range of DIEs. In this approach, a random forest (RF) method and probability distributions are integrated to forecast the DIEs. The study was carried out based on the recorded DIEs in a Canadian company producing assembly parts for automotive industry. The performance of the proposed methodology for forecasting the production DIEs is evaluated by determining the predicted total downtime (TD) in percent of the expected processing time. The proposed hybrid model yields an overall accuracy of 92.82% in predicting the TD, compared to an overall accuracy of 75.64% when a single RF is used for prediction.

Instability of SRPT, SERPT and SJF multiclass queueing networks

We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol. Both of them are reentrant lines with two servers and eight customer classes. The customer service times in our first system are deterministic, yielding an example of an unstable shortest remaining expected processing time (SERPT) network. In the second one, the service times in one customer class are randomized. Both our examples show also system instability under the shortest job first (SJF) discipline. A simulation study of robustness of our results with respect to changes in the customer interarrival and service times is also provided. Our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and in fact cause instability effects. This is in sharp contrast with their satisfactory performance for single-server queues.

Inpatient Discharge Planning Under Uncertainty

Delay in inpatient discharge processes reduces patient satisfaction and increases hospital congestion and length of stay. Further, flow congestion manifests as patient boarding, where new patients awaiting admission are blocked by bed unavailability. Finally, length of stay is extended if the discharge delay incurs an extra overnight stay. These factors are often in conflict, thus, good hospital performance can only be achieved through careful balancing. We formulate the discharge planning problem as a two-stage stochastic program with uncertain discharge processing and bed request times. The model minimizes a combination of discharge lateness, patient boarding, and deviation from preferred discharge times. Patient boarding is integrated by aligning bed requests with bed releases. The model is solved for different instances generated using data from a large hospital in Texas. Stochastic decomposition is compared with the extensive form and the L-shaped algorithm. A shortest expected processing time heuristic is also investigated. Computational experiments indicate that stochastic decomposition outperforms the L-shaped algorithm and the heuristic, with a significantly shorter computational time and small deviation from optimal. The L-shaped method solves only small problems within the allotted time budget. Simulation experiments demonstrate that our model improves discharge lateness and patient boarding compared to current practice.

Data quality-aware task offloading in Mobile Edge Computing: An Optimal Stopping Theory approach

An important use case of the Mobile Edge Computing (MEC) paradigm is task and data offloading. Computational offloading is beneficial for a wide variety of mobile applications on different platforms including autonomous vehicles and smartphones. With the envision deployment of MEC servers along the roads and while mobile nodes are moving and having certain tasks (or data) to be offloaded to edge servers, choosing an appropriate time and an ideally suited MEC server to guarantee the Quality of Service (QoS) is challenging. We tackle the data quality-aware offloading sequential decision making problem by adopting the principles of Optimal Stopping Theory (OST) to minimize the expected processing time. A variety of OST stochastic models and their applications to the offloading decision making problem are investigated and assessed. A performance evaluation is provided using simulation approach and real world data sets together with the assessment of baseline deterministic and stochastic offloading models. The results show that the proposed OST models can significantly minimize the expected processing time for analytics task execution and can be implemented in the mobile nodes efficiently.

Single machine earliness/tardiness scheduling problem with grey processing times and the grey common due date

PurposeThis paper presents a mixed-integer programming model for a single machine earliness/tardiness scheduling problem where the objective is to minimize total earliness/tardiness duration when the uncertainty of parameters such as processing times and due date is coded with grey numbers.Design/methodology/approachGrey theory and grey numbers are used for illustrating the uncertainty of parameters in processing times and common due date, where the objective is to minimize the total earliness/tardiness duration. The paper proposes a 0–1 mathematical model for the problem and an effective heuristic method for the problem by using expected processing times for ordering jobs.FindingsThe uncertainty of the processing times and common due date are encoded with grey numbers and a position-dependent mixed-integer mathematical programming model is proposed for the problem in order to minimize total grey earliness/tardiness duration of jobs having grey processing times and a common due date. By using expected processing times for ranking grey processing times, V-shaped property of the problem and an efficient heuristic method for the problem are proposed. Solutions obtained from the heuristic method show that the heuristic is effective. The experimental study also reveals that while differences between upper and lower bounds of grey processing times decrease, the proposed heuristic's performance decreases.Originality/valueThe grey theory and grey numbers have been rarely used as machine scheduling problems. Therefore, this study provides an important contribution to the literature.

Energy-Efficient Real-Time Multi-Core Assignment Scheme for Asymmetric Multi-Core Mobile Devices

The big.LITTLE architecture has been extensively integrated into smart mobile devices for better performance and higher energy efficiency. However, the desired energy savings obtained by the big.LITTLE architecture is not sufficiently achieved because the LITTLE cores are not fully utilized while running real-time user applications. In this study, an energy efficient big.LITTLE core assignment algorithm is proposed to reduce the energy consumption of the mobile device by utilizing the LITTLE core as much as possible while guaranteeing the real-time performance of the mobile application. By applying the proposed multi-core assignment technique on a real test-bed of an off-the-shelf smartphone, we prove that the proposed technique can improve the energy saving effect while guaranteeing real-time performance. The energy efficiency of the proposed scheme is compared with that of the legacy scheduler in various environments. In addition, we propose a machine learning-based method to predict the expected processing time more accurately for a task before assigning to one of multi-cores. The presented prediction method is expected to reduce the chances of missing a deadline when employed on the proposed multi-core assignment scheme.

Static Routing in Stochastic Scheduling: Performance Guarantees and Asymptotic Optimality

Scheduling problems have a deep and well-developed literature in both operations research and computer science. Stochastic scheduling problems with many jobs are notoriously difficult, and optimal policies may require constant tracking of the elapsed time of all jobs in process. When the processors (or “machines”) are identical, a policy that simply schedules jobs in fixed order of job weight to expected processing time—the WSEPT rule—is asymptotically optimal when the number of jobs is large. Much less understood is the case with specialized (or “unrelated”) machines (i.e., each job’s processing distribution may vary across machines). In “Static Routing in Stochastic Scheduling: Performance Guarantees and Asymptotic Optimality,” Balseiro, Brown, and Chen study stochastic scheduling with unrelated machines. The authors study a simple static routing policy that (i) assigns jobs to machines up front and (ii) schedules the jobs on each machine in the WSEPT order. This static routing policy depends only on job processing times through their expected values and is easy to compute with a single convex optimization problem. The authors explicitly characterize the performance loss of this static routing policy relative to an optimal scheduling policy; this result implies that this static routing policy is asymptotically optimal in the regime of many jobs.

Stochastic analysis of BPMN with time in rewriting logic

A business process is a set of structured activities that provide a certain service or product. Business processes can be modeled using the BPMN standard, and several industrial platforms have been developed for supporting their design, modeling, and simulation. This paper presents a rewriting logic executable specification of BPMN with time and extended with probabilities. Duration times and delays for tasks and flows can be specified as stochastic expressions, while probabilities are associated to various forms of branching behavior in gateways. These quantities enable discrete-event simulation and automatic stochastic verification of properties such as expected processing time, expected synchronization time at merge gateways, and domain-specific quantitative assertions. The mechanization of the stochastic analysis tasks is done with Maude's statistical model checker PVeStA. The approach is illustrated with a running example and further experimental results encompass specifications from the literature. • An executable specification in rewriting logic of a subset of BPMN. • We handle inclusive splits, loops, and unbalanced gateways. • We support stochastic specification of time and branching constructs, and statistical model checking. • We provide automated verification of stochastic properties such as expected processing and synchronization time. • The approach has been validated on several real-world BPMN processes.

Robust allocation of operating rooms: A cutting plane approach to handle lognormal case durations

The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert’s projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the longest expected processing time first (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.

Task scheduling and resource allocation in cloud computing using a heuristic approach

Cloud computing is required by modern technology. Task scheduling and resource allocation are important aspects of cloud computing. This paper proposes a heuristic approach that combines the modified analytic hierarchy process (MAHP), bandwidth aware divisible scheduling (BATS) + BAR optimization, longest expected processing time preemption (LEPT), and divide-and-conquer methods to perform task scheduling and resource allocation. In this approach, each task is processed before its actual allocation to cloud resources using a MAHP process. The resources are allocated using the combined BATS + BAR optimization method, which considers the bandwidth and load of the cloud resources as constraints. In addition, the proposed system preempts resource intensive tasks using LEPT preemption. The divide-and-conquer approach improves the proposed system, as is proven experimentally through comparison with the existing BATS and improved differential evolution algorithm (IDEA) frameworks when turnaround time and response time are used as performance metrics.

Processing Time Ambiguity and Port Competitiveness

Container seaports play an important role in cross‐border logistics as firms increasingly expand their global footprint in sourcing, manufacturing and distribution. Besides convenience of access to hinterland regions, a key metric for a port's attractiveness is its processing time, that is, its ability to clear goods within a consistent, predictable time frame. Due to differences in infrastructure, government regulations, and operating procedures, ports may exhibit different degrees of predictability in processing times: some are more predictable while others are more ambiguous. We study how ambiguity in processing times affects a port's attractiveness under various circumstances. We find that even if a port maintains a consistent expected processing time, increased ambiguity can still affect its attractiveness to firms, although not always negatively. The effect of ambiguity depends on its nature, whether the shipments are time‐sensitive, attitudes toward ambiguity, and trade terms surrounding shipments.

On the n-job, m-machine permutation flow shop scheduling problems with makespan criterion and rework

This paper addresses an n-job, m-machine permutation flow shop scheduling problem (PFSSP) with unlimited intermediate buffers and rework activities. The concept of rework means that processing of a job on a machine may not meet a predefined quality level through its first process. Thus we have a probabilistic cycle of operations for jobs on different machines which is based on two concepts: (1) a failure probability of a job on a machine and, (2) a descent rate that reduces the processing times for rework phase. In this case, the processing times of jobs on machines become random variables with a known probability distribution. The aim of this paper is to examine possible solution approaches for generating the efficient job sequences with the least potential makespan. A wide range of simulation-based approaches are applied to address the proposed problem. These methods contain mathematical formulation, heuristic algorithms, and metaheuristics. The mechanism of the solution approaches is based on firstly using expected processing times to find a job sequence; then evaluating the obtained job sequences by several simulated trials. Using the one-way ANOVA test, these methods have been compared together, and the results show the superiority of metaheuristics, especially simulated annealing, over the other methods

Discretionary Task Ordering: Queue Management in Radiological Services

Work scheduling research typically prescribes task sequences implemented by managers. Yet employees often have discretion to deviate from their prescribed sequence. Using data from 2.4 million radiological diagnoses, we find that doctors prioritize similar tasks (batching) and those tasks they expect to complete faster (shortest expected processing time). Moreover, they exercise more discretion as they accumulate experience. Exploiting random assignment of tasks to doctors’ queues, instrumental variable models reveal that these deviations erode productivity. This productivity decline lessens as doctors learn from experience. Prioritizing the shortest tasks is particularly detrimental to productivity. Actively grouping similar tasks also reduces productivity, in stark contrast to productivity gains from exogenous grouping, indicating deviation costs outweigh benefits from repetition. By analyzing task completion times, our work highlights the trade-offs between the time required to exercise discretion and the potential gains from doing so, which has implications for how discretion over scheduling should be delegated. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2810 . This paper was accepted by Serguei Netessine, operations management.

Stochastic single-machine scheduling with random resource arrival times

Scheduling in an uncertain environment remains a meaningful yet challenging direction of research. In this paper, we consider a new scheduling setting from practical complex business applications, where resources (e.g., raw materials) used for processing jobs arrive randomly, due to reasons such as unstable transportation service caused by extreme weather conditions, unreliable suppliers, unpredictable industrial actions, etc. Further, jobs must be processed one by one and preemption is not allowed. The processing times of jobs are not known but their distribution. We incorporate these factors into a stochastic single-machine scheduling model and examine two different common types of objectives: minimizing total expected weighted completion time and minimizing total expected weighted squared completion time. We derive and prove a natural and intuitive optimal policy for the model with the first objective. Besides, we find that, under some mild conditions, the well-known policy in stochastic scheduling, WSEPT (weighted shortest expected processing time), still holds optimal for achieving either of objectives. The numerical example further supports and illustrates our results, which provide decision-makers insights into tricky uncertain scheduling problems.

Stochastic Single-Machine Scheduling With Learning Effect

Learning is ubiquitous in the modern scheduling environment. While the deterministic scheduling problems with known processing time and learning rate have been extensively studied, limited work exists to address the problems with both learning effect and uncertainty. In this paper, the single-machine scheduling problem with random nominal processing time and/or random job-based learning rate is studied, with the objective of minimizing the expected total flow time and expected makespan. Several optimal policies are obtained: first, the shortest expected processing time is optimal when only the nominal processing time is random; second, when the job-based learning rate is random, the optimal policy can be obtained by solving an assignment problem with random assignment cost. Computational study is conducted to offer insights on the behavior of optimal policy. The expected value of perfect information (EVPI) is calculated as the difference between the expected objective value found by the optimal policy, and the expected objective value with perfect information. EVPI offers a practical way for decision makers to quantify the incentive and benefit of reducing uncertainty for the addressed problem. The results show that the performance of optimal policy will be negatively impacted by high variation of random parameters.