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We investigate dynamic algorithms for the interval scheduling problem. Our algorithm runs in amortised time $O(\log n)$ for query operation and $O(d\log^2 n)$ for insertion and removal operations, where $n$ and $d$ are the maximal numbers of intervals and pairwise overlapping intervals respectively. We also show that for a monotonic set, that is when no interval properly contains another interval, the amortised complexity is $O(\log n)$ for both query and update operations. We compare the two algorithms for the monotonic interval sets using experiments.

The problem of attaining energy efficiency in distributed systems is of importance, but a general, non-domain-specific theory of energy-minimal scheduling is far from developed. In this paper, we classify the problems of energy-minimal scheduling and present theoretical foundations of the same. We derive results concerning energy-minimal scheduling of independent jobs in a distributed system with functionally similar machines with different working and idle power ratings. The machines considered in our system can have identical as well as different speeds. If the jobs can be divided into arbitrary parts, we show that the minimum-energy schedule can be generated in linear time and give exact scheduling algorithms. For the cases where jobs are non-divisible, we prove that the scheduling problems are NP-hard and also give approximation algorithms for the same along with their bounds.

The problem of attaining energy efficiency in distributed systems is of importance, but a general, non-domain-specific theory of energy-minimal scheduling is far from developed. In this paper, we classify the problems of energy-minimal scheduling and present theoretical foundations of the same. We derive results concerning energy-minimal scheduling of independent jobs in a distributed system with functionally similar machines with different working and idle power ratings. The machines considered in our system can have identical as well as different speeds. If the jobs can be divided into arbitrary parts, we show that the minimum-energy schedule can be generated in linear time and give exact scheduling algorithms. For the cases where jobs are non-divisible, we prove that the scheduling problems are NP-hard and also give approximation algorithms for the same along with their bounds.

The problem of attaining energy efficiency in distributed systems is of importance, but a general, non-domain-specific theory of energy-minimal scheduling is far from developed. In this paper, we classify the problems of energy-minimal scheduling and present theoretical foundations of the same. We derive results concerning energy-minimal scheduling of independent jobs in a distributed system with functionally similar machines with different working and idle power ratings. The machines considered in our system can have identical as well as different speeds. If the jobs can be divided into arbitrary parts, we show that the minimum-energy schedule can be generated in linear time and give exact scheduling algorithms. For the cases where jobs are non-divisible, we prove that the scheduling problems are NP-hard and also give approximation algorithms for the same along with their bounds.

This paper discusses problems that arose in calendaring cases for an appellate court. The first problem is to distribute cases among panels of judges so as to equalize work loads. We give a worst case analysis of a heuristic for this NP-complete problem. For a given distribution denote by z the heaviest work load. We wish to minimize z. The ratio of the heuristic value z-bar to that of the true optimum z* is shown to be z-bar/z* or = (k + 3)/(k + 2) where all the case weights in (0, (1/k)z*), generalizing a result of Graham on multiprocessor scheduling. Under a restrictive assumption on the case weights, some generalizations of this scheduling problem are solved. Characterizations for feasible calendars and polynomial algorithms for finding these feasible solutions are given. Algorithms are given for choosing an optimal subset of the backlogged cases that can be calendared. (Author)

The Computer Aided Prototyping System (CAPS) and the Prototype system Description Language (PSDL) represent a pioneering effort in the field of software development. Execution Support System (ESS) within the framework of CAPS. The Static Scheduler is one of the critical elements of the ESS which extracts critical timing constraints and precedence constraints for operators and schedules the time-critical operators to guarantee that their timing constraints will be met. The Static Scheduler uses the information of timing constraints and precedence constraints to determine whether a feasible schedule can be built. This construction provides the foundation for handling the execution for Real-Time systems. The goal of this thesis is to provide improved versions of the Static Scheduler.

Intelligent perturbation algorithms for space scheduling optimization are presented in the form of the viewgraphs. The following subject areas are covered: optimization of planning, scheduling, and manifesting; searching a discrete configuration space; heuristic algorithms used for optimization; use of heuristic methods on a sample scheduling problem; intelligent perturbation algorithms are iterative refinement techniques; properties of a good iterative search operator; dispatching examples of intelligent perturbation algorithm and perturbation operator attributes; scheduling implementations using intelligent perturbation algorithms; major advances in scheduling capabilities; the prototype ISF (industrial Space Facility) experiment scheduler; optimized schedule (max revenue); multi-variable optimization; Space Station design reference mission scheduling; ISF-TDRSS command scheduling demonstration; and example task - communications check.

This paper investigates co-scheduling algorithms for processing a set of parallel applications. Instead of executing each application one by one, using a maximum degree of parallelism for each of them, we aim at scheduling several applications concurrently. We partition the original application set into a series of packs, which are executed one by one. A pack comprises several applications, each of them with an assigned number of processors, with the constraint that the total number of processors assigned within a pack does not exceed the maximum number of available processors. The objective is to determine a partition into packs, and an assignment of processors to applications, that minimize the sum of the execution times of the packs. We thoroughly study the complexity of this optimization problem, and propose several heuristics that exhibit very good performance on a variety of workloads, whose application execution times model profiles of parallel scientific codes. We show that co-scheduling leads to to faster workload completion time and to faster response times on average (hence increasing system throughput and saving energy), for significant benefits over traditional scheduling from both the user and system perspectives.

Most classical scheduling formulations assume a fixed and known duration for each activity. In this paper, we weaken this assumption, requiring instead that each duration can be represented by an independent random variable with a known mean and variance. The best solutions are ones which have a high probability of achieving a good makespan. We first create a theoretical framework, formally showing how Monte Carlo simulation can be combined with deterministic scheduling algorithms to solve this problem. We propose an associated deterministic scheduling problem whose solution is proved, under certain conditions, to be a lower bound for the probabilistic problem. We then propose and investigate a number of techniques for solving such problems based on combinations of Monte Carlo simulation, solutions to the associated deterministic problem, and either constraint programming or tabu search. Our empirical results demonstrate that a combination of the use of the associated deterministic problem and Monte Carlo simulation results in algorithms that scale best both in terms of problem size and uncertainty. Further experiments point to the correlation between the quality of the deterministic solution and the quality of the probabilistic solution as a major factor responsible for this success.

This report presents design principles and algorithms for building a real-time scheduler of arrival aircraft based on a first-come-first-served (FCFS) scheduling protocol. The algorithms provide the conceptual and computational foundation for the Traffic Management Advisor (TMA) of the Center/terminal radar approach control facilities (TRACON) automation system, which comprises a set of decision support tools for managing arrival traffic at major airports in the United States. The primary objective of the scheduler is to assign arrival aircraft to a favorable landing runway and schedule them to land at times that minimize delays. A further objective of the scheduler is to allocate delays between high-altitude airspace far away from the airport and low-altitude airspace near the airport. A method of delay allocation is described that minimizes the average operating cost in the presence of errors in controlling aircraft to a specified landing time. This report is a revision of an earlier paper first presented as part of an Advisory Group for Aerospace Research and Development (AGARD) lecture series in September 1995. The authors, during vigorous discussions over the details of this paper, felt it was important to the air-trafficmanagement (ATM) community to revise and extend the original 1995 paper, providing more detail and clarity and thereby allowing future researchers to understand this foundational work as the basis for the TMA's scheduling algorithms.

Motivated by the Quality-of-Service (QoS) buffer management problem, we consider online scheduling of packets with hard deadlines in a finite capacity queue. At any time, a queue can store at most $b \in \mathbb Z^+$ packets. Packets arrive over time. Each packet is associated with a non-negative value and an integer deadline. In each time step, only one packet is allowed to be sent. Our objective is to maximize the total value gained by the packets sent by their deadlines in an online manner. Due to the Internet traffic's chaotic characteristics, no stochastic assumptions are made on the packet input sequences. This model is called a {\em finite-queue model}. We use competitive analysis to measure an online algorithm's performance versus an unrealizable optimal offline algorithm who constructs the worst possible input based on the knowledge of the online algorithm. For the finite-queue model, we first present a deterministic 3-competitive memoryless online algorithm. Then, we give a randomized ($\phi^2 = ((1 + \sqrt{5}) / 2)^2 \approx 2.618$)-competitive memoryless online algorithm. The algorithmic framework and its theoretical analysis include several interesting features. First, our algorithms use (possibly) modified characteristics of packets; these characteristics may not be same as those specified in the input sequence. Second, our analysis method is different from the classical potential function approach.

Due to the current trend towards smaller cells, an increasing number of users of cellular networks reside at the edge between two cells; these users typically receive poor service as a result of the relatively weak signal and strong interference. Coordinated Multi-Point (CoMP) with Joint Transmission (JT) is a cellular networking technique allowing multiple Base Stations (BSs) to jointly transmit to a single user. This improves the users' reception quality and facilitates better service to cell-edge users. We consider a CoMP-enabled network, comprised of multiple BSs interconnected via a backhaul network. We formulate the OFDMA Joint Scheduling (OJS) problem of determining a subframe schedule and deciding if and how to use JT in order to maximize some utility function. We show that the OJS problem is NP-hard. We develop optimal and approximation algorithms for specific and general topologies, respectively. We consider a time dimension and study a queueing model with packet arrivals in which the service rates for each subframe are obtained by solving the OJS problem. We prove that when the problem is formulated with a specific utility function and solved optimally in each subframe, the resulting scheduling policy is throughput-optimal. Via extensive simulations we show that the bulk of the gains from CoMP with JT can be achieved with low capacity backhaul. Moreover, our algorithms distribute the network resources evenly, increasing the inter-cell users' throughput at only a slight cost to the intra-cell users. This is the first step towards a rigorous, network-level understanding of the impact of cross-layer scheduling algorithms on CoMP networks.

In any computing environment, the availability of resources is finite, so effective utilization of resources is very important. To achieve effective management of the available resources in a scalable environment optimal mechanism is required. In order to do this, choosing of scheduling algorithm is important. The scheduling techniques should beselected in such a way that the various user demands are satisfied. In this paper, an overview of different scheduling techniques like cost and energy aware scheduling, cloud based workflow scheduling, an improved ant colony algorithm in cloud computing environment are analysed. S. Saranya Devi | V. Venkatesa Kumar | M. Newlin Rajkumar"Scheduling Algorithms in Cloud Computing - An Extensive Survey" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd5840.pdf  http://www.ijtsrd.com/engineering/electrical-engineering/5840/scheduling-algorithms-in-cloud-computing---an-extensive-survey/s-saranya-devi

Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of evolutionary algorithms for a dynamic variant of a classical combinatorial optimization problem, namely makespan scheduling. We study the model of a strong adversary which is allowed to change one job at regular intervals. Furthermore, we investigate the setting of random changes. Our results show that randomized local search and a simple evolutionary algorithm are very effective in dynamically tracking changes made to the problem instance.

Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of evolutionary algorithms for a dynamic variant of a classical combinatorial optimization problem, namely makespan scheduling. We study the model of a strong adversary which is allowed to change one job at regular intervals. Furthermore, we investigate the setting of random changes. Our results show that randomized local search and a simple evolutionary algorithm are very effective in dynamically tracking changes made to the problem instance.

We have identified clear trade-offs in algorithm design for the scheduling under uncertainty problem that relate to the sources of the uncertainty. We also identified plateaus as a significant barrier to superb performance of local search on scheduling and have studied several canonical discrete optimization problems to discover and model the nature of plateaus. From this, we have developed lower and upper bound predictive models of plateau size in a significant optimization problem: MAXSAT. We also develop new theoretical results on the nature of plateaus in Elementary Landscapes.

Motivated by applications in grid computing and project management, we study multiprocessor scheduling in scenarios where there is uncertainty in the successful execution of jobs when assigned to processors. We consider the problem of multiprocessor scheduling under uncertainty, in which we are given n unit-time jobs and m machines, a directed acyclic graph C giving the dependencies among the jobs, and for every job j and machine i, the probability p_{ij} of the successful completion of job j when scheduled on machine i in any given particular step. The goal of the problem is to find a schedule that minimizes the expected makespan, that is, the expected completion time of all the jobs. The problem of multiprocessor scheduling under uncertainty was introduced by Malewicz and was shown to be NP-hard even when all the jobs are independent. In this paper, we present polynomial-time approximation algorithms for the problem, for special cases of the dag C. We obtain an O(log(n))-approximation for the case of independent jobs, an O(log(m)log(n)log(n+m)/loglog(n+m))-approximation when C is a collection of disjoint chains, an O(log(m)log^2(n))-approximation when C is a collection of directed out- or in-trees, and an O(log(m)log^2(n)log(n+m)/loglog(n+m))-approximation when C is a directed forest.

We study online scheduling problems on a single processor that can be viewed as extensions of the well-studied problem of minimizing total weighted flow time. In particular, we provide a framework of analysis that is derived by duality properties, does not rely on potential functions and is applicable to a variety of scheduling problems. A key ingredient in our approach is bypassing the need for "black-box" rounding of fractional solutions, which yields improved competitive ratios. We begin with an interpretation of Highest-Density-First (HDF) as a primal-dual algorithm, and a corresponding proof that HDF is optimal for total fractional weighted flow time (and thus scalable for the integral objective). Building upon the salient ideas of the proof, we show how to apply and extend this analysis to the more general problem of minimizing $\sum_j w_j g(F_j)$, where $w_j$ is the job weight, $F_j$ is the flow time and $g$ is a non-decreasing cost function. Among other results, we present improved competitive ratios for the setting in which $g$ is a concave function, and the setting of same-density jobs but general cost functions. We further apply our framework of analysis to online weighted completion time with general cost functions as well as scheduling under polyhedral constraints.

We introduce and study a general scheduling problem that we term the Packing Scheduling problem. In this problem, jobs can have different arrival times and sizes; a scheduler can process job $j$ at rate $x_j$, subject to arbitrary packing constraints over the set of rates ($\vec{x}$) of the outstanding jobs. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling. In this paper, we design non-clairvoyant online algorithms for PSP and its special cases -- in this setting, the scheduler is unaware of the sizes of jobs. Our two main results are, 1) a constant competitive algorithm for minimizing total weighted completion time for PSP and 2)a scalable algorithm for minimizing the total flow-time on unrelated machines, which is a special case of PSP.

We obtain fast parallel algorithms for several scheduling problems. Some of the problems considered are: scheduling to minimize the number of tardy jobs; job sequencing with deadlines; scheduling to minimize earliness and tardiness penalties; channel assignment; and minimizing the mean finish time. The shared memory model of parallel computers is used. (Author)

In any computing environment, the availability of resources is finite, so effective utilization of resources is very important. To achieve effective management of the available resources in a scalable environment optimal mechanism is required. In order to do this, choosing of scheduling algorithm is important. The scheduling techniques should beselected in such a way that the various user demands are satisfied. In this paper, an overview of different scheduling techniques like cost and energy aware scheduling, cloud based workflow scheduling, an improved ant colony algorithm in cloud computing environment are analysed. S. Saranya Devi | V. Venkatesa Kumar | M. Newlin Rajkumar"Scheduling Algorithms in Cloud Computing - An Extensive Survey" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd5840.pdf Article URL: http://www.ijtsrd.com/engineering/electrical-engineering/5840/scheduling-algorithms-in-cloud-computing---an-extensive-survey/s-saranya-devi

Modern data centers face new scheduling challenges in optimizing job-level performance objectives, where a significant challenge is the scheduling of highly parallel data flows with a common performance goal (e.g., the shuffle operations in MapReduce applications). Chowdhury and Stoica introduced the coflow abstraction to capture these parallel communication patterns, and Chowdhury et al. proposed effective heuristics to schedule coflows efficiently. In our previous paper, we considered the strongly NP-hard problem of minimizing the total weighted completion time of coflows with release dates, and developed the first polynomial-time scheduling algorithms with O(1)-approximation ratios. In this paper, we carry out a comprehensive experimental analysis on a Facebook trace and extensive simulated instances to evaluate the practical performance of several algorithms for coflow scheduling, including the approximation algorithms developed in our previous paper. Our experiments suggest that simple algorithms provide effective approximations of the optimal, and that the performance of our approximation algorithms is relatively robust, near optimal, and always among the best compared with the other algorithms, in both the offline and online settings.

42 p. 28 cm

42 p. 28 cm

We consider scheduling problems in wireless networks with respect to flexible data rates. That is, more or less data can be transmitted per time depending on the signal quality, which is determined by the signal-to-interference-plus-noise ratio (SINR). Each wireless link has a utility function mapping SINR values to the respective data rates. We have to decide which transmissions are performed simultaneously and (depending on the problem variant) also which transmission powers are used. In the capacity-maximization problem, one strives to maximize the overall network throughput, i.e., the summed utility of all links. For arbitrary utility functions (not necessarily continuous ones), we present an O(log n)-approximation when having n communication requests. This algorithm is built on a constant-factor approximation for the special case of the respective problem where utility functions only consist of a single step. In other words, each link has an individual threshold and we aim at maximizing the number of links whose threshold is satisfied. On the way, this improves the result in [Kesselheim, SODA 2011] by not only extending it to individual thresholds but also showing a constant approximation factor independent of assumptions on the underlying metric space or the network parameters. In addition, we consider the latency-minimization problem. Here, each link has a demand, e.g., representing an amount of data. We have to compute a schedule of shortest possible length such that for each link the demand is fulfilled, that is the overall summed utility (or data transferred) is at least as large as its demand. Based on the capacity-maximization algorithm, we show an O(log^2 n)-approximation for this problem.

This paper presents a Feedback Control real-time Scheduling (FCS) framework for adaptive realtime systems. An advantage of the FCS framework is its use of feedback control theory (rather than ad hoc solutions) as a scientific underpinning. We apply a control theory based methodology to systematically design FCS algorithms to satisfy the transient and steady state performance specifications of real-time systems. In particular, we establish dynamic models of real-time systems and develop performance analyses of FCS algorithms, which are major challenges and key steps for the design of control theory based adaptive real-time systems. We also present a FCS architecture that allows plug-ins of different real-time scheduling policies and QoS optimization algorithms. Based on our framework, we identify different categories of real-time applications where different FCS algorithms should be applied. Performance evaluation results demonstrate that our analytically tuned FCS algorithms provide robust transient and steady state performance guarantees for periodic and aperiodic tasks even when the task execution times vary by as much as 100% from the initial estimate.

This work studies online scheduling algorithms for buffer management, develops new algorithms, and analyzes their performances. Packets arrive at a release time r, with a non-negative weight w and an integer deadline d. At each time step, at most one packet is scheduled. The modified greedy (MG) algorithm is 1.618-competitive for the objective of maximizing the sum of weights of packets sent, assuming agreeable deadlines. We analyze the empirical behavior of MG in a situation with arbitrary deadlines and demonstrate that it is at a disadvantage when frequently preferring maximum weight packets over early deadline ones. We develop the MLP algorithm, which remedies this problem whilst mimicking the behavior of the offline algorithm. Our comparative analysis shows that, although the competitive ratio of MLP is not as good as that of MG, it performs better in practice. We validate this by simulating the behavior of both algorithms under a spectrum of simulated parameter settings. Finally, we propose the design of three additional algorithms, which may help in improving performance in practice.

This work studies online scheduling algorithms for buffer management, develops new algorithms, and analyzes their performances. Packets arrive at a release time r, with a non-negative weight w and an integer deadline d. At each time step, at most one packet is scheduled. The modified greedy (MG) algorithm is 1.618-competitive for the objective of maximizing the sum of weights of packets sent, assuming agreeable deadlines. We analyze the empirical behavior of MG in a situation with arbitrary deadlines and demonstrate that it is at a disadvantage when frequently preferring maximum weight packets over early deadline ones. We develop the MLP algorithm, which remedies this problem whilst mimicking the behavior of the offline algorithm. Our comparative analysis shows that, although the competitive ratio of MLP is not as good as that of MG, it performs better in practice. We validate this by simulating the behavior of both algorithms under a spectrum of simulated parameter settings. Finally, we propose the design of three additional algorithms, which may help in improving performance in practice.

In any computing environment, the availability of resources is finite, so effective utilization of resources is very important. To achieve effective management of the available resources in a scalable environment optimal mechanism is required. In order to do this, choosing of scheduling algorithm is important. The scheduling techniques should beselected in such a way that the various user demands are satisfied. In this paper, an overview of different scheduling techniques like cost and energy aware scheduling, cloud based workflow scheduling, an improved ant colony algorithm in cloud computing environment are analysed. S. Saranya Devi | V. Venkatesa Kumar | M. Newlin Rajkumar"Scheduling Algorithms in Cloud Computing - An Extensive Survey" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd5840.pdf Article URL: http://www.ijtsrd.com/engineering/electrical-engineering/5840/scheduling-algorithms-in-cloud-computing---an-extensive-survey/s-saranya-devi

In any computing environment, the availability of resources is finite, so effective utilization of resources is very important. To achieve effective management of the available resources in a scalable environment optimal mechanism is required. In order to do this, choosing of scheduling algorithm is important. The scheduling techniques should beselected in such a way that the various user demands are satisfied. In this paper, an overview of different scheduling techniques like cost and energy aware scheduling, cloud based workflow scheduling, an improved ant colony algorithm in cloud computing environment are analysed. S. Saranya Devi | V. Venkatesa Kumar | M. Newlin Rajkumar"Scheduling Algorithms in Cloud Computing - An Extensive Survey" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd5840.pdf Article URL: http://www.ijtsrd.com/engineering/electrical-engineering/5840/scheduling-algorithms-in-cloud-computing---an-extensive-survey/s-saranya-devi

Cloud computing is an essential tool for sharing resources across virtual machines, and it relies on scheduling and load balancing to ensure that tasks are assigned to the most appropriate resources. Multiple independent tasks need to be handled by cloud computing, and static and dynamic scheduling plays a crucial role in allocating tasks to the right resources. This is especially important in heterogeneous environments, where algorithms can improve load balancing and enhance cloud computing's efficiency. This paper aims to evaluate and discuss algorithms that can improve load balancing in cloud systems.

Traffic congestion are among the most important issue that a country needs to confront due to increasing volume of vehicles around the world, particularly in the large urban areas. As a result, the requirement begins for modeling and improving traffic management procedures to improve the growing need. In order to address traffic problems in urban areas a smart traffic management method is the need of time. The solution in this paper is found through the dimensions of traffic mass on the roads. The core objective of this paper is to highlight latest techniques algorithm which has been used for scheduling traffic lights and a comparison based on achieved accuracy.

We obtain fast parallel algorithms for several scheduling problems. Some of the problems considered are: scheduling to minimize the number of tardy jobs; job sequencing with deadlines; scheduling to minimize earliness and tardiness penalties; channel assignment; and minimizing the mean finish time. The shared memory model of parallel computers is used. (Author)

Abstract: Scheduling is the process of allocating processes to the CPU in order to optimize some objective function. There are many algorithms used to schedule processes. The Round Robin (RR) CPU scheduling algorithm is one of these algorithms which is effective in time sharing and real time operating systems. It gives reasonable response time. But it suffers from several disadvantages such as high turnaround time, high waiting time and many context switches. There are large numbers of algorithms proposed to enhance the standard Round Robin algorithm. In this paper we present a survey with results analysis that conclude recommendations for an Enriched Round Robin algorithm that ameliorates the performance of average waiting time and average turnaround time. http://www.icgst.com/paper.aspx?pid=P1111744588

Consider an airlift operation which consists of several routes, each having missions which are subject to given time schedules. The aircraft are manned with aircrews that are required to rest for a certain period of time after each leg of a mission. A mission may be continued whenever a rested aircrew is available at the location. Given the number of missions that are needed to be flown on the different routes, and given the schedule timetable that is associated with those missions, we consider the problems: (1) What is the minimum number of crews that are needed to maintain the operation? (2) How many aircrews are needed to be staged at each location? (3) If the number of available aircrews is less than the minimum needed, which legs of what missions may be delayed so that the minimum required number of aircrews is reduced? We will exclude from the analysis the trivial case where the rest period of the aircrews is always less than the period of time for which the aircrafts are delayed. If this is the case, then it is clear that the minimum number of aircrews is equal to the number of missions and all the aircrews must be staged initially at the home base.

We obtain fast parallel algorithms for several scheduling problems. Some of the problems considered are: scheduling to minimize the number of tardy jobs; job sequencing with deadlines; scheduling to minimize earliness and tardiness penalties; channel assignment; and minimizing the mean finish time. The shared memory model of parallel computers is used. (Author)

The Time Warp multiprocessing scheme promises speed-up for object- oriented discrete-event simulation. The Concurrent Processing for Advanced Simulation project has constructed a LISP-based Time Warp system for implementing simulations with many large, complex objects. Since many objects share a single processor, the CPU time allocated to each object must be scheduled. Since object events are not preempted, the authors are scheduling which objects have events process rather than CPU time per object. They developed approaches to scheduling, ranging from a simple round-robin mechanism to complex ones involving queue length. The authors developed ten different scheduling algorithms which they named: Worst Case, Conventional Round Robin, Lowest Local Virtual Time (LVT) First, Priority LVT, Largest Queue Priority, Bradford/Fitch, Anti-Penalty, Queue Anti-Penalty, Queue Cycle, and Positive Infinity. Results show that LVT, anti-messages, rollbacks, returned messages, and anti-reminders are good parameters for scheduling of system resources. Input queue size is also an important factor, but when taken with or without LVT, it does not produce results at good as using LVT alone. The round-robin scheduler was one of the worst performers. The poor performance of the simple round-robin scheduler indicates the advantages of using state information to determine the scheduling order in the Time Warp system. Benchmarks of the schedulers showed that the Anti-Penalty scheduler performed better than the others. The Anti- Penalty algorithm is based on a composite measure of simulation advance rate, flow control, and the appearance of specific message types. Computerized Simulation, Multiprocessors, Scheduling, Algorithms.

This article is from Sensors (Basel, Switzerland) , volume 11 . Abstract As a promising tool for monitoring the physical world, directional sensor networks (DSNs) consisting of a large number of directional sensors are attracting increasing attention. As directional sensors in DSNs have limited battery power and restricted angles of sensing range, maximizing the network lifetime while monitoring all the targets in a given area remains a challenge. A major technique to conserve the energy of directional sensors is to use a node wake-up scheduling protocol by which some sensors remain active to provide sensing services, while the others are inactive to conserve their energy. In this paper, we first address a Maximum Set Covers for DSNs (MSCD) problem, which is known to be NP-complete, and present a greedy algorithm-based target coverage scheduling scheme that can solve this problem by heuristics. This scheme is used as a baseline for comparison. We then propose a target coverage scheduling scheme based on a genetic algorithm that can find the optimal cover sets to extend the network lifetime while monitoring all targets by the evolutionary global search technique. To verify and evaluate these schemes, we conducted simulations and showed that the schemes can contribute to extending the network lifetime. Simulation results indicated that the genetic algorithm-based scheduling scheme had better performance than the greedy algorithm-based scheme in terms of maximizing network lifetime.

This article is from Sensors (Basel, Switzerland) , volume 11 . Abstract As a promising tool for monitoring the physical world, directional sensor networks (DSNs) consisting of a large number of directional sensors are attracting increasing attention. As directional sensors in DSNs have limited battery power and restricted angles of sensing range, maximizing the network lifetime while monitoring all the targets in a given area remains a challenge. A major technique to conserve the energy of directional sensors is to use a node wake-up scheduling protocol by which some sensors remain active to provide sensing services, while the others are inactive to conserve their energy. In this paper, we first address a Maximum Set Covers for DSNs (MSCD) problem, which is known to be NP-complete, and present a greedy algorithm-based target coverage scheduling scheme that can solve this problem by heuristics. This scheme is used as a baseline for comparison. We then propose a target coverage scheduling scheme based on a genetic algorithm that can find the optimal cover sets to extend the network lifetime while monitoring all targets by the evolutionary global search technique. To verify and evaluate these schemes, we conducted simulations and showed that the schemes can contribute to extending the network lifetime. Simulation results indicated that the genetic algorithm-based scheduling scheme had better performance than the greedy algorithm-based scheme in terms of maximizing network lifetime.

We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $ $, along with a profit; the processor wishes to send data between $u$ and $v$. Towards that goal, the processor needs to select a graph network accessible to it and a path connecting $u$ and $v$ within the selected network. The processor requires exclusive access to the chosen path, in order to route the data. Thus, the processors are competing for routes/channels. A feasible solution selects a subset of demands and schedules each selected demand on a graph network accessible to the processor owning the demand; the solution also specifies the paths to use for this purpose. The requirement is that for any two demands scheduled on the same graph network, their chosen paths must be edge disjoint. The goal is to output a solution having the maximum aggregate profit. Prior work has addressed the above problem in a distibuted setting for the special case where all the graph networks are simply paths (i.e, line-networks). Distributed constant factor approximation algorithms are known for this case. The main contributions of this paper are twofold. First we design a distributed constant factor approximation algorithm for the more general case of tree-networks. The core component of our algorithm is a tree-decomposition technique, which may be of independent interest. Secondly, for the case of line-networks, we improve the known approximation guarantees by a factor of 5. Our algorithms can also handle the capacitated scenario, wherein the demands and edges have bandwidth requirements and capacities, respectively.

The allocation of radio resources is one of the most critical functions performed by the Radio Resource Management (RRM) mechanisms in the downlink Long Term Evolution-Advanced (LTE-Advanced). Packet scheduling concerns itself with allocation of these radio resources in an intelligent manner such that system throughput/capacity can be maximized whilst the required multimedia Quality of Service (QoS) is met. Majority of the previous studies of packet scheduling algorithms for LTE-Advanced did not take the effect of channel impairments into account. However, in real world the channel impairments cannot be obliterated completely and have a direct impact on the packet scheduling performance. As such, this work studies the impact of channel impairments on packet scheduling performance in a practical downlink LTE-Advanced. The simulation results obtained demonstrate the efficacy of RM2 scheduling algorithm over other scheduling algorithms in maximizing the system capacity and is more robust on the effect of the cellular channel impairments.

The allocation of processes to processors has long been of interest to engineers. The processor allocation problem considered here assigns multiple applications onto a computing system. With this algorithm researchers could more efficiently examine real-time sensor data like that used by United States Air Force digital signal processing efforts or real-time aerosol hazard detection as examined by the Department of Homeland Security. Different choices for the design of a load balancing algorithm are examined in both the problem and algorithm domains. Evolutionary algorithms are used to find near-optimal solutions. These algorithms incorporate multiobjective coevolutionary and parallel principles to create an effective and efficient algorithm for real-world allocation problems. Three evolutionary algorithms (EA) are developed. The primary algorithm generates a solution to the processor allocation problem. This allocation EA is capable of evaluating objectives in both an aggregate single objective and a Pareto multiobjective manner. The other two EAs are designed for fine turning returned allocation EA solutions. One coevolutionary algorithm is used to optimize the parameters of the allocation algorithm. This meta-EA is parallelized using a coarse-grain approach to improve performance. Experiments are conducted that validate the improved effectiveness of the parallelized algorithm. Pareto multiobjective approach is used to optimize both effectiveness and efficiency objectives. The other coevolutionary algorithm generates difficult allocation problems for testing the capabilities of the allocation EA. The effectiveness of both coevolutionary algorithms for optimizing the allocation EA is examined quantitatively using standard statistical methods. Also the allocation EAs objective tradeoffs are analyzed and compared.

Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. In this paper we focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics, which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, and we delineate circumstances under which they are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.

As an environment-friendly substitute for conventional fuel-powered vehicles, electric vehicles (EVs) and their components have been widely developed and deployed worldwide. The large-scale integration of EVs into power grid brings both challenges and opportunities to the system performance. On one hand, the load demand from EV charging imposes large impact on the stability and efficiency of power grid. On the other hand, EVs could potentially act as mobile energy storage systems to improve the power network performance, such as load flattening, fast frequency control, and facilitating renewable energy integration. Evidently, uncontrolled EV charging could lead to inefficient power network operation or even security issues. This spurs enormous research interests in designing charging coordination mechanisms. A key design challenge here lies in the lack of complete knowledge of events that occur in the future. Indeed, the amount of knowledge of future events significantly impacts the design of efficient charging control algorithms. This article focuses on introducing online EV charging scheduling techniques that deal with different degrees of uncertainty and randomness of future knowledge. Besides, we highlight the promising future research directions for EV charging control.

Bell System Technical Journal, 48: 9. November 1969 pp 2963-2974. Work-Scheduling Algorithms: A Nonprobabilistic Queuing Study (with Possible Application to No. 1 ESS). (Kruskal, Joseph B.)

The link scheduling in wireless multi-hop networks is addressed. Different from most of work that adopt the protocol interference model which merely take consideration of packet collisions, our proposed algorithms use the physical interference model to reflect the aggregated signal to interference and noise ratio (SINR), which is a more accurate abstraction of the real scenario. We first propose a centralized scheduling method based on the Integer Linear Programming (ILP) and resolve it by an approximate solution based on the randomized rounding method. The probability bound of getting a guaranteed approximate factor is given. We then extend the centralized algorithm to a distributed solution, which is favorable in wireless networks. It is proven that with the distributed scheduling method, all links can transmit without interference, and the approximate ratio of the algorithm is also given.

The link scheduling in wireless multi-hop networks is addressed. Different from most of work that adopt the protocol interference model which merely take consideration of packet collisions, our proposed algorithms use the physical interference model to reflect the aggregated signal to interference and noise ratio (SINR), which is a more accurate abstraction of the real scenario. We first propose a centralized scheduling method based on the Integer Linear Programming (ILP) and resolve it by an approximate solution based on the randomized rounding method. The probability bound of getting a guaranteed approximate factor is given. We then extend the centralized algorithm to a distributed solution, which is favorable in wireless networks. It is proven that with the distributed scheduling method, all links can transmit without interference, and the approximate ratio of the algorithm is also given.

In this paper, we focus on batch state estimation for linear systems. This problem is important in applications such as environmental field estimation, robotic navigation, and target tracking. Its difficulty lies on that limited operational resources among the sensors, e.g., shared communication bandwidth or battery power, constrain the number of sensors that can be active at each measurement step. As a result, sensor scheduling algorithms must be employed. Notwithstanding, current sensor scheduling algorithms for batch state estimation scale poorly with the system size and the time horizon. In addition, current sensor scheduling algorithms for Kalman filtering, although they scale better, provide no performance guarantees or approximation bounds for the minimization of the batch state estimation error. In this paper, one of our main contributions is to provide an algorithm that enjoys both the estimation accuracy of the batch state scheduling algorithms and the low time complexity of the Kalman filtering scheduling algorithms. In particular: 1) our algorithm is near-optimal: it achieves a solution up to a multiplicative factor 1/2 from the optimal solution, and this factor is close to the best approximation factor 1/e one can achieve in polynomial time for this problem; 2) our algorithm has (polynomial) time complexity that is not only lower than that of the current algorithms for batch state estimation; it is also lower than, or similar to, that of the current algorithms for Kalman filtering. We achieve these results by proving two properties for our batch state estimation error metric, which quantifies the square error of the minimum variance linear estimator of the batch state vector: a) it is supermodular in the choice of the sensors; b) it has a sparsity pattern (it involves matrices that are block tri-diagonal) that facilitates its evaluation at each sensor set.

This paper considers an energy-efficient packet scheduling problem over quasi-static block fading channels. The goal is to minimize the total energy for transmitting a sequence of data packets under the first-in-first-out rule and strict delay constraints. Conventionally, such design problem is studied under the assumption that the packet transmission rate can be characterized by the classical Shannon capacity formula, which, however, may provide inaccurate energy consumption estimation, especially when the code blocklength is finite. In this paper, we formulate a new energy-efficient packet scheduling problem by adopting a recently developed channel capacity formula for finite blocklength codes. The newly formulated problem is fundamentally more challenging to solve than the traditional one because the transmission energy function under the new channel capacity formula neither can be expressed in closed form nor possesses desirable monotonicity and convexity in general. We analyze conditions on the code blocklength for which the transmission energy function is monotonic and convex. Based on these properties, we develop efficient offline packet scheduling algorithms as well as a rolling-window based online algorithm for real-time packet scheduling. Simulation results demonstrate not only the efficacy of the proposed algorithms but also the fact that the traditional design using the Shannon capacity formula can considerably underestimate the transmission energy for reliable communications.

We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of $2$ and $\min\{m-k+1, \tilde{O}(\sqrt{k})\}$ respectively, matching the approximation ratios of best known polynomial-time \emph{algorithms} (for max-min fairness, the latter claim is true for certain ratios of the number of goods $m$ to people $k$). Our mechanisms are obtained by establishing a polynomial-time approximation-sensitive reduction from the problem of designing approximately optimal {\em mechanisms} for some arbitrary objective ${\cal O}$ to that of designing bi-criterion approximation {\em algorithms} for the same objective ${\cal O}$ plus a linear allocation cost term. Our reduction is itself enabled by extending the celebrated "equivalence of separation and optimization"[GLSS81,KP80] to also accommodate bi-criterion approximations. Moreover, to apply the reduction to the specific problems of makespan and max-min fairness we develop polynomial-time bi-criterion approximation algorithms for makespan minimization with costs and max-min fairness with costs, adapting the algorithms of [ST93], [BD05] and [AS07] to the type of bi-criterion approximation that is required by the reduction.