Joint computation offloading and parallel scheduling to maximize delay-guarantee in cooperative MEC systems

The growing development of the Internet of Things(IoT)is accelerating the emergence and growth of new IoT services and applications,which will result in massive amounts of data being generated,transmitted and pro-cessed in wireless communication networks.Mobile Edge Computing(MEC)is a desired paradigm to timely process the data from IoT for value maximization.In MEC,a number of computing-capable devices are deployed at the network edge near data sources to support edge computing,such that the long network transmission delay in cloud computing paradigm could be avoided.Since an edge device might not always have sufficient resources to process the massive amount of data,computation offloading is significantly important considering the coop-eration among edge devices.However,the dynamic traffic characteristics and heterogeneous computing capa-bilities of edge devices challenge the offloading.In addition,different scheduling schemes might provide different computation delays to the offloaded tasks.Thus,offloading in mobile nodes and scheduling in the MEC server are coupled to determine service delay.This paper seeks to guarantee low delay for computation intensive applica-tions by jointly optimizing the offloading and scheduling in such an MEC system.We propose a Delay-Greedy Computation Offloading(DGCO)algorithm to make offloading decisions for new tasks in distributed computing-enabled mobile devices.A Reinforcement Learning-based Parallel Scheduling(RLPS)algorithm is further designed to schedule offloaded tasks in the multi-core MEC server.With an offloading delay broadcast mechanism,the DGCO and RLPS cooperate to achieve the goal of delay-guarantee-ratio maximization.Finally,the simulation results show that our proposal can bound the end-to-end delay of various tasks.Even under slightly heavy task load,the delay-guarantee-ratio given by DGCO-RLPS can still approximate 95%,while that given by benchmarked algorithms is reduced to intolerable value.The simulation results are demonstrated the effective-ness of DGCO-RLPS for delay guarantee in MEC.

An SPN analysis method for parallel scheduling in Ad Hoc networks

In this paper, a new analytic method for modeling and evaluating mobile ad hoc networks (MANET) is proposed. Petri nets technique is introduced into MANET and a packet-flow parallel scheduling scheme is presented using Stochastic Petri Nets (SPN). The flowing of tokens is used in graphics mode to characterize dynamical features of sharing a single wireless channel. Through SPN reachability analysis and isomorphic continuous time Markov process equations, some network parameters, such as channel efficiency, one-hop transmission delay etc., can be obtained. Compared with conventional performance evaluation methods, the above parameters are mathematical expressions instead of test results from a simulator.

Parallel scheduling strategy of web-based spatial computing tasks in multi-core environment

In order to improve the concurrent access performance of the web-based spatial computing system in cluster,a parallel scheduling strategy based on the multi-core environment is proposed,which includes two levels of parallel processing mechanisms.One is that it can evenly allocate tasks to each server node in the cluster and the other is that it can implement the load balancing inside a server node.Based on the strategy,a new web-based spatial computing model is designed in this paper,in which,a task response ratio calculation method,a request queue buffer mechanism and a thread scheduling strategy are focused on.Experimental results show that the new model can fully use the multi-core computing advantage of each server node in the concurrent access environment and improve the average hits per second,average I/O Hits,CPU utilization and throughput.Using speed-up ratio to analyze the traditional model and the new one,the result shows that the new model has the best performance.The performance of the multi-core server nodes in the cluster is optimized;the resource utilization and the parallel processing capabilities are enhanced.The more CPU cores you have,the higher parallel processing capabilities will be obtained.

IOPS:computational graph optimization based on inter-operators parallel scheduling

To improve the inference efficiency of convolutional neural networks(CNN),the existing neural networks mainly adopt heuristic and dynamic programming algorithms to realize parallel scheduling among operators.Heuristic scheduling algorithms can generate local optima easily,while the dynamic programming algorithm has a long convergence time for complex structural models.This paper mainly studies the parallel scheduling between operators and proposes an inter-operator parallelism schedule(IOPS)scheduling algorithm that guarantees the minimum similar execution delay.Firstly,a graph partitioning algorithm based on the largest block is designed to split the neural network model into multiple subgraphs.Then,the operators that meet the conditions is replaced according to the defined operator replacement rules.Finally,the optimal scheduling method based on backtracking is used to schedule the computational graph.Network models such as Inception-v3,ResNet-50,and RandWire are selected for testing.The experimental results show that the algorithm designed in this paper can achieve a 1.6×speedup compared with the existing sequential execution methods.

Self-adaptive large neighborhood search algorithm for parallel machine scheduling problems

A self-adaptive large neighborhood search method for scheduling n jobs on m non-identical parallel machines with mul- tiple time windows is presented. The problems＇ another feature lies in oversubscription, namely not all jobs can be scheduled within specified scheduling horizons due to the limited machine capacity. The objective is thus to maximize the overall profits of processed jobs while respecting machine constraints. A first-in- first-out heuristic is applied to find an initial solution, and then a large neighborhood search procedure is employed to relax and re- optimize cumbersome solutions. A machine learning mechanism is also introduced to converge on the most efficient neighborhoods for the problem. Extensive computational results are presented based on data from an application involving the daily observation scheduling of a fleet of earth observing satellites. The method rapidly solves most problem instances to optimal or near optimal and shows a robust performance in sensitive analysis.

A novel hybrid estimation of distribution algorithm for solving hybrid flowshop scheduling problem with unrelated parallel machine

The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.

Rule-based scheduling of multi-stage multi-product batch plants with parallel units

A novel rule-based model for multi-stage multi-product scheduling problem(MMSP)in batch plants with parallel units is proposed.The scheduling problem is decomposed into two sub-problems of order assignment and order sequencing.Firstly,hierarchical scheduling strategy is presented for solving the former sub-problem,where the multi-stage multi-product batch process is divided into multiple sequentially connected single process stages,and then the production of orders are arranged in each single stage by using forward order assignment strategy and backward order assignment strategy respectively according to the feature of scheduling objective.Line-up competition algorithm(LCA)is presented to find out optimal order sequence and order assignment rule,which can minimize total flow time or maximize total weighted process time.Computational results show that the proposed approach can obtain better solutions than those of the literature for all scheduling problems with more than 10 orders.Moreover,with the problem size increasing,the solutions obtained by the proposed approach are improved remarkably.The proposed approach has the potential to solve large size MMSP.

Generalized multiple time windows model based parallel machine scheduling for TDRSS

The scheduling efficiency of the tracking and data relay satellite system（TDRSS）is strictly limited by the scheduling degrees of freedom（DoF）,including time DoF defined by jobs＇ flexible time windows and spatial DoF brought by multiple servable tracking and data relay satellites（TDRSs）.In this paper,ageneralized multiple time windows（GMTW）model is proposed to fully exploit the time and spatial DoF.Then,the improvements of service capability and job-completion probability based on the GMTW are theoretically proved.Further,an asymmetric path-relinking（APR）based heuristic job scheduling framework is presented to maximize the usage of DoF provided by the GMTW.Simulation results show that by using our proposal 11%improvement of average jobcompletion probability can be obtained.Meanwhile,the computing time of the time-to-target can be shorten to 1/9 of the GRASP.

Genetic Algorithm for Scheduling Reentrant Jobs on Parallel Machines with a Remote Server

This paper considers a reentrant scheduling problem on parallel primary machines with a remote server machine, which is required to carry out the setup operation. In this problem, each job has three operations. The first and last operations are performed by the same primary machine, implying the reentrance, and the second operation is processed on the single server machine. The order of jobs is predetermined in our context. The challenge is to assign jobs to the primary machines to minimize the makespan. We develop a genetic algorithm(GA) to solve this problem. Based on a simple strategy of assigning jobs in batches on the parallel primary machines, the standardized random key vector representation is employed to split the jobs into batches. Comparisons among the proposed algorithm, the branch and bound(BB) algorithm and the heuristic algorithm, coordinated scheduling(CS), which is only one heuristic algorithm to solve this problem in the literature, are made on the benchmark data. The computational experiments show that the proposed genetic algorithm outperforms the heuristic CS and the maximum relative improvement rate in the makespan is 1.66%.

A parallel scheduling algorithm for reinforcement learning in large state space

The main challenge in the area of reinforcement learning is scaling up to larger and more complex problems. Aiming at the scaling problem of reinforcement learning, a scalable reinforcement learning method, DCS-SRL, is proposed on the basis of divide-and-conquer strategy, and its convergence is proved. In this method, the learning problem in large state space or continuous state space is decomposed into multiple smaller subproblems. Given a specific learning algorithm, each subproblem can be solved independently with limited available resources. In the end, component solutions can be recombined to obtain the desired result. To ad- dress the question of prioritizing subproblems in the scheduler, a weighted priority scheduling algorithm is proposed. This scheduling algorithm ensures that computation is focused on regions of the problem space which are expected to be maximally productive. To expedite the learning process, a new parallel method, called DCS-SPRL, is derived from combining DCS-SRL with a parallel scheduling architecture. In the DCS-SPRL method, the subproblems will be distributed among processors that have the capacity to work in parallel. The experimental results show that learning based on DCS-SPRL has fast convergence speed and good scalability.

Parallel Machine Scheduling Models with Fuzzy Parameters and Precedence Constraints: A Credibility Approach

A method for modeling the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure is provided. For the given n jobs to be processed on m machines, it is assumed that the processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive, crisp numbers. Based on credibility measure, three parallel machine scheduling problems and a goal-programming model are formulated. Feasible schedules are evaluated not only by their objective values but also by the credibility degree of satisfaction with their precedence constraints. The genetic algorithm is utilized to find the best solutions in a short period of time. An illustrative numerical example is also given. Simulation results show that the proposed models are effective, which can deal with the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure.

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

Currently,energy conservation draws wide attention in industrial manufacturing systems.In recent years,many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach.This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects.In it,the real processing time of jobs is calculated by using their processing speed and normal processing time.To describe this problem in a mathematical way,amultiobjective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated.Furthermore,we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it.In this approach,the multi-verse optimization is adopted to find favorable solutions from the huge solution domain,while the stochastic simulation method is employed to assess them.By conducting comparison experiments on test problems,it can be verified that the developed approach has better performance in coping with the considered problem,compared to two classic multi-objective evolutionary algorithms.

An approximation algorithm for parallel machine scheduling with simple linear deterioration

In this paper, a parallel machine scheduling problem was considered , where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.

An effective estimation of distribution algorithm for parallel litho machine scheduling with reticle constraints

In order to improve the scheduling efficiency of photolithography,bottleneck process of wafer fabrications in the semiconductor industry,an effective estimation of distribution algorithm is proposed for scheduling problems of parallel litho machines with reticle constraints,where multiple reticles are available for each reticle type.First,the scheduling problem domain of parallel litho machines is described with reticle constraints and mathematical programming formulations are put forward with the objective of minimizing total weighted completion time.Second,estimation of distribution algorithm is developed with a decoding scheme specially designed to deal with the reticle constraints.Third,an insert-based local search with the first move strategy is introduced to enhance the local exploitation ability of the algorithm.Finally,simulation experiments and analysis demonstrate the effectiveness of the proposed algorithm.

Optimal online algorithms for scheduling on two identical machines under a grade of service

This work is aimed at investigating the online scheduling problem on two parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels, so each job and machine are labelled with the GoS levels, and each job can be processed by a particular machine only when its GoS level is no less than that of the machine. The goal is to minimize the makespan. For non-preemptive version, we propose an optimal online al-gorithm with competitive ratio 5/3. For preemptive version, we propose an optimal online algorithm with competitive ratio 3/2.

Adaptive subsequence adjustment with evolutionary asymmetric path-relinking for TDRSS scheduling

Due to the limited transmission resources for data relay in the tracking and data relay satellite system （TDRSS）, there are many job requirements in busy days which will be discarded in the conventional job scheduling model. Therefore, the improvement of scheduling efficiency in the TDRSS can not only help to increase the resource utilities, but also to reduce the scheduling failure ratio. A model of nonhomogeneous parallel machines scheduling problems with time window （NPM-TW） is firstly built up for the TDRSS, considering the distinct features of the variable preparation time and the nonhomogeneous transmission rates for different types of antennas on each tracking and data relay satellite （TDRS）. Then, an adaptive subsequence adjustment （ASA） framework with evolutionary asymmetric path-relinking （EvAPR） is proposed to solve this problem, in which an asymmetric progressive crossover operation is involved to overcome the local optima by the conventional job inserting methods. The numerical results show that, compared with the classical greedy randomized adaptive search procedure （GRASP） algorithm, the scheduling failure ratio of jobs can be reduced over 11% on average by the proposed ASA with EvAPR.

Dynamical Artificial Bee Colony for Energy-Efficient Unrelated Parallel Machine Scheduling with Additional Resources and Maintenance

Unrelated parallel machine scheduling problem(UPMSP)is a typical scheduling one and UPMSP with various reallife constraints such as additional resources has been widely studied;however,UPMSP with additional resources,maintenance,and energy-related objectives is seldom investigated.The Artificial Bee Colony(ABC)algorithm has been successfully applied to various production scheduling problems and demonstrates potential search advantages in solving UPMSP with additional resources,among other factors.In this study,an energy-efficient UPMSP with additional resources and maintenance is considered.A dynamical artificial bee colony(DABC)algorithm is presented to minimize makespan and total energy consumption simultaneously.Three heuristics are applied to produce the initial population.Employed bee swarm and onlooker bee swarm are constructed.Computing resources are shifted from the dominated solutions to non-dominated solutions in each swarm when the given condition is met.Dynamical employed bee phase is implemented by computing resource shifting and solution migration.Computing resource shifting and feedback are used to construct dynamical onlooker bee phase.Computational experiments are conducted on 300 instances from the literature and three comparative algorithms and ABC are compared after parameter settings of all algorithms are given.The computational results demonstrate that the new strategies of DABC are effective and that DABC has promising advantages in solving the considered UPMSP.

Parallel Machine Scheduling with Special Jobs

This paper considers parallel machine scheduling with special jobs. Normal jobs can be processed on any of the parallel machines, while the special jobs can only be processed on one machine. The problem is analyzed for various manufacturing conditions and service requirements. The off-line scheduling problem is transformed into a classical parallel machine scheduling problem. The on-line scheduling uses the FCFS （first come, first served）, SWSC （special window for special customers）, and FFFS （first fit, first served） algorithms to satisfy the various requirements. Furthermore, this paper proves that FCFS has a competitive ratio of m, where m is the number of parallel machines, and this bound is asymptotically tight, SWSC has a competitive ratio of 2 and FFFS has a competitive ratio of 3- 2/m, and these bounds are tight.

AN ON-LINE SCHEDULING PROBLEM OF PARALLEL MACHINES WITH COMMON MAINTENANCE TIME

In this paper, the authors consider an on-line scheduling problem of rn （m≥ 3） identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive 1 ratio 4 - 1/m. In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is 10/3.

Fuzzy Scheduling of Coupled Customers toa Queueing Network with Parallel Servers

In this paper we consider a queueing network consisting of two parallel servers and threearrival streams generated by independent Poisson sources. Each server has its own queue and receivescustomers from its own arrival stream. A third arrival stream consists of customers which place resourcedemands on both servers, which are handled separately by each server once the request is made. Eachservice time is independent and exponentially distributed. Each customer in the system pays a holdingcost per unit time. The objective is to dynamically determine the optimal scheduling policy to the thirdstream of conupled customers. based on the state of the system, so as to minimize the average cost. Thismodel is new, and has Policy implications for computer or communication networks. A fuzzy approachis presented to solve this problem. Simulation shows that the approach is efficient and promising.