Randomized Work Stealing Versus Sharing in Large-Scale Systems With Non-Exponential Job Sizes

Abstract

Work sharing and work stealing are two scheduling paradigms to redistribute work when performing distributed computations. In work sharing, processors attempt to migrate pending jobs to other processors in the hope of reducing response times. In work stealing, on the other hand, underutilized processors attempt to steal jobs from other processors. Both paradigms generate a certain communication overhead and the question addressed in this paper is which of the two reduces the response time the most given that they use the same amount of communication overhead.Prior work presented explicit bounds, for large scale systems, on when randomized work sharing outperforms randomized work stealing in case of Poisson arrivals and exponential job sizes and indicated that work sharing is best when the load is below φ − 1 ≈ 0.6180, with φ being the golden ratio.In this paper we revisit this problem and study the impact of the job size distribution using a mean field model. We present an efficient method to determine the boundary between the regions where sharing or stealing is best for a given job size distribution, as well as bounds that apply to any (phase-type) job size distribution. The main insight is that work stealing benefits significantly from having more variable job sizes and work sharing may become inferior to work stealing for loads as small as 1/2 + for any > 0.

Performance Analysis of Work Stealing in Large-scale Multithreaded Computing

“…More recent work based on mean field models for work stealing and sharing includes [8,15,22,25]. A model for stealing in a network composed of a number of homogeneous clusters and exponential job sizes is presented in [8], where an important difference with prior work lies in the fact that half of the jobs are stolen instead of just one job at a time.…”

“…A model for stealing in a network composed of a number of homogeneous clusters and exponential job sizes is presented in [8], where an important difference with prior work lies in the fact that half of the jobs are stolen instead of just one job at a time. The main motivation for the work presented in [15,22,25] was to provide a more fair comparison between load stealing and sharing strategies. For the more traditional strategies considered in [6,17] the communication overhead of the stealing and sharing strategies is not the same, which made the comparison somewhat biased.…”

“…For the more traditional strategies considered in [6,17] the communication overhead of the stealing and sharing strategies is not the same, which made the comparison somewhat biased. Exponential job sizes were considered in [15,22] for homogeneous and heterogeneous networks and homogeneous networks with non-exponential job sizes were considered in [25].…”

“…We also compare the performance of this system with a system in which only parent jobs can be stolen. Note that in such case jobs are again transferred as a whole and therefore we can make use of the results in [25] by considering the parent job together with its spawned child jobs as a single non-exponential job. The analysis relies on the same overall approach for the parent and child job stealing systems: we define a mean field model and a structured Markov chain and show that the unique fixed point of the mean field model is the steady state of the structured Markov chain.…”

Global Attraction of ODE-based Mean Field Models with Hyperexponential Job Sizes

“…In this example it is possible to show that for λ < 1 the set of ODEs has a unique fixed point that can be computed by determining the invariant distribution of an ergodic asi-Birth-Death Markov chain [32]. Note that the issue of global a raction is not addressed in [32]. Assumption A1 is readily verified.…”