Online Load Balancing on Uniform Machines with Limited Migration

In the problem of online load balancing on uniformly related machines with bounded migration, jobs arrive online one after another and have to be immediately placed on one of a given set of machines without knowledge about jobs that may arrive later on. Each job has a size and each machine has a speed, and the load due to a job assigned to a machine is obtained by dividing the first value by the second. The goal is to minimize the maximum overall load any machine receives. However, unlike in the pure online case, each time a new job arrives it contributes a migration potential equal to the product of its size and a certain migration factor. This potential can be spend to reassign jobs either right away (non-amortized case) or at any later time (amortized case). Semi-online models of this flavor have been studied intensively for several fundamental problems, e.g., load balancing on identical machines and bin packing, but uniformly related machines have not been considered up to now. In the present paper, the classical doubling strategy on uniformly related machines is combined with migration to achieve an $(8/3+\varepsilon)$-competitive algorithm and a $(4+\varepsilon)$-competitive algorithm with $O(1/\varepsilon)$ amortized and non-amortized migration, respectively, while the best known competitive ratio in the pure online setting is roughly $5.828$

Parallelization of a treecode

I describe here the performance of a parallel treecode with individual particle timesteps. The code is based on the Barnes-Hut algorithm and runs cosmological N-body simulations on parallel machines with a distributed memory architecture using the MPI message-passing library. For a configuration with a constant number of particles per processor the scalability of the code was tested up to P=128 processors on an IBM SP4 machine. In the large $P$ limit the average CPU time per processor necessary for solving the gravitational interactions is $\sim 10$ higher than that expected from the ideal scaling relation. The processor domains are determined every large timestep according to a recursive orthogonal bisection, using a weighting scheme which takes into account the total particle computational load within the timestep. The results of the numerical tests show that the load balancing efficiency $L$ of the code is high ($>=90$) up to P=32, and decreases to $L\sim 80$ when P=128. In the latter case it is found that some aspects of the code performance are affected by machine hardware, while the proposed weighting scheme can achieve a load balance as high as $L\sim 90$ even in the large $P$ limit.Comment: 30 pages, 3 tables, 9 figures, accepted for publication in New Astronom

Bi-Criteria Approximation Algorithms for Load Balancing on Unrelated Machines with Costs

We study a generalized version of the load balancing problem on unrelated machines with cost constraints: Given a set of m machines (of certain types) and a set of n jobs, each job j processed on machine i requires p_{i,j} time units and incurs a cost c_{i,j}, and the goal is to find a schedule of jobs to machines, which is defined as an ordered partition of n jobs into m disjoint subsets, in such a way that some objective function of the vector of the completion times of the machines is optimized, subject to the constraint that the total costs by the schedule must be within a given budget B. Motivated by recent results from the literature, our focus is on the case when the number of machine types is a fixed constant and we develop a bi-criteria approximation scheme for the studied problem. Our result generalizes several known results for certain special cases, such as the case with identical machines, or the case with a constant number of machines with cost constraints. Building on the elegant technique recently proposed by Jansen and Maack [K. Jansen and M. Maack, 2019], we construct a more general approach that can be used to derive approximation schemes to a wider class of load balancing problems with constraints

Dynamic load balancing based on live migration of virtual machines: Security threats and effects

Live migration of virtual machines (VMs) is the process of transitioning a VM from one virtual machine monitor (VMM) to another without halting the guest operating system, often between distinct physical machines, has opened new opportunities in computing. It allows a clean separation between hardware and software, and facilitates fault management, load balancing, and low-level system maintenance. Implemented by several existing virtualization products, live migration also aids in aspects such as high availability services, transparent mobility and consolidated management. While virtualization and live migration enable important new functionality, the combination introduces novel security challenges. A virtual machine monitor that incorporates a vulnerable implementation of live migration functionality may expose both the guest and host operating system to attack and result in a compromise of integrity. Given the large and increasing market for virtualization technology, a comprehensive understanding of virtual machine migration security is essential. So the main idea behind this thesis is to create a test environment that is suitable for experimenting and analyzing the security implications in case of exploitation of Live Migration of Virtual Machines. Using Live VM migration for dynamic load balancing or scheduling, this study determines workload hotspots in physical environment and through use of effective Live Migration process; tries to carry out resource profiling. By carrying out effective profiling, this thesis research is able to determine how much of each resource needs to be allocated to a VM. To understand exactly why process migration would not work in such scenarios and better understand Live VM Migration, this thesis tries to provide requisite incites as to which model is most appropriate for automatic load balancing for virtual machine infrastructure based on resource consumption. The security implications of exploiting the process of migration may end in unexpected results or results that are not noticeable. The scope of this thesis research is identifying these results and the causes for them

Multi-processor Scheduling to Minimize Flow Time with epsilon Resource Augmentation

We investigate the problem of online scheduling of jobs to minimize flow time and stretch on m identical machines. We consider the case where the algorithm is given either (1 + ε)m machines or m machines of speed (1 + ε), for arbitrarily small ε \u3e 0. We show that simple randomized and deterministic load balancing algorithms, coupled with simple single machine scheduling strategies such as SRPT (shortest remaining processing time) and SJF (shortest job first), are O(poly(1/ε))-competitive for both flow time and stretch. These are the first results which prove constant factor competitive ratios for flow time or stretch with arbitrarily small resource augmentation. Both the randomized and the deterministic load balancing algorithms are non- migratory and do immediate dispatch of jobs. The randomized algorithm just allocates each incoming job to a random machine. Hence this algorithm is non- clairvoyant, and coupled with SETF (shortest elapsed time first), yields the first non-clairvoyant algorithm which is con- stant competitive for minimizing flow time with arbitrarily small resource augmentation. The deterministic algorithm that we analyze is due to Avrahami and Azar. For this algorithm, we show O(1/ε)-competitiveness for total flow time and stretch, and also for their Lp norms, for any fixed p ≥ 1

Dynamic load balancing strategies in heterogeneous distributed system

Distributed heterogeneous computing is being widely applied to a variety of large size computational problems. This computational environments are consists of multiple het- erogeneous computing modules, these modules interact with each other to solve the prob-lem. Dynamic load balancing in distributed computing system is desirable because it is an important key to establish dependability in a Heterogeneous Distributed Computing Systems (HDCS). Load balancing problem is an optimization problem with exponential solution space. The complexity of dynamic load balancing increases with the size of a HDCS and becomes difficult to solve effectively. The solution to this intractable problem is discussed under different algorithm paradigm.The load submitted to the a HDCS is assumed to be in the form of tasks. Dynamic allocation of n independent tasks to m computing nodes in heterogeneous distributed computing system can be possible through centralized or decentralized control. In central-ized approach,we have formulated load balancing problem considering task and machine heterogeneity as a linear programming problem to minimize the time by which all task completes the execution in makespan.The load balancing problem in HDCS aims to maintain a balanced allocation of tasks while using the computational resources. The system state changes with time on arrival of tasks from the users. Therefore,heterogeneous distributed system is modeled as an M/M/m queue. The task model is represented either as a consistent or an inconsistent expected time to compute (ETC) matrix. A batch mode heuristic has been used to de-sign dynamic load balancing algorithms for heterogeneous distributed computing systems with four different type of machine heterogeneity. A number of experiments have been conducted to study the performance of load balancing algorithms with three different ar-rival rate for the task. A better performance of the algorithms is observed with increasing of heterogeneity in the HDCS.A new codification scheme suitable to simulated annealing and genetic algorithm has been introduced to design dynamic load balancing algorithms for HDCS. These stochastic iterative load balancing algorithms uses sliding window techniques to select a batch of tasks, and allocate them to the computing nodes in the HDCS. The proposed dynamic genetic algorithm based load balancer has been found to be effective, especially in the case of a large number of tasks

Tighter Bounds on the Inefficiency Ratio of Stable Equilibria in Load Balancing Games

In this paper we study the inefficiency ratio of stable equilibria in load balancing games introduced by Asadpour and Saberi [3]. We prove tighter lower and upper bounds of 7/6 and 4/3, respectively. This improves over the best known bounds in problem (19/18 and 3/2, respectively). Equivalently, the results apply to the question of how well the optimum for the $L_2$ -norm can approximate the $L_{\infty}$-norm (makespan) in identical machines scheduling