Locally Optimal Load Balancing

This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of adjacent nodes differ by at most $1$. If the graph is a path ($\Delta = 2$), it is easy to solve the fractional version of the problem in $O(L)$ communication rounds, independently of the number of nodes. We show that this is tight, and we show that it is possible to solve also the discrete version of the problem in $O(L)$ rounds in paths. For the general case ($\Delta > 2$), we show that fractional load balancing can be solved in $\operatorname{poly}(L,\Delta)$ rounds and discrete load balancing in $f(L,\Delta)$ rounds for some function $f$, independently of the number of nodes.Comment: 19 pages, 11 figure

Anomalous Relations among Various Performance Objectives

Abstract Distributed computer systems consist of a set of heterogeneous host computers (i.e., nodes) connected by a communication network. A job that arrives at a node may either be processed locally or transferred to another node for remote processing, which we call load balancing. One possible performance objective of load balancing in distributed computer systems is to minimize the overall mean response time. We can characterize analytically the static load balancing policy whereby the mean overall response time is minimized, which we call the overall optimal policy. This policy, however, lacks fairness in the sense that, for example, two jobs arriving at the same node but being forwarded to different nodes may not have the same expected response time. To satisfy fairness among jobs we can consider an individually optimal load balancing policy whereby jobs arriving at the same node have the same (minimum) expected response time regardless of the nodes which process them. Furthermore, we can think of a node optimal load balancing policy whereby the mean response time of jobs arriving at each node is minimum given the decision by the other nodes of which jobs arriving at those nodes are forwarded. We report the existence of some seemingly anomalous phenomena in the mutual relation among the above policies

Using Negotiation to Reduce Redundant Autonomous Mobile Program Movements

Distributed load managers exhibit thrashing where tasks are repeatedly moved between locations due to incomplete global load information. This paper shows that systems of Autonomous Mobile Programs (AMPs) exhibit the same behaviour, identifying two types of redundant movement and terming them greedy effects. AMPs are unusual in that, in place of some external load management system, each AMP periodically recalculates network and program parameters and may independently move to a better execution environment. Load management emerges from the behaviour of collections of AMPs. The paper explores the extent of greedy effects by simulation, and then proposes negotiating AMPs (NAMPs) to ameliorate the problem. We present the design of AMPs with a competitive negotiation scheme (cNAMPs), and compare their performance with AMPs by simulation

Redundant movements in autonomous mobility: experimental and theoretical analysis

<p>Distributed load balancers exhibit thrashing where tasks are repeatedly moved between locations due to incomplete global load information. This paper shows that systems of autonomous mobile programs (AMPs) exhibit the same behaviour, and identifies two types of redundant movement (greedy effect). AMPs are unusual in that, in place of some external load management system, each AMP periodically recalculates network and program parameters and may independently move to a better execution environment. Load management emerges from the behaviour of collections of AMPs.</p> <p>The paper explores the extent of greedy effects by simulating collections of AMPs and proposes negotiating AMPs (NAMPs) to ameliorate the problem. We present the design of AMPs with a competitive negotiation scheme (cNAMPs), and compare their performance with AMPs by simulation. We establish new properties of balanced networks of AMPs, and use these to provide a theoretical analysis of greedy effects.</p&gt

The DUNE-ALUGrid Module

In this paper we present the new DUNE-ALUGrid module. This module contains a major overhaul of the sources from the ALUgrid library and the binding to the DUNE software framework. The main changes include user defined load balancing, parallel grid construction, and an redesign of the 2d grid which can now also be used for parallel computations. In addition many improvements have been introduced into the code to increase the parallel efficiency and to decrease the memory footprint. The original ALUGrid library is widely used within the DUNE community due to its good parallel performance for problems requiring local adaptivity and dynamic load balancing. Therefore, this new model will benefit a number of DUNE users. In addition we have added features to increase the range of problems for which the grid manager can be used, for example, introducing a 3d tetrahedral grid using a parallel newest vertex bisection algorithm for conforming grid refinement. In this paper we will discuss the new features, extensions to the DUNE interface, and explain for various examples how the code is used in parallel environments.Comment: 25 pages, 11 figure