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We study the fundamental network capacity of a multi-user wireless downlink under two assumptions: (1) Channels are not explicitly measured and thus instantaneous states are unknown, (2) Channels are modeled as ON/OFF Markov chains. This is an important network model to explore because channel probing may be costly or infeasible in some contexts. In this case, we can use channel memory with ACK/NACK feedback from previous transmissions to improve network throughput. Computing in closed form the capacity region of this network is difficult because it involves solving a high dimension partially observed Markov decision problem. Instead, in this paper we construct an inner and outer bound on the capacity region, showing that the bound is tight when the number of users is large and the traffic is symmetric. For the case of heterogeneous traffic and any number of users, we propose a simple queue-dependent policy that can stabilize the network with any data rates strictly within the inner capacity bound. The stability analysis uses a novel frame-based Lyapunov drift argument. The outer-bound analysis uses stochastic coupling and state aggregation to bound the performance of a restless bandit problem using a related multi-armed bandit system. Our results are useful in cognitive radio networks, opportunistic scheduling with delayed/uncertain channel state information, and restless bandit problems.

Efficient spectrum use in wireless sensor networks through spatial reuse requires effective models of packet reception at the physical layer in the presence of interference. Despite recent progress in analytic and simulations research into worst-case behavior from interference effects, these efforts generally assume geometric path loss and isotropic transmission, assumptions which have not been borne out in experiments. Our paper aims to provide a methodology for grounding theoretical results into wireless interference in experimental reality. We develop a new framework for wireless algorithms in which distance-based path loss is replaced by an arbitrary gain matrix, typically obtained by measurements of received signal strength (RSS). Gain matrices allow for the modeling of complex environments, e.g., with obstacles and walls. We experimentally evaluate the framework in two indoors testbeds with 20 and 60 motes, and confirm superior predictive performance in packet reception rate for a gain matrix model over a geometric distance-based model. At the heart of our approach is a new parameter $\zeta$ called metricity which indicates how close the gain matrix is to a distance metric, effectively measuring the complexity of the environment. A powerful theoretical feature of this parameter is that all known SINR scheduling algorithms that work in general metric spaces carry over to arbitrary gain matrices and achieve equivalent performance guarantees in terms of $\zeta$ as previously obtained in terms of the path loss constant. Our experiments confirm the sensitivity of $\zeta$ to the nature of the environment. Finally, we show analytically and empirically how multiple channels can be leveraged to improve metricity and thereby performance. We believe our contributions will facilitate experimental validation for recent advances in algorithms for physical wireless interference models.

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.)

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 United States Air Force has put an increased emphasis on the timely delivery of precision weapons. Part of this effort has been to us multiple bay aircraft such the B-1B Lancer and B-52 Stratofortress to provide Close Air Support and responsive strikes using 1760 weapons. In order to provide greater flexibility, the aircraft carry heterogeneous payloads which can require deconfiction in order to drop multiple different types of weapons. Current methods of deconfiction and weapon selection are highly crew dependant and work intensive. This research effort investigates the optimization of an algorithm for weapon release which allows the aircraft to perform deconfiction automatically. This reduces crew load and response time in order to deal with time-sensitive targets. The overall problem maps to the Job-Shop Scheduling problem. Optimization of the algorithm is done through the General Multiobjective Parallel Genetic Algorithm (GENMOP). We examine the results from pedagogical experiments and real-world test scenarios in the light of improving decision making. The results are encouraging in that the program proves capable of nding acceptable release schedules, however the solution space is such that applying the program to real world situations is unnecessary. We present visualizations of the schedules which demonstrate these conclusions.

16 p. 28 cm

16 p. 28 cm

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)

42 p. 28 cm

42 p. 28 cm

42 p. 28 cm

42 p. 28 cm

42 p. 28 cm

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.

Wireless sensor networks are normally characterized by resource challenged nodes. Since communication costs the most in terms of energy in these networks, minimizing this overhead is important. We consider minimum length node scheduling in regular multi-hop wireless sensor networks. We present collision-free decentralized scheduling algorithms based on TDMA with spatial reuse that do not use message passing, this saving communication overhead. We develop the algorithms using graph-based k-hop interference model and show that the schedule complexity in regular networks is independent of the number of nodes and varies quadratically with k which is typically a very small number. We follow it by characterizing feasibility regions in the SINR parameter space where the constant complexity continues to hold while simultaneously satisfying the SINR criteria. Using simulation, we evaluate the efficiency of our solution on random network deployments.

It was shown recently that CSMA (Carrier Sense Multiple Access)-like distributed algorithms can achieve the maximal throughput in wireless networks (and task processing networks) under certain assumptions. One important, but idealized assumption is that the sensing time is negligible, so that there is no collision. In this paper, we study more practical CSMA-based scheduling algorithms with collisions. First, we provide a Markov chain model and give an explicit throughput formula which takes into account the cost of collisions and overhead. The formula has a simple form since the Markov chain is "almost" time-reversible. Second, we propose transmission-length control algorithms to approach throughput optimality in this case. Sufficient conditions are given to ensure the convergence and stability of the proposed algorithms. Finally, we characterize the relationship between the CSMA parameters (such as the maximum packet lengths) and the achievable capacity region.

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.

We consider Lagrangian duality based approaches to design and analyze algorithms for online energy-efficient scheduling. First, we present a primal-dual framework. Our approach makes use of the Lagrangian weak duality and convexity to derive dual programs for problems which could be formulated as convex assignment problems. The duals have intuitive structures as the ones in linear programming. The constraints of the duals explicitly indicate the online decisions and naturally lead to competitive algorithms. Second, we use a dual-fitting approach, which also based on the weak duality, to study problems which are unlikely to admit convex relaxations. Through the analysis, we show an interesting feature in which primal-dual gives idea for designing algorithms while the analysis is done by dual-fitting. We illustrate the advantages and the flexibility of the approaches through problems in different setting: from single machine to unrelated machine environments, from typical competitive analysis to the one with resource augmentation, from convex relaxations to non-convex relaxations.

The limited availability and high cost of crew time and scarce resources make optimization of space operations critical. Advances in computer technology coupled with new iterative search techniques permit the near optimization of complex scheduling problems that were previously considered computationally intractable. Described here is a class of search techniques called Intelligent Perturbation Algorithms. Several scheduling systems which use these algorithms to optimize the scheduling of space crew, payload, and resource operations are also discussed.

We examine a set of dynamic scheduling techniques for parallel adaptive algorithms in a distributed computational environment. We consider three basic scheduling approaches: centralized scheduling, which uses a master- slave model of computation; distributed scheduling, which uses local information about processor workload to determine when tasks should be requested from or sent to other processors; and a new approach that we refer to as centralized mediation, that uses aspects of both centralized and distributed scheduling. We use both distributed implementation and simulation to examine the performance and scalability of these three scheduling and simulation to examine the performance and scalability of these three scheduling approaches when applied to a parallel adaptive algorithm for solving the global optimization problem. In these experiments, the new centralized mediation approach appears to provide the best combination of robustness, efficiency, and ease of implementation.

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.

The recent advances in the area of wireless networking present novel opportunities for network operators to expand their services to infrastructure-less wireless systems. Such networks, often referred to as ad-hoc or multi-hop or peer-to-peer networks, require architectures which do not necessarily follow the cellular paradigm. They consist of entirely wireless nodes, mixed and/or mobile, that require multiple hops (and hence relaying by intermediate nodes) to transmit their messages to the desired destinations. The distinguishing features of such all-wireless network architectures give rise to new trade-offs between traditional concerns in wireless communications (such as spectral efficiency, and energy conservation) and the notions of routing, scheduling and resource allocation. The purpose of this work is to identify and study some of these novel issues, propose solutions in the context of network control and evaluate the usual network performance measures as functions of the new trade-offs. To these ends, we address first the problem of routing connection-oriented traffic with energy efficiency in all-wireless multi-hop networks. We take advantage of the flexibility of wireless nodes to transmit at different power levels and define a framework for formulating the problem of session routing from the perspective of energy expenditure. A set of heuristics are developed for determining end-to-end unicast paths with sufficient bandwidth and transceiver resources, in which nodes use local information in order to select their transmission power and bandwidth allocation. We propose a set of metrics that associate each link transmission with a cost and consider both the cases of plentiful and limited bandwidth resources, the latter jointly with a set of channel allocation algorithms.

The recent advances in the area of wireless networking present novel opportunities for network operators to expand their services to infrastructure-less wireless systems. Such networks, often referred to as ad-hoc or multi-hop or peer-to-peer networks, require architectures which do not necessarily follow the cellular paradigm. They consist of entirely wireless nodes, mixed and/or mobile, that require multiple hops (and hence relaying by intermediate nodes) to transmit their messages to the desired destinations. The distinguishing features of such all-wireless network architectures give rise to new trade-offs between traditional concerns in wireless communications (such as spectral efficiency, and energy conservation) and the notions of routing, scheduling and resource allocation. The purpose of this work is to identify and study some of these novel issues, propose solutions in the context of network control and evaluate the usual network performance measures as functions of the new trade-offs. To these ends, we address first the problem of routing connection-oriented traffic with energy efficiency in all-wireless multi-hop networks. We take advantage of the flexibility of wireless nodes to transmit at different power levels and define a framework for formulating the problem of session routing from the perspective of energy expenditure. A set of heuristics are developed for determining end-to-end unicast paths with sufficient bandwidth and transceiver resources, in which nodes use local information in order to select their transmission power and bandwidth allocation. We propose a set of metrics that associate each link transmission with a cost and consider both the cases of plentiful and limited bandwidth resources, the latter jointly with a set of channel allocation algorithms.

Given the rapid increase in traffic, greater demands have been put on high-speed switching systems. Such systems have to simultaneously meet several constraints, e.g., high throughput, low delay and low complexity. This makes it challenging to design an efficient scheduling algorithm, and has consequently drawn considerable research interest. However, previous results either cannot provide a $100\%$ throughput guarantee without a speedup, or require a complex centralized scheduler. In this paper, we design a {\it distributed} $100 \%$ throughput algorithm for crosspoint buffered switches, called DISQUO, with very limited message passing. We prove that DISQUO can achieve $100\%$ throughput for any admissible Bernoulli traffic, with a low time complexity of $O(1)$ per port. To the best of our knowledge, it is the first distributed algorithm that can provide a $100\%$ throughput for a crosspoint buffered switch.

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.

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)

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)

One of the most important computer architecture innovations to appear in the market place during the last ten years is parallel processing on a shared memory multicomputer. This report presents new algorithms for a variety of network models along with empirical analysis on both sequential and parallel computers. An empirical study on the AT and T KORBX system is also presented. This system uses eight processors each of which has vector capability. Our research program objective is to develop and empirically test new parallel algorithms and software for a wide variety of optimization problems. The problems studied this past year include the shortest path problem, the assignment problem, the semi-assignment problem, the transportation problem, and the generalized network problem. Algorithms for all of these models have been developed and empirically tested on a variety of computers. In addition, we worked with the Military Airlift Command to test the AT&T KORBX system located at Scott Air Force Base. (kr)

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)

Book Source: Digital Library of India Item 2015.182200 dc.contributor.author: A K Krishna dc.date.accessioned: 2015-07-07T15:30:59Z dc.date.available: 2015-07-07T15:30:59Z dc.date.digitalpublicationdate: 0008-09-05 dc.identifier.barcode: 1990010086471 dc.identifier.origpath: /rawdataupload/upload/0086/471 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/182200 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 63 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: I I T Kanpur dc.rights: Out_of_copyright dc.source.library: I I T Kanpur dc.subject.classification: Technology dc.subject.classification: Depart Of Industrial And Magement dc.title: Algorithms For Bicriterion And Constrained Scheduling Problems

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.

Scheduling is referring to the process of allocating resources to User Equipment based on scheduling algorithms that is located at the LTE base station. Various algorithms have been proposed as the execution of scheduling algorithm, which represents an open issue in Long Term Evolution (LTE) standard. This paper makes an attempt to study and compare the performance of three well-known uplink schedulers namely, Maximum Throughput (MT), First Maximum Expansion (FME), and Round Robin (RR). The evaluation is considered for a single cell with interference for three flows such as Best effort, Video and VoIP in a pedestrian environment using the LTE-SIM network simulator. The performance evaluation is conducted in terms of system throughput, fairness index, delay and packet loss ratio (PLR). The simulations results show that RR algorithm always reaches the lowest PLR, delivering highest throughput for video and VoIP flows among all those strategies. Thus, RR is the most suitable scheduling algorithm for VoIP and video flows while MT and FME is appropriate for BE flows in LTE networks.

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

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

http://uf.catalog.fcla.edu/uf.jsp?st=UF024458560%26ix=pm%26I=0%26V=D%26pm=1

http://uf.catalog.fcla.edu/uf.jsp?st=UF024458560%26ix=pm%26I=0%26V=D%26pm=1

The back-pressure algorithm is a well-known throughput-optimal algorithm. However, its delay performance may be quite poor even when the traffic load is not close to network capacity due to the following two reasons. First, each node has to maintain a separate queue for each commodity in the network, and only one queue is served at a time. Second, the back-pressure routing algorithm may route some packets along very long routes. In this paper, we present solutions to address both of the above issues, and hence, improve the delay performance of the back-pressure algorithm. One of the suggested solutions also decreases the complexity of the queueing data structures to be maintained at each node.

This paper presents scheduling algorithms for procrastinators, where the speed that a procrastinator executes a job increases as the due date approaches. We give optimal off-line scheduling policies for linearly increasing speed functions. We then explain the computational/numerical issues involved in implementing this policy. We next explore the online setting, showing that there exist adversaries that force any online scheduling policy to miss due dates. This impossibility result motivates the problem of minimizing the maximum interval stretch of any job; the interval stretch of a job is the job's flow time divided by the job's due date minus release time. We show that several common scheduling strategies, including the "hit-the-highest-nail" strategy beloved by procrastinators, have arbitrarily large maximum interval stretch. Then we give the "thrashing" scheduling policy and show that it is a \Theta(1) approximation algorithm for the maximum interval stretch.

We study scheduling problems motivated by recently developed techniques for microprocessor thermal management at the operating systems level. The general scenario can be described as follows. The microprocessor's temperature is controlled by the hardware thermal management system that continuously monitors the chip temperature and automatically reduces the processor's speed as soon as the thermal threshold is exceeded. Some tasks are more CPU-intensive than other and thus generate more heat during execution. The cooling system operates non-stop, reducing (at an exponential rate) the deviation of the processor's temperature from the ambient temperature. As a result, the processor's temperature, and thus the performance as well, depends on the order of the task execution. Given a variety of possible underlying architectures, models for cooling and for hardware thermal management, as well as types of tasks, this scenario gives rise to a plethora of interesting and never studied scheduling problems. We focus on scheduling real-time jobs in a simplified model for cooling and thermal management. A collection of unit-length jobs is given, each job specified by its release time, deadline and heat contribution. If, at some time step, the temperature of the system is t and the processor executes a job with heat contribution h, then the temperature at the next step is (t+h)/2. The temperature cannot exceed the given thermal threshold T. The objective is to maximize the throughput, that is, the number of tasks that meet their deadlines. We prove that, in the offline case, computing the optimum schedule is NP-hard, even if all jobs are released at the same time. In the online case, we show a 2-competitive deterministic algorithm and a matching lower bound.

In a multiprogramming system, multiple processes exist concurrently in main memory. Each process alternates between using a processor and waiting for some event to occur, such as the completion of an I O operation. The processor or processors are kept busy by executing one process while the others wait. The key to multiprogramming is scheduling. CPU scheduling deals with the problem of deciding which of the processes in the ready queue is to be allocated the CPU. By switching the CPU among processor the operating system can make the computer more productive. Scheduling affectes the performance of the system because it determines which processes will wait and which will progress. In this paper, simulation of various scheduling algorithm First Come First Served FCFS , Round Robin RR , Shortest Process Next SPN and Shortest Remaining Time SRT is done over C Daw Khin Po "Simulation of Process Scheduling Algorithms" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd25124.pdf Paper URL: https://www.ijtsrd.com/computer-science/operating-system/25124/simulation-of-process-scheduling-algorithms/daw-khin-po

The aim of power management policies is to reduce the amount of energy consumed by computer systems while maintaining satisfactory level of performance. One common method for saving energy is to simply suspend the system during the idle times. No energy is consumed in the suspend mode. However, the process of waking up the system itself requires a certain fixed amount of energy, and thus suspending the system is beneficial only if the idle time is long enough to compensate for this additional energy expenditure. In the specific problem studied in the paper, we have a set of jobs with release times and deadlines that need to be executed on a single processor. Preemptions are allowed. The processor requires energy L to be woken up and, when it is on, it uses one unit of energy per one unit of time. It has been an open problem whether a schedule minimizing the overall energy consumption can be computed in polynomial time. We solve this problem in positive, by providing an O(n^5)-time algorithm. In addition we provide an O(n^4)-time algorithm for computing the minimum energy schedule when all jobs have unit length.

The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed processing not only on multiple machines, but on multiple clusters. We consider a scheduling problem to minimize weighted average completion time of N jobs on M distributed clusters of parallel machines. In keeping with the scale of the problems motivating this work, we assume that (1) each job is divided into M "subjobs" and (2) distinct subjobs of a given job may be processed concurrently. When each cluster is a single machine, this is the NP-Hard concurrent open shop problem. A clear limitation of such a model is that a serial processing assumption sidesteps the issue of how different tasks of a given subjob might be processed in parallel. Our algorithms explicitly model clusters as pools of resources and effectively overcome this issue. Under a variety of parameter settings, we develop two constant factor approximation algorithms for this problem. The first algorithm uses an LP relaxation tailored to this problem from prior work. This LP-based algorithm provides strong performance guarantees. Our second algorithm exploits a surprisingly simple mapping to the special case of one machine per cluster. This mapping-based algorithm is combinatorial and extremely fast. These are the first constant factor approximations for this problem.

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 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.

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.

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 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.

It is well known that for ergodic channel processes the Generalized Max-Weight Matching (GMWM) scheduling policy stabilizes the network for any supportable arrival rate vector within the network capacity region. This policy, however, often requires the solution of an NP-hard optimization problem. This has motivated many researchers to develop sub-optimal algorithms that approximate the GMWM policy in selecting schedule vectors. One implicit assumption commonly shared in this context is that during the algorithm runtime, the channel states remain effectively unchanged. This assumption may not hold as the time needed to select near-optimal schedule vectors usually increases quickly with the network size. In this paper, we incorporate channel variations and the time-efficiency of sub-optimal algorithms into the scheduler design, to dynamically tune the algorithm runtime considering the tradeoff between algorithm efficiency and its robustness to changing channel states. Specifically, we propose a Dynamic Control Policy (DCP) that operates on top of a given sub-optimal algorithm, and dynamically but in a large time-scale adjusts the time given to the algorithm according to queue backlog and channel correlations. This policy does not require knowledge of the structure of the given sub-optimal algorithm, and with low overhead can be implemented in a distributed manner. Using a novel Lyapunov analysis, we characterize the throughput stability region induced by DCP and show that our characterization can be tight. We also show that the throughput stability region of DCP is at least as large as that of any other static policy. Finally, we provide two case studies to gain further intuition into the performance of DCP.

Many Air Force applications can be modeled as some extension of a pure network problem. These extensions may require additional side constraints, arcs that involve attrition or flow of multiple commodities on a single arc. In all cases, the network models require integer programming model. Since some of these applications demand computer hardware several orders of magnitude faster than the fastest machines available, we have investigated the use of parallelism to increase the computational speed of these algorithms. Very powerful hardware (in terms of millions of floating point operations per second) can be built using many low cost standard chips, all designed to operate in parallel. Our research program objective is to develop and empirically test new serial and parallel algorithms and software for network based models. The problems studied during the past eighteen months include the generalized network problem, the transportation problem, sparse and dense assignment problems, the one-to-one shortest path problem problem, and the singly constrained assignment problem. Algorithms for all of these models have been developed and empirically tested on a variety of sequential and parallel computers.

This document presents a new serial and parallel algorithms for the on-to-one shortest problem. This is the current best algorithms for this problem and we believe that our software implementation is the world's fastest code. Other algorithms for various network models, including the pure network problem, the generalized problem, the multicommodity network problem with a piecewise linear convex cost function are also presented.