Non-Asymptotic Delay Bounds for Multi-Server Systems with Synchronization Constraints

Fidler, Markus; Walker, Brenton; Jiang, Yuming

doi:10.1109/tpds.2017.2779872

Cited by 21 publications

(23 citation statements)

References 46 publications

(117 reference statements)

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“…Compared to the fork-join model, where tasks are bound to particular servers and a large task can block tasks of subsequent jobs, in the singlequeue fork-join model small jobs can overtake jobs with large straggler tasks. Mean sojourn times for such systems are derived in [25], and bounds on the sojourn time are derived using network calculus in [17].…”

Section: Systems Models and Stability Regionsmentioning

confidence: 99%

“…3 shows how job sojourn time scales with the number of servers for these three models in the case with k = l and exponential inter-arrival and task service times. The plot shows performance bounds derived using network calculus in [16] and [17], simulation results, and experimental results from an Apache Spark cluster, and demonstrates that a Spark system may behave like any of these three parallel models, depending on how it is configured and how the driver program behaves. For comparison, the plot includes the equivalent sojourn time statistics for the ideal job partition.…”

Section: Systems Models and Stability Regionsmentioning

confidence: 99%

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The Tiny-Tasks Granularity Trade-Off: Balancing overhead vs. performance in parallel systems

Bora¹,

Walker²,

Fidler³

2022

Preprint

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Models of parallel processing systems typically assume that one has l workers and jobs are split into an equal number of k = l tasks. Splitting jobs into k > l smaller tasks, i.e. using "tiny tasks", can yield performance and stability improvements because it reduces the variance in the amount of work assigned to each worker, but as k increases, the overhead involved in scheduling and managing the tasks begins to overtake the performance benefit. We perform extensive experiments on the effects of task granularity on an Apache Spark cluster, and based on these, developed a four-parameter model for task and job overhead that, in simulation, produces sojourn time distributions that match those of the real system. We also present analytical results which illustrate how using tiny tasks improves the stability region of split-merge systems, and analytical bounds on the sojourn and waiting time distributions of both split-merge and single-queue fork-join systems with tiny tasks. Finally we combine the overhead model with the analytical models to produce an analytical approximation to the sojourn and waiting time distributions of systems with tiny tasks which include overhead. Though no longer strict analytical bounds, these approximations matched the Spark experimental results very well in both the split-merge and forkjoin cases.

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Section: Systems Models and Stability Regionsmentioning

confidence: 99%

Section: Systems Models and Stability Regionsmentioning

confidence: 99%

The Tiny-Tasks Granularity Trade-Off: Balancing overhead vs. performance in parallel systems

Bora¹,

Walker²,

Fidler³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note that, ours is a more general model that not only consider transmission failures (erasures), but also the errors in transmission due to imperfect communication links or fading channels. The system models used in different applications such as distributed max plus systems [22], [23], distributed detection and target tracking [24], distributed sensor fusion [25] and multi-agent control systems [21] literature resembles our model.…”

Section: System Modelmentioning

confidence: 99%

Analysis and Design of Robust Max Consensus for Wireless Sensor Networks

Muniraju

Tepedelenlioğlu

Spanias

2019

IEEE Trans. on Signal and Inf. Process. over Networks

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A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.Index Terms-Max consensus, spectral radius, max-plus algebra, wireless sensor networks.

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“…Transient and steady-state solutions of the FJ queue in terms of virtual waiting times are obtained in [21]. Network calculus techniques have also been used to derive bounds [22], [23]. Results for FJ systems with two servers having exponential service times under Poissonian job arrivals are shown in [24].…”

Section: Related Workmentioning

confidence: 99%

Provisioning and Performance Evaluation of Parallel Systems with Output Synchronization

KhudaBukhsh

Kar

Rizk

et al. 2019

ACM Trans. Model. Perform. Eval. Comput. Syst.

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Frameworks, such as MapReduce and Hadoop are abundant nowadays. They seek to reap benefits of parallelization, albeit subject to a synchronization constraint at the output. Fork-Join (FJ) queuing models are used to analyze such systems. Arriving jobs are split into tasks each of which is mapped to exactly one server. A job leaves the system when all of its tasks are executed.As a metric of performance, we consider waiting times for both work-conserving and non-work conserving server systems under a mathematical set-up general enough to take into account possible phase-type behavior of the servers, and as suggested by recent evidences, bursty arrivals.To this end, we present a Markov-additive process framework for an FJ system and provide computable bounds on tail probabilities of steady-state waiting times, for both types of servers separately. We apply our results to three scenarios, namely, nonrenewal (Markov-modulated) arrivals, servers showing phasetype behavior, and Markov-modulated arrivals and services. We compare our bounds against estimates obtained through simulations and also provide a theoretical conceptualization of provisions in FJ systems. Finally, we calibrate our model with real data traces, and illustrate how our bounds can be used to devise provisions.

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Non-Asymptotic Delay Bounds for Multi-Server Systems with Synchronization Constraints

Cited by 21 publications

References 46 publications

The Tiny-Tasks Granularity Trade-Off: Balancing overhead vs. performance in parallel systems

The Tiny-Tasks Granularity Trade-Off: Balancing overhead vs. performance in parallel systems

Analysis and Design of Robust Max Consensus for Wireless Sensor Networks

Provisioning and Performance Evaluation of Parallel Systems with Output Synchronization

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