Delta probing policies for redundancy

Raaijmakers, Youri; Borst, Sem; Boxma, Onno

doi:10.1145/3308897.3308931

Cited by 14 publications

(11 citation statements)

References 5 publications

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“…Several papers have noted that when the i.i.d. exponential assumptions are eliminated, mean response time no longer decreases as d increases in the collaborative model [25], hence recently there has been a focus on developing new dispatching and scheduling policies for systems with correlated or general service times [25,29,30,36]. Finally, some work focuses on deriving the stability region under redundancy-d, which becomes much more complicated absent the i.i.d.…”

Section: Related Workmentioning

confidence: 99%

Product Forms for FCFS Queueing Models with Arbitrary Server-Job Compatibilities: An Overview

Gardner¹,

Righter²

2020

Preprint

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In recent years a number of models involving different compatibilities between jobs and servers in queueing systems, or between agents and resources in matching systems, have been studied, and, under Markov assumptions and appropriate stability conditions, the stationary distributions have been shown to have product forms. We survey these results and show how, under an appropriate detailed description of the state, many are corollaries of similar results for the Order Independent Queue. We also discuss how to use the product form results to determine distributions for steady-state response times.

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Section: Related Workmentioning

confidence: 99%

Product Forms for FCFS Queueing Models with Arbitrary Server-Job Compatibilities: An Overview

Gardner¹,

Righter²

2020

Preprint

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“…The following theorem gives the asymptotic behavior of the spectral gap of round-robin and BIBD structures. And the indefinite growth of the spectral gap of BIBD incident structure is clear from (29).…”

Section: Bibd Structurementioning

confidence: 98%

“…The performance metric we are concerned with is the average job queuing time. In systems with redundancy, analysis of the average queuing time is complex [29]. In this work, we introduce performance indicators for scheduling policies.…”

Section: System Performance and Its Indicatorsmentioning

confidence: 99%

Balanced Nonadaptive Redundancy Scheduling

Behrouzi-Far¹,

Soljanin²

2022

Preprint

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Distributed computing systems implement redundancy to reduce the job completion time and variability. Despite a large body of work about computing redundancy, the analytical performance evaluation of redundancy techniques in queuing systems is still an open problem. In this work, we take one step forward to analyze the performance of scheduling policies in systems with redundancy. In particular, we study the pattern of shared servers among replicas of different jobs. To this end, we employ combinatorics and graph theory and define and derive performance indicators using the statistics of the overlaps. We consider two classical nonadaptive scheduling policies: random and round-robin. We then propose a scheduling policy based on combinatorial block designs. Compared with conventional scheduling, the proposed scheduling improves the performance indicators. We study the expansion property of the graphs associated with round-robin and block design-based policies. It turns out the superior performance of the block design-based policy results from better expansion properties of its associated graph. As indicated by the performance indicators, the simulation results show that the block design-based policy outperforms random and round-robin scheduling in different scenarios. Specifically, it reduces the average waiting time in the queue to up to 25% compared to the random policy and up to 100% compared to the round-robin policy.

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“…A natural topic for further research would be to extend our analysis to heterogeneous servers or even more generally to job types that can have different speeds at the various servers, see for example the model in [24].…”

Section: Conclusion and Suggestions For Further Researchmentioning

confidence: 99%

Fork-join and redundancy systems with heavy-tailed job sizes

Raaijmakers¹,

Borst²,

Boxma³

2021

Preprint

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We investigate the tail asymptotics of the response time distribution for the cancel-on-start (c.o.s.) and cancel-on-completion (c.o.c.) variants of redundancyd scheduling and the fork-join model with heavy-tailed job sizes. We present bounds, which only differ in the pre-factor, for the tail probability of the response time in the case of the first-come first-served (FCFS) discipline. For the c.o.s. variant we restrict ourselves to redundancy-d scheduling, which is a special case of the fork-join model. In particular, for regularly varying job sizes with tail index −ν the tail index of the response time for the c.o.s. variant of redundancyd equals − min{d cap (ν − 1), ν}, where d cap = min{d, N − k}, N is the number of servers and k is the integer part of the load. This result indicates that for d cap < ν ν−1 the waiting time component is dominant, whereas for d cap > ν ν−1 the job size component is dominant. Thus, having d = ⌈min{ ν ν−1 , N − k}⌉ replicas is sufficient to achieve the optimal asymptotic tail behavior of the response time. For the c.o.c. variant of the fork-join(n F , n J ) model the tail index of the response time, under some assumptions on the load, equals 1 − ν and 1 − (n F + 1 − n J )ν, for identical and i.i.d. replicas, respectively; here the waiting time component is always dominant.

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Delta probing policies for redundancy

Cited by 14 publications

References 5 publications

Product Forms for FCFS Queueing Models with Arbitrary Server-Job Compatibilities: An Overview

Product Forms for FCFS Queueing Models with Arbitrary Server-Job Compatibilities: An Overview

Balanced Nonadaptive Redundancy Scheduling

Fork-join and redundancy systems with heavy-tailed job sizes

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