Minimizing mean flow time with release time constraint

Du, Jianzhong; Leung, Jyt; Young, Gilbert H.

doi:10.1016/0304-3975(90)90100-v

Cited by 62 publications

(31 citation statements)

References 2 publications

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“…When the release date of each job is 0 and the machines are identical, McNaughton [lo] showed that no preemptions are needed in order to minimize the average completion time; therefore the polynomial-time algorithm for the nonpreemptive version of this problem [2, 51 solves it directly. When release dates are introduced, however, even the two machine problem becomes NP-hard [3]. When one attempts, in addition, to minimize the average weighted completion time even the one machine version of the problem becomes NP-hard [7].…”

Section: +~mentioning

confidence: 99%

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Scheduling jobs that arrive over time

Phillips

Stein

Wein³

1995

Lecture Notes in Computer Science

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A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order t o minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when ad jobs are available at time 0, ad the problems that we consider are NP-hard, and essentially nothing was known about constructing good approximations in polynonid time.We give the first constant-factor approximation algorithms for several variants of the single and parallel machine model. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of average weighted completion time as well. IntroductionTwo important characteristics of many real-world scheduling problems are that (1) the tasks to be scheduled arrive over time and (2) the goal is to optimize some function of average performance or satisfaction. In this pa& we study several scheduling models that include both of these characteristics; in particular we study the minimization of the average (weighted) completion time of a set of jobs with release dates. In most of these models polynomial-time algorithms were known to minimize average completion time when all the jobs were available at time 0; the introduction of release dates makes these problems NP-hard and little was known about approximation algorithms.Our major contribution is to give the first constant-factor approximation algorithms for the minimization of average completion time in these models. Our performance bounds come from the combination of two different types of results. First, we prove structural theorems about the relative quality of preemptive versus nonpreemptive schedules, and give algorithms t o convert from 1I the former to the latter with only a small degradation in schedule quality. Second, we give the first constant-approximation algorithms for preemptively scheduling parallel machines with release dates. When the machines are identical, we give a combinatorial algorithm which yields a two approximation. For unrelated machines, we give a new integer programming formulation. We then solve the linear programming relaxation and give methods to round the fractional solution to valid preemptive schedules; it is possible that these methods mill be of use in other settings.Models: We are given n jobs J 1 : . . . . J, where job J; has associated processing time p j , and a release date r j y before which it can not be processed on any machine. We will also be given m machines M I y . . . , M,. We will focus both on the one machine ( m = 1) environment and two fundamental variants of parallel machine scheduling. In the identical parallel machine environment , job Jj runs in time pj on every machine [8]. In the unrelated parallel machine scheduli...

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Section: +~mentioning

confidence: 99%

“…The nonpreemptive versions of these problems are NP-hard due to the NP-hardness of the one-machine problem. When preemption is allowed, as noted, the one machine problem is solvable in polynomial-time but the scheduling of even two identical machines is NP-hard [3].…”

Section: A Conversion Algorithm For Identical Parallel Machinesmentioning

confidence: 99%

Scheduling jobs that arrive over time

Phillips

Stein

Wein³

1995

Lecture Notes in Computer Science

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“…Second, we would like to make the update rate interval (i.e., how often R(t) is updated) a user-defined parameter, T . 4 The desired aggregate change in traffic over one average RTT is α(C − y(t)) − β q(t) d0 , and to update the rate more often than once per RTT, we scale this aggregate change by T /d 0 . And,N (t) = C/R(t − T ).…”

Section: A Rate Control Protocol (Rcp)mentioning

confidence: 99%

“…In general, it is not possible to provably minimize the FCT for flows in a general network, even if their arrival times and durations are known [4] [5]. In a real network flows start and finish all the time, and different flows take different paths, and so minimizing FCT is intractable.…”

Section: Introductionmentioning

confidence: 99%

Why flow-completion time is the right metric for congestion control

Dukkipati

McKeown

2006

SIGCOMM Comput. Commun. Rev.

261

147

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Abstract-Users typically want their flows to complete as quickly as possible: They want a web-page to download quickly, or a file transfer to complete as rapidly as possible. In other words, Flow Completion Time (FCT) is an important -arguably the most important -performance metric for the user. Yet research on congestion control focuses almost entirely on maximizing flow throughput, link utilization and fairness, which matter more to the operator than the user. In this paper we show that existing (TCP Reno) and proposed (XCP) congestion control algorithms make flows last much longer than necessary -often one or two orders of magnitude longer than they need to; and we argue that over time, as the network bandwidth-delay product increases, the discrepancy will get worse. In contrast, we show how a new and practical algorithm -RCP (Rate Control Protocol) -enables flows to complete close to the minimum possible.

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“…The related scenarios are studied: scheduling malleable tasks [5], scheduling chainstructured tasks [6], and scheduling with release time constraint [7]. However, they are focus on the complexity analysis, and they cannot directly applied in our multiple phases scenario.…”

Section: Introductionmentioning

confidence: 99%

Performance analysis of work-conserving schedulers for minimizing total flow-time with phase precedence

Zheng

Sinha

Shroff

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-We consider the problem of minimizing the total flow time of multiple jobs in a pool of multiple homogenous machines, where the jobs arrive over time and have to be served with phase precedence. This is a common occurrence in job scheduling for the increasingly popular data center oriented systems, where jobs need to be processed through a MAP and Reduce procedure before leaving the system. For this problem, one can construct an arrival pattern such that no scheduler can achieve a constant competitive ratio. However, what we find is that by using a slightly weaker metric of performance, which we call the efficiency ratio. We say that a scheduler achieves an efficiency ratio of γ when the flow time incurred by that scheduler divided by the minimum flow time achieved over all possible schedulers is less than or equal to γ almost surely, when the time slots or job arrivals go to infinity. We show a surprising property that any work-conserving scheduler for the flow time problem with phase precedence has a constant efficiency ratio in both preemptive and non-preemptive scenarios under some weak assumptions. We provide numerical results to support our analysis.

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Minimizing mean flow time with release time constraint

Cited by 62 publications

References 2 publications

Scheduling jobs that arrive over time

Scheduling jobs that arrive over time

Why flow-completion time is the right metric for congestion control

Performance analysis of work-conserving schedulers for minimizing total flow-time with phase precedence

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