Preemptive stochastic online scheduling on two uniform machines

https://doi.org/10.1016/j.ipl.2008.12.008Get rights and content

Abstract

This paper addresses a stochastic online scheduling problem in which a set of independent jobs are to be processed by two uniform machines whose speeds are 1 and s (s1). Each job has a processing time, which is a random variable with an arbitrary distribution, and all the jobs are arriving overtime, which means that no information of the job is known in advance before its arrival. During the processing, jobs are allowed to be preempted and resumed later. The objective is to minimize the sum of expected weighted completion times. In this paper, the optimal policy, named SMPR, is designed for the single-machine preemptive stochastic scheduling problem where jobs have a common arriving time. Based on SMPR, the online approximative policy-UMPR, is devised for the preemptive stochastic online scheduling on two uniform machines. Then, UMPR is proved to have an approximation factor of 2. Furthermore, it is concluded that UMPR could not have a smaller approximation factor than 2, which means 2 is the approximation ratio of UMPR for the two-uniform-machine scheduling problem.

References (13)

  • D. Chazan et al.

    A note on time sharing

    Journal of Combinatorial Theory

    (1968)
  • M.H. Rothkopf

    Scheduling with random service times

    Management Science

    (1966)
  • J.L. Bruno et al.

    Sequencing tasks with exponential service times to minimize the expected flowtime or makespan

    Journal of the ACM

    (1981)
  • T. Kämpke

    Optimal scheduling of jobs with exponential service times on identical parallel processors

    Operations Research

    (1989)
  • C.-F. Mabel Chou et al.

    On the asymptotic optimality of a simple on-line algorithm for the stochastic single machine weighted completion time problem and its extensions

    Operations Research

    (2006)
  • R.H. Möhring et al.

    Approximation in stochastic scheduling: the power of LP-based priority policies

    Journal of the ACM

    (1999)
There are more references available in the full text version of this article.

Cited by (0)

View full text