Infinite parallel job allocation (extended abstract)

  • Authors:

  • Petra Berenbrink;Artur Czumaj;Tom Friedetzky;Nikita D. Vvedenskaya

  • Affiliations:

  • Dept. of Mathematics & Computer Science, Paderborn University, D-33095 Paderborn, Germany;Department of Computer and Information Science, New Jersey Institute of Technology, University Heights, Newark, NJ;Institut für Informatik, Technische Universität München, D-80290 München, Germany;Institute of Information Transmission Problems, Russian Academy of Science, Moscow 101447, Russia

  • Venue:
  • Proceedings of the twelfth annual ACM symposium on Parallel algorithms and architectures
  • Year:
  • 2000

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Abstract

In recent years, the task of allocating jobs to servers has been studied with the “balls and bins” abstraction. Results in this area exploit the large decrease in maximum load that can be achieved by allowing each job (ball) a little freedom in choosing its destination server (bin).In this paper we examine an infinite and parallel allocation process (see [ABS98]) which is related to the “balls and bins” abstraction. The simple process can be used to model many problems arising in applications like load balancing, data accesses for parallel data servers, hashing, and PRAM simulations.Unfortunately, the parallel allocation process behaves in a highly non-uniform manner which makes its analysis challenging. Even the typically simple question of for which arrival rates the process is stable, is highly non-trivial. In order to cope with this non-uniform behavior we introduce a new sequential process and show (via simulations) that the sequential process models the behavior of the parallel one very accurately. We develop a system of ordinary differential equations in order to describe the behavior of our sequential process and present a thorough analysis of the performance this process. For example, we show that the queue length distribution decreases double-exponentially. Finally, we present simulation results indicating that the solutions to the differential equations very well predict the queue length distribution of our sequential process and the largest injection rate for which it is stable.Summarizing, we can conclude that in all the performance characteristics we have measured experimentally, the parallel and the sequential process are closely related. This indicates that the obtained solution of the differential equations and the results presented above are applicable to the parallel process, too.