Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan

Bruno, John; Downey, Peter; Frederickson, Greg N.

doi:10.1145/322234.322242

Cited by 113 publications

(83 citation statements)

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“…On the other hand, it reduces to the nonpreemptive shortest expected processing time (Sept) policy when the hazard rate is increasing. The optimality of this static policy, Sept, has been shown earlier for exponentially distributed processing times by Glazebrook [11], Weiss and Pinedo [42], and Bruno et al [2]. In the case when processing times are not drawn from a distribution with monotone hazard rates, Coffman et al [6] have shown that this policy is not optimal, even if all processing times follow the same two-point distribution and even if we deal with only two processors.…”

Section: Previous Workmentioning

confidence: 72%

“…If processing times are exponentially distributed and release dates are absent, F-Gipp coincides with the preemptive Wsept rule. As mentioned above, this classical policy is optimal if all weights are equal (Glazebrook [11], Weiss and Pinedo [42], Bruno et al [2]) or, more generally, if they are agreeable (Kämpke [13]). If there is only a single machine available and jobs have arbitrary release dates, then F-Gipp coincides with preemptive Wsept and is optimal (Pinedo [25]).…”

Section: Our Contributionmentioning

confidence: 99%

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A Tight 2-Approximation for Preemptive Stochastic Scheduling

Megow

Vredeveld

2014

Mathematics of OR

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We consider dynamic stochastic scheduling of preemptive jobs with processing times that follow independent discrete probability distributions. We derive a policy with a guaranteed performance ratio of 2 for the problem of minimizing the sum of weighted completion times on identical parallel machines subject to release dates. The analysis is tight. Our policy as well as their analysis applies also to the more general model of stochastic online scheduling.In contrast to previous results for nonpreemptive stochastic scheduling, our preemptive policy yields an approximation guarantee that is independent of the processing time distributions. However, our policy extensively utilizes information on the distributions other than the first (and second) moments. We also introduce a new nontrivial lower bound on the expected value of an unknown optimal policy. It relies on a relaxation to the basic problem on a single machine without release dates, which is known to be solved optimally by the Gittins index priority rule. This dynamic priority index is crucial to the analysis and also inspires the design of our policy.Keywords: scheduling; stochastic; approximation algorithm; total weighted completion time MSC2000 subject classification: Primary: 90B36; secondary: 68W40 OR/MS subject classification: Primary: production/scheduling; secondary: approximation/heuristic History: Received August 15, 2011; revised March 9, 2014. Published online in Articles in Advance.1. Introduction. Stochastic scheduling problems have attracted researchers for about four decades. A full range of articles is concerned with criteria that guarantee the optimality of simple policies for special scheduling problems; see, e.g., Pinedo [26]. It is only recently that research also focuses on approximations for less restrictive problem settings (Möhring et al. All these results apply to nonpreemptive scheduling, and we are not aware of any approximation results when job preemption is allowed and processing times are stochastic.In this paper, we give the first constant factor approximation for the stochastic version of the classical problem of scheduling jobs preemptively, with or without release dates, on identical parallel machines. The objective is to minimize the expected sum of weighted completion times.We provide a very natural scheduling policy and show that it has an expected objective value of at most twice the expected optimal value. The analysis of our policy is tight. Both, the policy and its analysis are also valid in the model of stochastic online scheduling (Megow et al. [19], Chou et al. [5], Vredeveld [39]). They rely on the celebrated Gittins index priority rule (Gittins [9, 10]), which is an optimal policy for the setting when there is only one machine and there are no nontrivial release dates (Sevcik [33], Weiss [41]). Under deterministic input, our policy corresponds to the preemptive weighted shortest processing time (WSPT) rule, which is known to have a tight performance guarantee of 2 on identical parallel machines (Megow and Schulz...

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Section: Previous Workmentioning

confidence: 72%

Section: Our Contributionmentioning

confidence: 99%

A Tight 2-Approximation for Preemptive Stochastic Scheduling

Megow

Vredeveld

2014

Mathematics of OR

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“…Instead, literature reflects a variety of research on restricted problems as those with special probability distributions for processing times or special job weights [1,29,19,5,9,30].…”

Section: Definition 1 a (Online) Stochastic Policymentioning

confidence: 99%

“…If processing times are exponentially distributed and release dates are absent, our policy coincides with the Weighted shortest expected processing time (WSEPT) rule. This classical policy is known to be optimal if all weights are equal [1] or, more general, if they are agreeable, which means that for any two jobs i, j holds that [9]. If only one machine is available, we solve the weighted problem 1 | pmtn | E [ w j C j ] optimally by utilizing the Gittins index priority policy [11,24,30].…”

Section: Definition 1 a (Online) Stochastic Policymentioning

confidence: 99%

Approximation in Preemptive Stochastic Online Scheduling

Megow

Vredeveld

2006

Lecture Notes in Computer Science

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Abstract. We present a first constant performance guarantee for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive a policy with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem.Our policy applies to the recently introduced stochastic online scheduling model in which jobs arrive online over time. In contrast to the previously considered nonpreemptive setting, our preemptive policy extensively utilizes information on processing time distributions other than the first (and second) moments. In order to derive our result we introduce a new nontrivial lower bound on the expected value of an unknown optimal policy that we derive from an optimal policy for the basic problem on a single machine without release dates. This problem is known to be solved optimally by a Gittins index priority rule. This priority index also inspires the design of our policy.

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“…For example, the rule shortest expected processing time first (SEPT), i.e., schedule jobs in order of non-decreasing expected processing times, is known to be optimal for many variants, see, e.g., [21], [29], [3], [11], and [28]. Moreover, for the weighted single-machine problem, the rule weighted shortest expected processing time first (WSEPT) is optimal [18].…”

Section: Introductionmentioning

confidence: 99%

The Expected Competitive Ratio for Weighted Completion Time Scheduling

Souza

Steger

2004

Lecture Notes in Computer Science

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Abstract.A set of n independent jobs is to be scheduled without preemption on m identical parallel machines. For each job j, a diffuse adversary chooses the distribution F j of the random processing time P j from a certain class of distributions F j . The scheduler is given the expectation µ j = E[P j ], but the actual duration is not known in advance. A positive weight w j is associated with each job j and all jobs are ready for execution at time zero. The scheduler determines a list of the jobs, which is then scheduled in a non-preemptive manner. The objective is to minimise the total weighted completion time j w j C j . The performance of an algorithm is measured with respect to the expected competitive ratio max F∈F E[ j w j C j /OPT], where C j denotes the completion time of job j and OPT the offline optimum value.We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so-called new-better-than-used processing time distributions. This class includes, among others, the exponential distribution.As a special case, we consider the popular rule weighted shortest expected processing time first (WSEPT) in which jobs are processed according to the nondecreasing µ j /w j ratio. We show that it achieves E[WSEPT/OPT] ≤ 3 − 1/m for exponential distributed processing times.

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Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan

Cited by 113 publications

References 4 publications

A Tight 2-Approximation for Preemptive Stochastic Scheduling

A Tight 2-Approximation for Preemptive Stochastic Scheduling

Approximation in Preemptive Stochastic Online Scheduling

The Expected Competitive Ratio for Weighted Completion Time Scheduling

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