Scheduling for Minimum Total Loss Using Service Time Distributions
Journal of the ACM (JACM)
Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan
Journal of the ACM (JACM)
Approximation in stochastic scheduling: the power of LP-based priority policies
Journal of the ACM (JACM)
Models and Algorithms for Stochastic Online Scheduling
Mathematics of Operations Research
Computers and Operations Research
Hi-index | 0.89 |
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(s=1). 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.