Interval Scheduling Research Articles

A fairness‐aware distributed dual‐hop heterogeneous half and full‐duplex link scheduling for 6G network

AbstractCurrent network technologies evolve toward the sixth generation of mobile communications (6G) systems. To achieve the performance requirements of high data rate, low latency, and massive connection, full‐duplex (FD) wireless communication is one possible solution to provide high throughput and channel utilization. However, it is difficult to do so for legacy communication nodes. A distributed fairness‐aware full‐duplex dual‐hop link scheduling algorithm, named weighted full duplex (W‐FD), is proposed to achieve the efficient node selection and dynamic relay probing. The scheduling weight that considered traffic load, mutual interference, and response interval is employed to ensure link load balance. A node with a higher scheduling weight in the neighborhood is selected as the link establishment object to build a full‐duplex link. Better than conventional half‐duplex(HD) link scheduling, W‐FD reduces link scheduling interval and ensures the access opportunities for legacy nodes. Simulation result shows that throughput and delay performance are improved. Compared with the existed full‐duplex link scheduling, W‐FD could better reflect the fairness of scheduling in multi‐nodes and asymmetric‐packets networks, and ensure the throughput and delay performance.

Optimising the booking horizon in healthcare clinics considering no-shows and cancellations

Patient no-shows and cancellations are a significant problem to healthcare clinics, as they compromise a clinic's efficiency. Therefore, it is important to account for both no-shows and cancellations into the design of appointment systems. To provide additional empirical evidence on no-show and cancellation behaviour, we assess outpatient clinic data from two healthcare providers in the USA and EU: no-show and cancellation rates increase with the scheduling interval, which is the number of days from the appointment creation to the date the appointment is scheduled for. We show the temporal cancellation behaviour for multiple scheduling intervals is bimodally distributed. To improve the efficiency of clinics at a tactical level of control, we determine the optimal booking horizon such that the impact of no-shows and cancellations through high scheduling intervals is minimised, against a cost of rejecting patients. Where the majority of the literature only includes a fixed no-show rate, we include both a cancellation rate and a time-dependent no-show rate. We propose an analytical queuing model with balking and reneging, to determine the optimal booking horizon. Simulation experiments show that the assumptions of this model are viable. Computational results demonstrate general applicability of our model by case studies of two hospitals.

Intraday multi-objective hierarchical coordinated operation of a multi-energy system

An intraday, multi-objective, hierarchical and coordinated operation scheduling method for a multi-energy system (MES), which uses 15-min and 5-min scheduling intervals for different energy subsystems, is proposed. According to the characteristics of MES and the response time of energy conversion equipment, energy subsystems are dispatched on different dispatch intervals instead of unified dispatch intervals to dispatch energy subsystems. In a case study, the prediction error rate for a load is 5% and 2% when the dispatch interval is 15 min and 5 min, respectively; the prediction error rates for wind and solar energy output are 10% and 5%, respectively. Dispatching different subsystems with different intervals according to their characteristics reduces the impact of source and load uncertainties, which improves energy management. Multi-energy power dispatch considers exergy efficiency and the operation cost to improve the utilization energy efficiency. The Tchebycheff method, which considers the fuzzy entropy weight, is employed to balance the objectives between highest exergy efficiency and lowest operation cost. Numerical studies demonstrate that the operation cost of a multi-objective system is ¥500.8877 higher than that of a system with the objective of lowest operation cost. The exergy efficiency is increased by 3.94%, and the operation cost, which is reduced by ¥1706.9606, is 2.13% lower than that for the objective of highest exergy efficiency. Thus, the proposed method can balance the objectives between highest exergy efficiency and lowest operation cost. These findings provide a multi-dimensional dispatch scheme for dispatchers and highlight the development potential of an MES.

Resource Management in Wireless Networks via Multi-Agent Deep Reinforcement Learning

We propose a mechanism for distributed resource management and interference mitigation in wireless networks using multi-agent deep reinforcement learning (RL). We equip each transmitter in the network with a deep RL agent that receives delayed observations from its associated users, while also exchanging observations with its neighboring agents, and decides on which user to serve and what transmit power to use at each scheduling interval. Our proposed framework enables agents to make decisions simultaneously and in a distributed manner, unaware of the concurrent decisions of other agents. Moreover, our design of the agents' observation and action spaces is scalable, in the sense that an agent trained on a scenario with a specific number of transmitters and users can be applied to scenarios with different numbers of transmitters and/or users. Simulation results demonstrate the superiority of our proposed approach compared to decentralized baselines in terms of the tradeoff between average and $5^{th}$ percentile user rates, while achieving performance close to, and even in certain cases outperforming, that of a centralized information-theoretic baseline. We also show that our trained agents are robust and maintain their performance gains when experiencing mismatches between train and test deployments.

Feasibility interval and sustainable scheduling simulation with CRPD on uniprocessor platform

The use of hardware caches became essential in modern embedded systems to address the speed gap between processor and memory. In such systems, cache-related preemption delay (CRPD) may represent a significant proportion of task execution time. Addressing this delay in scheduling simulation of these systems stays an open and under-examined problem. Assumptions are often made to simplify the computation model used in simulation and capture the worst-case effect. Nevertheless, they can introduce situations in which scheduling simulation is considered not only pessimistic but also non-sustainable. In this article, we discuss the problem and propose a less pessimistic CRPD computation model that allows sustainable scheduling simulation regarding the capacity parameter. With the proposed model, a system that is schedulable with simulated worst-case execution times remains so when these parameters are reduced. These results improve the applicability of scheduling simulation in the early verification stage for systems with caches. Experiments conducted with our CRPD computation model show a 5% to 12% improvement of schedulability task set coverage and a 30% to 50% reduction of preemption cost with regard to existing CRPD computation models. An integration in a scheduling simulator and a performance evaluation are also realized for the proposed model.

Competitive Algorithms for the Online Minimum Peak Appointment Scheduling

This paper describes a fundamental online scheduling problem called the minimum peak appointment scheduling (MPAS) problem. In this problem, there is a sequence of arriving appointments, each with specified required duration. The goal is to schedule the appointments in an online manner and to minimize the resulting peak utilization throughout the scheduling interval. While described as appointment scheduling, the MPAS has far broader applicability that captures other settings. The paper provides a formal modeling framework to analyze the aforementioned MPAS problem. It is shown that the offline version of the MPAS problem is identical to the offline version of the well-known bin packing problem. However, in the online variant, there is additional flexibility regarding how appointments are packed into chairs (bins). The paper describes the first competitive online algorithm to the MPAS problem called the harmonic rematching (HR) algorithm. The analysis shows that the HR algorithm has an asymptotic competitive ratio of 1.5. Considering that the current best lower bound on randomized online algorithms is 1.536, this highlights the fact that the HR algorithm performs better than any bin packing online algorithm in this setting.

Mobility offer allocations in corporate settings

Corporate mobility is often based on a fixed assignment of vehicles to employees. Relaxing this fixation and including alternatives such as public transportation or taxis for business and private trips could increase fleet utilization and foster the use of battery electric vehicles. We introduce the mobility offer allocation problemas the core concept of a flexible booking system for corporate mobility. The problem is equivalent to interval scheduling on dedicated unrelated parallel machines. We show that the problem is NP-hard to approximate within any factor. We describe problem specific conflict graphs for representing and exploring the structure of feasible solutions. A characterization of all maximum cliques in these conflict graphs reveals symmetries which allow to formulate stronger integer linear programming models. We also present an adaptive large neighborhood search based approach which makes use of conflict graphs as well. In a computational study, the approaches are evaluated. It was found that greedy heuristics perform best if very tight run-time requirements are given, a solver for the integer linear programming model performs best on small and medium instances, and the adaptive large neighborhood search performs best on large instances.

Enhanced System Design and Scheduling Strategy for Switches in Time-Sensitive Networking

Time-Sensitive Networking (TSN) is a new set of amendments that guarantee the quality of service (QoS) of time-critical and safety-critical Ethernet applications. The guard band mechanism prevents time-sensitive traffic from colliding with non-time-sensitive traffic, causing potential bandwidth waste. Moreover, most of the existing scheduling strategies only consider Audio Video Bridging (AVB) traffic and Time-Triggered (TT) traffic, resulting in Best Effort (BE) traffic not being scheduled de facto. This article proposes a new system design and scheduling strategy for TSN switches. The size-aware group weighted round robin (SGWRR) strategy is proposed to schedule AVB queues according to subperiods, reducing the average scheduling intervals of the AVB frames. The entire scheduling cycle is divided into a protected slot and an unprotected slot, and dynamic programming is used to minimize guard band waste. An old queue priority (OQP) strategy is also proposed to provide scheduling opportunities for BE queues. A simulation of OMNet++ shows that SGWRR can achieve low average scheduling intervals while improving bandwidth utilization by 5.66% and that OQP can enhance BE scheduling opportunities by 21.9% under our experimental conditions compared with existing methods.

Effect of irrigation scheduling and zinc fertilization on growth and soil chemical properties under irrigated wheat (Triticum aestivum L.) cultivation

A field experiment was conducted to assess the effect of irrigation scheduling and zinc fertilization on growth and yield of wheat. The experiment was conducted at agricultural farm of Institute of Agricultural Sciences, Banaras Hindu University, Varanasi, India during 2014-2015 and 2015-2016, respectively. The treatments consisted of four irrigation scheduling intervals (I1 - CRI + Late Tillering + Flowering, I2- CRI + Late Jointing + Milking, I3- CRI + Flowering + Dough and I3- CRI + Milking + Dough) and five zinc fertilization doses at different stages of crop growth. The results indicated that irrigation scheduling and zinc fertilization significantly influenced plant height, crop growth rate (CGR), ear length and test weight. There was no significant variation in pH, EC, organic carbon and zinc with the irrigation scheduling interval. Application of zinc had significant increase in zinc content in soil. However, there was non-significant effect of irrigation scheduling and zinc fertilization on relative growth rate (RGR), net assimilation rate (NAR). On the basis of findings of two years experimentation, irrigation scheduling at CRI + Late Jointing+ Milking and zinc fertilization @ 10 kg Zn ha-1 as basal + 0.25% ZnSO4 foliar spray at Z 45 + 0.25% spray at Z 71 stages of wheat is recommended for wheat growth.

Application of Dynamically Search Space Squeezed Modified Firefly Algorithm to a Novel Short Term Economic Dispatch of Multi-Generation Systems

The absence of the global best component in the update equation of the conventional firefly algorithm degrades its exploration properties. This research proposes multi-update position criteria to enhance the exploration properties of the conventional firefly technique while including the effect of the global best solution on the movement of the fireflies in the search space of the objective function. Moreover, the dynamic search space squeezing is applied to constrict the movement of the fireflies within the certain limits to avoid their oscillatory movement as the solution approaches towards the global best by determining the optimal trajectory for each firefly. The robustness of the suggested firefly algorithm is tested on a hybrid energy system consisting of thermal, hydroelectric, and Photovoltaic (PV) energy source. The intermittent nature of the PV energy source is explained using fractional integral polynomial model and Auto Regressive Integrated Moving Average (ARIMA) model. The main dispatch problem is successfully computed using both the modified firefly and the simple firefly algorithm by determining the optimal power share of each energy source for different scheduling intervals. The suggested operational strategy reduces the overall generation cost of the system while preserving the various system constraints. Due to the stochastic nature of the meta-heuristic techniques, the two suggested algorithms are compared statistically for different test cases using the independent t-test results. The statistical comparison suggests that the performance of the modified firefly is superior to its conventional counterpart as the evaluation parameters of the modified firefly converge to relatively lower value as compared to the parameters of the simple firefly algorithm.

Techno-economic and environmental assessment of the coordinated operation of regional grid-connected energy hubs considering high penetration of wind power

Nowadays, the high penetration of renewable energy sources (RESs) with non-uniformly distributed patterns has created unprecedented challenges for regional power systems to maintain system flexibility and reliability. These technical challenges obligate power system operators to curtail part of the produced renewable energy at various scheduling intervals. Motivated by these challenges, grid-connected energy hubs are seen as a way forward to boost system flexibility, decrease the rate of renewable power curtailment, and increase energy efficiency. However, simplified models may significantly affect the performance of the grid-connected energy hubs in practice. Hence, this paper proposes a holistic structure to determine the optimal coordinated operation of the grid-connected energy hubs and the regional power system by relying on the high penetration of wind power. In this regard, various fundamental challenges that have not yet been addressed in an integrated manner, including the CO2 emission rate and the amount of curtailed renewable energy along with total operating costs of the integrated energy system, are among the main objectives of the optimization problem. The proposed structure is developed in the form of tractable mixed-integer nonlinear programming (MINLP) problem to handle the day-ahead security-constrained unit commitment (SCUC). The information-gap decision theory (IGDT)-based robust model is used for accurate modeling of wind power uncertainty. The characteristics of the proposed IGDT-based robust SCUC model and its benefits are investigated through several technical case studies conducted on the modified 6-bus and 24-bus test systems. The simulation results validate the effectiveness and feasibility of the proposed structure. According to the obtained results for the 6-bus test system, networked energy hubs can help the system operator to reduce the total operating cost, wind power curtailment cost, and CO2 emission cost by 16.62%, 100%, and 30.44%, respectively, through utilizing up-to-date energy conversion facilities and energy storage systems as well as managing energy demands. It can be seen that the proposed strategy is a very effective step towards achieving a 100% renewable energy system.

Fixed interval scheduling with third‐party machines

AbstractWe study a problem of scheduling n jobs on machines of two types: in‐house machines and third‐party machines. Scheduling on in‐house machines incurs no additional costs, while using third‐party machines implies costs depending on their number and the time of usage. Each job has a fixed time interval for being processed which can be divided and allocated among several machines, as long as there is only one machine processing the job at any time. No machine can process more than one job at a time. Jobs can be rejected, and they are of different importance that is reflected in the weight of each job. The objective is to find a subset of the jobs and the number of third‐party machines for any period of time so that the accepted jobs can be feasibly scheduled, the total weight of the accepted jobs is maximized, and the total machine usage costs does not exceed a given upper bound. We also study a similar problem in which the objective is to maximize the total time at which at least one job is processed. Both problems are encountered in situations in which certain activities with given start and completion times have to be serviced by human operators. Examples are air traffic control and the monitoring safe vehicle unloading. Other examples are the employment of subcontractors in agriculture, construction or transportation. We will present NP‐hardness proofs, polynomial and pseudo‐polynomial optimal algorithms and an approximation algorithm for these problems and their special cases. These problems admit graph‐theoretical interpretations associated with finding independent sets and a proper vertex coloring in interval graphs.

Quantifying accommodated domain of wind power for flexible look-ahead unit commitment

Properly scheduling flexible regulation resources plays a critical role in reliable operation of the power systems with high penetration of wind power. However, it remains an open question as to how to decide an operation guideline for this system to avoid the security violation and shortage of flexible ramping capacities (FRC). Amongst, it is crucial to determine the wind power injections that the system can accommodate by carefully considering FRC requirement from the whole scheduling interval. In this paper, the concept of accommodated domain of wind power (ADWP) is proposed as a metric for quantifying flexibility and an operational guideline. On this basis, two approaches for flexible look-ahead unit commitment (LAUC) are presented: Three-stage interval optimization approach, by which the largest ADWP is obtained and its corresponding operating cost is also optimized; and scenario-based stochastic optimization approach is used to minimize the overall cost, so as to obtain the most economical ADWP. Test results of IEEE 30-bus and IEEE 118-bus systems show that the proposed approaches for LAUC can effectively handle the ramping requirements and reduce the overall cost.

Multi-objective home appliance scheduling with implicit and interactive user satisfaction modelling

Residential consumers desire to minimize electricity bills while maximizing comfort by appropriate appliance scheduling. The conflicting nature of the objectives facilitates a multi-objective formulation that can provide a set of trade-off schedules enabling better decision making. In literature, user preference or comfort regarding each device at each time instance is obtained explicitly. In addition, scheduling interval of 1-hour is considered because reducing scheduling interval to 1 or 5 min drastically increases – (1) the dimensionality of search space and complicates the search process, and (2) the number of time instances for which the user has to explicitly provide the preference resulting in human fatigue. However, it is essential to schedule the devices at lower scheduling intervals to precisely-estimate the electricity consumption due to the presence of high power devices such as microwave that operate for shorter intervals (<5 min). In this work, we employ an efficient and scalable multi-objective evolutionary algorithm to solve the scheduling problem. In addition, the user preference is implicitly estimated from the past usage patterns obtained using energy disaggregation. And, if the estimated user preference deviates from the user expectation then the user can modify preference using weights referred to as priority weights. The novel implicit user satisfaction modeling and interactive customization through priority weights makes the proposed work a standalone approach suitable for any user. Experimental results and analysis for various user priorities and scheduling intervals (ranging from 1-minute to 1-hour) proves that the proposed framework is able to provide generalized schedules.

Primal-dual analysis for online interval scheduling problems

Online interval scheduling problems consider scheduling a sequence of jobs on machines to maximize the total reward. Various approaches and algorithms have been proposed for different problem formulations. This paper provides a primal-dual approach to analyze algorithms for online interval scheduling problems. This primal-dual technique can be used for both stochastic and adversarial job sequences, and hence, is universally and generally applicable. We use strong duality and complementary slackness conditions to derive exact algorithms for scheduling stochastic equal-length job sequences on a single machine. We use weak duality to obtain upper bounds for the optimal reward for scheduling stochastic equal-length job sequences on multiple machines and C-benevolent job sequences on a single machine.

An Exact Method and Ant Colony Optimization for Single Machine Scheduling Problem With Time Window Periodic Maintenance

This paper considers a time window periodic maintenance strategy with different duration windows and job scheduling activities in a single machine environment. The aim is to minimize the number of tardy jobs through the integration of production scheduling and periodic maintenance intervals. A mixed-integer linear programming model (MILP) is proposed to optimize small-sized test instances. Furthermore, an ant colony optimization (ACO) algorithm is developed to solve larger sized test instances. Subsequently, to measure the efficiency of the solutions obtained by ACO, Moore's algorithm is also developed to benchmark with ACO. To test the efficiency and the effectiveness of the ACO algorithm, a set of data for small and large sized problems was generated in which several parameters were adopted and then ten replicates were solved for each combination. The small sized instances were solved by the MILP. Then, the results obtained showed that the proposed ACO was able to obtain the exact solutions within reasonable CPU times, thus, it outperformed the CPLEX solver with respect to CPU. The large sized instances were solved by the Moore's algorithm and compared to ACO. Then, the results obtained showed that the ACO outperforms Moore's algorithm for all the instances tested. It can be concluded that the developed ACOis very efficient and effective in solving the problem considered in this paper.

Adaptive Scheduling Algorithm Based on CPI and Impact of Tasks for Multifunction Radar

An adaptive scheduling algorithm is proposed based on both the coherent processing interval (CPI) and impact of tasks for multifunction radar under multiple targets conditions, especially under full load. For conventional task scheduling algorithms, the scheduling interval is fixed and the impact of tasks is not taken into consideration. In the proposed algorithm, CPI is taken as the pace to set the task parameters so that the scheduling interval could be changed dynamically, and the model of task loss and the model of temporal margin are built with respect to the impact between tasks. In addition, the notion of temporal margin is proposed to reflect the effect of the current task on the following tasks. Simulation experiments show that, compared with the earliest deadline first algorithm (EDF) and the high priority and earliest deadline first algorithm (HPEDF), the proposed algorithm could greatly improve the performance of multifunction radar in aspects of time utilization ratio, the number of found targets and temporal margin.

Interval partition-based feedrate scheduling with axial drive constraints for five-axis spline toolpaths

The feedrate scheduling has received much attention recently because it is one of the most important tasks in the CNC (computer numerical control) spline interpolator which performs better than conventional linear interpolator in both machining smoothness and efficiency. It is acknowledged that the feedrate scheduling of five-axis machine tools under axial drive constraints is extremely challenging due to the complex-coupled motion relationship between five axes and tool tip/orientation. Existing methods mainly schedule five-axis feedrate with the time-optimal purpose, i.e., planning the feedrate as high as possible provided the drive constraints are not exceeded. However, this kind of methods will result in a frequent time-varying feedrate profile, and this doubtlessly goes against with the feed-motion stability. To deal with this problem, this paper proposes an interval partition-based five-axis feedrate scheduling method with the purpose of balancing feed-motion efficiency and stability, under the constraints of axial drive parameters in terms of velocity, acceleration, and jerk. To accomplish this purpose, the integral toolpath is partitioned into non-sensitive (NS), semi-sensitive (SS), and full-sensitive (FS) intervals, according to the relation between required and limited axial feed parameters. The constant speed is scheduled in each FS interval, and the smooth variable speed is scheduled in NS and SS intervals; thus, the feed-motion stability can be ensured without too much reduction of the feed-motion efficiency. Example tests are conducted to illustrate the application of the proposed approach, and it is shown from the illustration results that the proposed method can surely balance the feed-motion efficiency and stability of the five-axis spline toolpaths, under the axial drive constraints.

Online interval scheduling to maximize total satisfaction

The interval scheduling problem is one variant of the scheduling problem. In this paper, we propose a novel variant of the interval scheduling problem, whose definition is as follows: given jobs are specified by their release times, deadlines and profits. An algorithm must start a job at its release time on one of m identical machines, and continue processing until its deadline on the machine to complete the job. All the jobs must be completed and the algorithm can obtain the profit of a completed job as a user's satisfaction. It is possible to process more than one job at a time on one machine. The profit of a job is distributed uniformly between its release time and deadline, that is its interval, and the profit gained from a subinterval of a job decreases in reverse proportion to the number of jobs whose intervals intersect with the subinterval on the same machine. The objective of our variant is to maximize the total profit of completed jobs.This formulation is naturally motivated by best-effort requests and responses to them, which appear in many situations. In best-effort requests and responses, the total amount of available resources for users is always invariant and the resources are equally shared with every user. We study online algorithms for this problem. Specifically, we show that for the case where the profits of jobs are arbitrary, there does not exist an algorithm whose competitive ratio is bounded. Then, we consider the case in which the profit of each job is equal to its length, that is, the time interval between its release time and deadline. For this case, we prove that for m=2 and m≥3, the competitive ratios of a greedy algorithm are at most 4/3 and at most 3, respectively. Also, for each m≥2, we show a lower bound on the competitive ratio of any deterministic algorithm.

Real-Time Economic Dispatch by Accommodating Implications of Uncertain Renewable Energy Resources

The integration of considerable renewable energy resources in power grids has imposed high variability in the net load demand to be seen by conventional generating stations. The real-time economic dispatch (RTED) of modern power systems must consider minute-to-minute variability in the net load demand on the station during a scheduling interval of 5-15 min. The existing methods therefore may not explicitly handle economic implications of power system. This paper proposes a new method for RTED while fully addressing variability in power generation from renewable energy resources and load demand. The method suggests mean PFs for committed generators by conducting (off-line) economic dispatch for each subinterval of 1 min. Mean PFs are evaluated only once, that is just at the beginning of scheduling interval and will continued throughout the interval. This reduces complexity and dimensionality of the proposed method. The simulation results on a standard test bench validate economic competence of proposed approach over that conventional one.