Minimizing Total Flow Time and Total Completion Time with Immediate Dispatching

Avrahami, Nir; Azar, Yossi

doi:10.1007/s00453-006-0193-6

Cited by 27 publications

(35 citation statements)

References 21 publications

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“…Our results for the unicast setting are related to, and borrow ideas from, previous work on minimizing L p norms of response time and stretch [BP03] in the single machine and parallel machine settings [AA03,CGKK04].…”

Section: Resultssupporting

confidence: 62%

“…Our work shows that this analysis can be generalized for the delay factor metric. For multiple processors our analysis is inspired by the ideas from [AA03,CGKK04].…”

Section: Resultsmentioning

confidence: 99%

“…We begin our proof by showing that the volume of processing time of requests less than or equal to some slack class is almost the same on the different machines at any time. Several of these lemmas are essentially the same as in [AA03].…”

Section: Algorithm: Ssf-idmentioning

confidence: 98%

“…More recently, other metrics such as maximum and average stretch, which measure the waiting time in proportion to the size of a request, have been proposed [BCM98,KSW99,Sga98]; these measures were motivated by applications in databases and web server systems. Related metrics include L p norms of response times and stretch [BP03,AA03,CGKK04] for 1 ≤ p < ∞. In a variety of applications such as real-time systems and data gathering systems, requests have deadlines by which they desire to be fulfilled.…”

Section: Introductionmentioning

confidence: 99%

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Online Scheduling to Minimize the Maximum Delay Factor

Chekuri¹,

Moseley²

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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In this paper two scheduling models are addressed. First is the standard model (unicast) where requests (or jobs) are independent. The other is the broadcast model where broadcasting a page can satisfy multiple outstanding requests for that page. We consider online scheduling of requests when they have deadlines. Unlike previous models, which mainly consider the objective of maximizing throughput while respecting deadlines, here we focus on scheduling all the given requests with the goal of minimizing the maximum delay factor. The delay factor of a schedule is defined to be the minimum α ≥ 1 such that each request i is completed by time a i + α(d i − a i ) where a i is the arrival time of request i and d i is its deadline. Delay factor generalizes the previously defined measure of maximum stretch which is based only the processing times of requests [BCM98,BMR02].We prove strong lower bounds on the achievable competitive ratios for delay factor scheduling even with unit-time requests. Motivated by this, we then consider resource augmentation analysis [KP00] and prove the following positive results. For the unicast model we give algorithms that are (1 + ǫ)-speed O( 1 ǫ )-competitive in both the single machine and multiple machine settings. In the broadcast model we give an algorithm for similar-sized pages that is (2 + ǫ)-speed O( 1 ǫ 2 )-competitive. For arbitrary page sizes we give an algorithm that is (4 + ǫ)-speed O( 1 ǫ 2 )-competitive.

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Section: Resultssupporting

confidence: 62%

“…Our work shows that this analysis can be generalized for the delay factor metric. For multiple processors our analysis is inspired by the ideas from [AA03,CGKK04].…”

Section: Resultsmentioning

confidence: 99%

Section: Algorithm: Ssf-idmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Online Scheduling to Minimize the Maximum Delay Factor

Chekuri¹,

Moseley²

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Some researchers [20,4,6] have studied the online non-clairvoyant scheduling of serial jobs with arbitrary release time. It remains an interesting open problem to develop non-clairvoyant schedulers that minimizes mean response time for parallel jobs with arbitrary release times…”

Section: Discussionmentioning

confidence: 99%

Provably Efficient Online Nonclairvoyant Adaptive Scheduling

Hsu

Leiserson³

2008

IEEE Trans. Parallel Distrib. Syst.

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To the best of our knowledge, GRAD is the first nonclairvoyant scheduling algorithm that offers such guarantees. We also believe that our new approach of resource requestallotment protocol deserves further exploration.The simulation results show that, for non-batched jobs, the makespan produced by GRAD is no more than 1.39 times of the optimal on average. For batched jobs, the mean response time produced by GRAD is no more than 2.37 times of the optimal on average.

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New Resource Augmentation Analysis of the Total Stretch of SRPT and SJF in Multiprocessor Scheduling

Chan¹,

Lam²,

Liu³

et al. 2005

Mathematical Foundations of Computer Science 2005

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This paper studies online job scheduling on multiprocessors and, in particular, investigates the algorithms SRPT and SJF for minimizing total stretch, where the stretch of a job is its flow time (response time) divided by its processing time. SRPT is perhaps the most well-studied algorithm for minimizing total flow time or stretch. This paper gives the first resource augmentation analysis of the total stretch of SRPT, showing that it is indeed O(1)-speed 1-competitive. This paper also gives a simple lower bound result showing that SRPT is not s-speed 1-competitive for any s < 1.5. This paper also makes contribution to the analysis of SJF. Extending the work of [4], we are able to show that SJF is O(1)-speed 1-competitive for minimizing total stretch. More interestingly, we find that the competitiveness of SJF can be reduced arbitrarily by increasing the processor speed (precisely, SJF is O(s)-speed (1/s)-competitive for any s ≥ 1). We conjecture that SRPT also admits a similar result.

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Minimizing Total Flow Time and Total Completion Time with Immediate Dispatching

Cited by 27 publications

References 21 publications

Online Scheduling to Minimize the Maximum Delay Factor

Online Scheduling to Minimize the Maximum Delay Factor

Provably Efficient Online Nonclairvoyant Adaptive Scheduling

New Resource Augmentation Analysis of the Total Stretch of SRPT and SJF in Multiprocessor Scheduling

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