Completion Time Minimization Problem Research Articles

A theoretical and empirical study of job scheduling in cloud computing environments: the weighted completion time minimization problem with capacitated parallel machines

A theoretical and empirical study of job scheduling in cloud computing environments: the weighted completion time minimization problem with capacitated parallel machines

Multi-UAV Collaborative Sensing and Communication: Joint Task Allocation and Power Optimization

Compared to a single UAV with limited sensing coverage and communication capability, multi-UAV cooperation is able to provide more effective sensing and transmission (S&T) services. Nevertheless, most existing works on multi-UAV sensing mainly focus on mutually exclusive task allocation and independent data transmission, which did not fully exploit the benefit of multi-UAV sensing and communication. Motivated by this, we propose a novel multi-UAV cooperative S&T scheme with replicated sensing task allocation. Although replicated task allocation may sound counter-intuitive, it can actually foster cooperative transmission among multiple UAVs and thus reduce the overall sensing mission completion time. To obtain the optimal task allocation and transmit power of the proposed scheme, a mission completion time minimization problem is formulated. To solve this problem, a necessary condition for replicated sensing task allocation is derived. For the cases of replicated sensing, the considered problem is transformed into a monotonic optimization and is solved by the generic Polyblock algorithm. To efficiently evaluate the mission completion time in each iteration of the Polyblock algorithm, new auxiliary variables are introduced to decouple the otherwise sophisticated joint optimization of transmission time and power. While for the degenerated case of non-replicated sensing, the closed-form expression of the optimal transmission time is derived

Heuristic task scheduling on heterogeneous UAVs: A combinatorial optimization approach

A fleet of unmanned aerial vehicles (UAVs) provide a new and unique type of distributed computing paradigm and platform. This is a distributed computing environment with mobile servers, where a server (i.e., a UAV) moves around to process tasks. Task scheduling for UAVs has several unique characteristics, such as heterogeneity, mobility, and locality. UAVs are heterogeneous in the sense that they have different initial positions, flight speeds, and execution times. While task assignment and flight planning have been studied extensively, there has been little research of task scheduling on heterogeneous UAVs within the framework of combinatorial optimization, i.e., heuristic algorithms for NP-hard problems and their performance evaluation when compared with optimal solutions. In this paper, we take a combinatorial optimization approach to addressing the issues in task scheduling for heterogeneous UAVs. The main contributions are summarized as follows. We define eight combinatorial optimization problems, i.e., four time-centric problems including the completion time minimization problem, the total time minimization problem, the finished tasks maximization with time constraint problem, the reward maximization with time constraint problem; and four distance-centric problems including the longest distance minimization problem, the total distance minimization problem, the finished tasks maximization with distance constraint problem, the reward maximization with distance constraint problem. We prove that all these problems are NP-hard. We develop two efficient and effective heuristic algorithmic frameworks to solve our problems, one for minimization problems and one for maximization problems. We derive lower/upper bounds for the optimal solutions. We evaluate the performance of our heuristic algorithms by comparing their solutions with optimal solutions and show that they are able to produce near-optimal solutions. To the best of the author’s knowledge, this is the first paper which studies task scheduling on heterogeneous UAVs using a combinatorial optimization approach.

Completion time minimization for UAV enabled data collection with communication link constrained

This paper studies unmanned aerial vehicles (UAV) enabled industrial Internet of Things while a UAV dispatched to collect data of low-power ground sensor nodes (SNs) in multi-obstacle environment. The authors aim to minimize the completion time while satisfying the communication link constraints of each SN and obstacle avoidance, data collection requirements etc. To this end, the authors first formulate the completion time minimization problem by jointly optimizing the UAV trajectory and collection sequence of SNs. The problem is difficult to be optimally solved, as it is non-convex. To tackle this problem, the authors first transform the original problem to a Traveling Salesman Problem-like (TSP-like) problem based on a hover point that can naturally satisfy the communication link constraints of data collection. The dynamic programming (DP) algorithm to figure out the order in which the UAV collects each SN, which gives the initial path of the UAV traversing each SN from the beginning point to the end point. Next, the authors consider the general scenarios of data collection tasks where the UAV also communicates while flying. The authors construct an equivalent problem with integer variable constraints for the original problem with indicative function constraints. The authors rewrite the non-convex constraints of the equal problem by introducing slack variables and leveraging the SCA, and add the discrete region threat constraints for the traditional path discretization method. Finally, the simulation results verify the effectiveness of the proposed algorithm under different parameter configurations.

Completion Time Minimization in Fog-RANs Using D2D Communications and Rate-Aware Network Coding

The device-to-device communication-aided fog radio access network, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D2D-aided</i> F-RAN, takes advantage of caching at enhanced remote radio heads (eRRHs) and D2D proximity for improved system performance. For D2D-aided F-RAN, we develop a framework that exploits the cached contents at eRRHs, their transmission rates/powers, and previously received contents by different users to deliver the requesting contents to users with a minimum completion time. Given the intractability of the completion time minimization problem, we formulate it at each transmission by approximating the completion time and decoupling it into two subproblems. In the first subproblem, we minimize the possible completion time in eRRH downlink transmissions, while in the second subproblem, we maximize the number of users to be scheduled on D2D links. We design two theoretical graphs, namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">interference-aware</i> instantly decodable network coding (IA-IDNC) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D2D conflict</i> graphs to reformulate two subproblems as maximum weight clique and maximum independent set problems, respectively. Using these graphs, we heuristically develop joint and coordinated scheduling approaches. Simulation results show that the proposed two approaches achieve a considerable performance gain in terms of the completion time minimization.

Completion Time and Energy Optimization in the UAV-Enabled Mobile-Edge Computing System

Completion time and energy consumption of the unmanned aerial vehicle (UAV) are two important design aspects in UAV-enabled applications. In this article, we consider a UAV-enabled mobile-edge computing (MEC) system for Internet-of-Things (IoT) computation offloading with limited or no common cloud/edge infrastructure. We study the joint design of computation offloading and resource allocation, as well as UAV trajectory for minimization of energy consumption and completion time of the UAV, subject to the IoT devices' task and energy budget constraints. We first consider the UAV energy minimization problem without predetermined completion time, a discretized nonconvex equivalent problem is obtained by using the path discretization technique. An efficient alternating optimization algorithm for the discretized problem is proposed by decoupling it into two subproblems and addressing the two subproblems with successive convex approximation (SCA)-based algorithms iteratively. Subsequently, we focus on the completion time minimization problem, which is nonconvex and challenging to solve. By using the same path discretization approximation model to reformulate problem, a similar alternating optimization algorithm is proposed. Furthermore, we study the Pareto-optimal solution that balances the tradeoff between the UAV energy and completion time. The simulation results are provided to corroborate this article and show that the proposed designs outperform the baseline schemes. Our results unveil the tradeoff between completion time and energy consumption of the UAV for the MEC system, and the proposed solution can provide the performance close to the lower bound.

Energy Efficient Federated Learning Over Wireless Communication Networks

In this paper, the problem of energy efficient transmission and computation resource allocation for federated learning (FL) over wireless communication networks is investigated. In the considered model, each user exploits limited local computational resources to train a local FL model with its collected data and, then, sends the trained FL model to a base station (BS) which aggregates the local FL model and broadcasts it back to all of the users. Since FL involves an exchange of a learning model between users and the BS, both computation and communication latencies are determined by the learning accuracy level. Meanwhile, due to the limited energy budget of the wireless users, both local computation energy and transmission energy must be considered during the FL process. This joint learning and communication problem is formulated as an optimization problem whose goal is to minimize the total energy consumption of the system under a latency constraint. To solve this problem, an iterative algorithm is proposed where, at every step, closed-form solutions for time allocation, bandwidth allocation, power control, computation frequency, and learning accuracy are derived. Since the iterative algorithm requires an initial feasible solution, we construct the completion time minimization problem and a bisection-based algorithm is proposed to obtain the optimal solution, which is a feasible solution to the original energy minimization problem. Numerical results show that the proposed algorithms can reduce up to 59.5% energy consumption compared to the conventional FL method.

Energy-Constrained Completion Time Minimization in UAV-Enabled Internet of Things

Unmanned-aerial-vehicles (UAVs)-enabled wireless communication for Internet-of-Things (IoT) applications has attracted increasing attention. This article studies a UAV-assisted data dissemination system, where a rotary-wing UAV is dispatched to disseminate data to terrestrial IoT devices. We target to minimize the completion time via a joint optimization of the UAV trajectory and transmit power, while considering the indispensable constraints which cover the maximum energy budget, speed, transmit power of the UAV, and data requirement for each IoT device. First, we formulate the UAV data dissemination as a completion time minimization problem. To tackle the nonconvex optimization problem, the original problem is transformed into two subproblems: 1) the trajectory optimization and 2) the transmit power optimization, respectively, by introducing auxiliary variables and leveraging the concave–convex procedure. Then, we develop a joint trajectory and transmit power algorithm via tailoring the successive convex approximation and alternating descent method. We further improve the algorithm by maximizing the throughput instead of minimizing the completion time in the transmit power optimization process. The improved algorithm not only reduces the computational complexity but also enhances the achieved performance. In addition, simulation results demonstrate the superior performance of the proposed algorithms under various parameter configurations.

Efficient Privacy Preserving Data Collection and Computation Offloading for Fog-Assisted IoT

The property of performing data processing near the source of data (i.e., at the edge of the network) enables fog computing that can effectively reduce computation latency, bandwidth and energy consumption, especially for big data network scenarios. For the sake of achieving efficient and secure big sensory data collection in fog-assisted Internet of Things (IoT), this paper proposes an efficient privacy preserving data collection and computation offloading scheme. In the proposed scheme, first, the designed layer-aware fog computing architecture provides effective support for efficient and secure data collection and fog computation offloading. Then the proposed sampling perturbation encryption method protects data privacy against eavesdroppers and active attackers without sacrificing data correlation, and it also facilitates the simultaneous execution of decrypting and decompressing operations on encrypted sampling data. Furthermore, the developed data processing method at fog nodes reduces the amount of redundant data transmissions significantly, and the formulated optimization model for the measurement matrix ensures the high precision of data reconstruction at the end user. Particularly, a completion time minimization problem is formulated for fog computation offloading, and an efficient offloading decision algorithm is developed to find the minimum completion time by determining the optimal offloading proportion with joint optimal allocation of local CPU, external CPU and channel bandwidth resources. Finally, the illustrative results reveal that the proposed scheme is an efficient data collection and computation offloading scheme with a strong privacy preservation property. For example, when the temporal compression ratio is 0.5, the redundant data can be reduced by 65 percent at fog node with a low relative recovery error 0.0139. At the same time when the task size is 9 Mb, the completion time of compression computation task at fog node can be reduced by 14.6 percent compared with other computation offloading method.

Efficient Scheduling of Weighted Coflows in Data Centers

Traditional network resource management mechanisms are mainly flow or packet based. Recently, coflow has been proposed as a new abstraction to capture the communication patterns in a rich set of data parallel applications in data centers. Coflows effectively model the application-level semantics of network resource usage, so high-level optimization goals, such as reducing the transfer latency of applications, can be better achieved by taking coflows as the basic elements in network resource allocation or scheduling. Although efficient coflow scheduling methods have been studied, in this paper, we advocate to schedule weighted coflows as a further step in this direction, where weights are used to express the importances or priorities of different coflows or their corresponding applications. We propose the Weighted Coflow Completion Time (WCCT) minimization problem and a (2-2/n+1)-approximate optimal offline algorithm, where n is the concurrent number of coflows. We then design an information-agnostic online algorithm named IAOA to dynamically schedule coflows according to their weights and the instantaneous network condition. We also design and implement a coflow scheduling system named FlyTransfer, which can use the online algorithm as its scheduling method. We test the performance of FlyTransfer by trace-driven simulations as well as real deployment in openstack. Our evaluation results show that, compared to the latest information-agnostic coflow scheduling algorithms, FlyTransfer can reduce more than 40 percent of the WCCT, and more than 30 percent of the completion time for coflows with above-the-average level of importance. It even outperforms the most efficient clairvoyant coflow scheduling method by reducing around 30 percent WCCT, and 25- 30 percent of the completion time for coflows with above-the-average importance, respectively.

Completion Time Minimization With Path Planning for Fixed-Wing UAV Communications

Unmanned aerial vehicles (UAVs) have attracted increasing attention in wireless communications due to the high mobility. This paper investigates a fixed-wing UAV-to-UAV (U2U) communications system, with the aim of minimizing the information transmission time via proactively designing the UAV paths. First, we propose a general optimization framework for U2U communications, which covers the communication throughput requirement, interference from terrestrial transmitters, UAV maximum/minimum speeds and accelerations, and minimum U2U distance. To tackle the formulated optimization, the communication throughput constraint that contains uncertain locations of terrestrial transmitters is transformed into a deterministic expression with the aid of S-procedure, and the nonlinear equality constraints on the UAV paths are replaced by linear equality constraints with additional positive semidefinite matrix constraints. Then, we develop a path planning algorithm based on the exact penalty method and successive convex approximation. Furthermore, we design a heuristic path planning algorithm that solves the completion time minimization problem by iteratively addressing a series of throughput maximization problems. The proposed heuristic algorithm strikes a good tradeoff between the computational complexity and the achievable performance. Finally, the simulation results are presented to verify the proposed path planning algorithms under various parameter configurations.

Optimal Transmission Policies for Multi-Hop Energy Harvesting Systems

In this paper, we consider a multi-hop energy harvesting (EH) communication system in a full-duplex mode, considering arrival data and harvested energy curves in the source and the relays. Our model covers all possible harvesting profiles by considering a general function (including both continuous and discrete functions). This model includes the EH system with discrete arrival processes as a special case. We investigate the throughput maximization problem considering least utilized energy in the source and relays and find the optimal offline algorithm. We propose a three-step algorithm: 1) solving a point-to-point throughput maximization problem at the source; 2) solving a point-to-point throughput maximization problem at the relay (after applying the solution of first step as the input of this second problem); and 3) minimizing utilized energy in the source. We show this algorithm gives the optimal throughput. In addition, we find the relation between the optimal algorithm for the completion time minimization problem and the proposed algorithm for the throughput maximization problem. Further, for the throughput maximization problem, we propose an online algorithm and show that it is more efficient than the benchmark one (which is a direct application of an existing point-to-point online algorithm to the multi-hop system).

Permutation flowshop manufacturing cell scheduling problems with deteriorating jobs and sequence dependent setup times under dominant machines

This paper investigates permutation flowshop manufacturing cell scheduling problems with deteriorating jobs and sequence dependent setup times under dominant machines. In the proposed models, we need to make joint decisions on part families sequencing and jobs sequencing within each family. To solve the makespan minimization problem, the structural properties of the optimal solutions are derived, based on which an optimization algorithm is developed. Then, we consider the total completion time minimization problem and propose a useful lemma for the optimal solutions. Finally, we discuss two special cases of the problem and propose optimization algorithms to solve them respectively.

Multicast Transmission for Asynchronous Data Requests

This paper considers a two-user asynchronous multicast scenario where both users request the same content at different time instances, and a base station simultaneously serves them with nonorthogonal transmission. To serve the asynchronous requests of the same content, we develop three nonorthogonal transmission schemes. The first scheme serves the asynchronous requests by unicast transmission and the second scheme enables multicast transmission for the asynchronous requests based on interference decoding capability at receiver. The third scheme combines the first and second schemes. For the three proposed schemes, we formulate completion time minimization problems that aim to minimize the time required to complete serving users, while ensuring a given quality constraint of streaming content. For each scheme, the feasibility condition in terms of transmit power and optimal rate control are investigated. In addition, we analytically compare the performance of the proposed schemes, and additionally, propose an opportunistic transmission that opportunistically switches three proposed schemes depending on the channel and power conditions.

Makespan minimization scheduling with ready times, group technology and shortening job processing times

We investigate a group scheduling problem with shortening job processing times on a single machine in which the shortening is proportional-linear shortening and the setup time of a group is fixed. For the maximum completion time (i.e. the makespan) minimization problem with ready times, we show that the general case of the problem can be solved in polynomial time if the number of groups is a given constant. We also prove that some special cases of the problem can be optimally solved by a lower order algorithm respectively.

Complexity of Scheduling with Proportional Deterioration and Release Dates

In this paper, we analyze the computational complexity of single-machine scheduling problems with deteriorating jobs having non-zero release dates. The processing time of each job is a proportional increasing function of its starting time. The objectives are to minimize the total weighted completion time, the number of tardy jobs and the total completion time, respectively. We first show that the total weighted completion time minimization problem and the number of tardy jobs minimization problem are binary NP-hard. Then, we present some optimal properties for the two problems under the restriction that the jobs have identical deteriorating rates. Finally, we show that the total completion time minimization problem with deadline is binary NP-hard, and in the case when the jobs have identical deadlines, agreeable release dates and deterioration rates, it can be solved in \(O(n\log n)\) time.

Optimal Rate Schedules with Data Sharing in Energy Harvesting Communication Systems.

Despite the abundant research on energy-efficient rate scheduling polices in energy harvesting communication systems, few works have exploited data sharing among multiple applications to further enhance the energy utilization efficiency, considering that the harvested energy from environments is limited and unstable. In this paper, to overcome the energy shortage of wireless devices at transmitting data to a platform running multiple applications/requesters, we design rate scheduling policies to respond to data requests as soon as possible by encouraging data sharing among data requests and reducing the redundancy. We formulate the problem as a transmission completion time minimization problem under constraints of dynamical data requests and energy arrivals. We develop offline and online algorithms to solve this problem. For the offline setting, we discover the relationship between two problems: the completion time minimization problem and the energy consumption minimization problem with a given completion time. We first derive the optimal algorithm for the min-energy problem and then adopt it as a building block to compute the optimal solution for the min-completion-time problem. For the online setting without future information, we develop an event-driven online algorithm to complete the transmission as soon as possible. Simulation results validate the efficiency of the proposed algorithm.

Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines

We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.

The Study of Group Scheduling Problems with General Dual-Position-Based Job Processing Times

Scheduling with group technology has been a vivid research area in the past decades. However, group technology with general dual-effect variable processing times needs to be further explored although this kind of group technology plays an important role in some actual manufacturing scenarios. Accordingly, this paper considers group scheduling problems with a kind of general group variable processing times model, where the actual processing time of each job in group is variable due to the dual effect of both the job position and the group position. The objectives of two types of considered problems are to minimize the makespan and the total completion time, respectively. Based on the decomposition analysis, the mathematical logic analysis and the computational complexity proof, it is obtained that the makespan minimization problem and the total completion time minimization problem are both polynomially solvable under the condition that the group number is constant. For three special cases of considered problems, polynomial solving algorithms with lower computational complexity are proposed.

Rate Aware Instantly Decodable Network Codes

This paper addresses the problem of reducing the delivery time of data messages to cellular users using instantly decodable network coding (IDNC) with physical-layer rate awareness. While most of the existing literature on IDNC does not consider any physical layer complications and abstracts the model as equally slotted time for all users, this paper proposes a cross-layer scheme that incorporates the different channel rates of the various users in the decision process of both the transmitted message combinations and the rates with which they are transmitted. The consideration of asymmetric rates for receivers reflects more practical application scenarios and introduces a new tradeoff between the choice of coding combinations for various receivers and the broadcasting rates. The completion time minimization problem in such a scenario is first shown to be intractable. The problem is thus approximated by reducing, at each transmission, the increase of an anticipated version of the completion time. This paper solves the problem by formulating it as a maximum weight clique problem over a newly designed rate-aware IDNC graph. The highest weight clique in the created graph being potentially not unique, this paper further suggests a multi-layer version of the proposed solution to improve the obtained results from the employed completion time approximation. Simulation results indicate that the cross-layer design largely outperforms the uncoded transmissions strategies and the classical IDNC scheme.