Order Independent Queues

Krzesinski, A. E.

doi:10.1007/978-1-4419-6472-4_2

Cited by 23 publications

(56 citation statements)

References 23 publications

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“…that the arrival rate per server is smaller than the service rate, is also sufficient, see both [13] and [7]. An important observation made in [13] is that the c.o.c model is a special case of the Order Independent queue [15], which provides a direct path to derive the steady-state distribution. However we note that the departure rates from a state under the c.o.s model fail to satisfy the order independence condition, which in turn implies the necessity of a different approach from that used in [13] to analyze c.o.s.…”

Section: Related Workmentioning

confidence: 99%

On a unifying product form framework for redundancy models

Ayesta

Bodas

Verloop

2019

SIGMETRICS Perform. Eval. Rev.

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In this paper, we present a unifying analysis for redundancy systems with cancel-on-start (c.o.s.) and cancel-on-complete (c.o.c.) with exponentially distributed service requirements. With c.o.s. (c.o.c.) all redundant copies are removed as soon as one of the copies starts (completes) service. As a consequence, c.o.s. does not waste any computing resources, as opposed to c.o.c.. We show that the c.o.s. model is equivalent to a queueing system with multi-type jobs and servers, which was analyzed in [1], and show that c.o.c. (under the assumption of i.i.d. copies) can be analyzed by a generalization of [1] where state-dependent departure rates are permitted. This allows us to show that the stationary distribution for both the c.o.c. and c.o.s. models have a product form. We give a detailed first-time analysis for c.o.s and derive a closed form expression for important metrics like mean number of jobs in the system, and probability of waiting. We also note that the c.o.s. model is equivalent to Join-Shortest-Work queue with redundancy (JSW(d)). In the latter, an incoming job is dispatched to the server with smallest workload among d randomly chosen ones. Thus, all our results apply mutatis-mutandis to JSW(d). Comparing the performance of c.o.s. with that of c.o.c. with i.i.d copies gives the unexpected conclusion (since c.o.s. does not waste any resources) that c.o.s. is worse in terms of mean number of jobs. As part of ancillary results, we illustrate that this is primarily due to the assumption of i.i.d copies in case of c.o.c. (together with exponentially distributed requirements) and that such assumptions might lead to conclusions that are qualitatively different from that observed in practice.

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Section: Related Workmentioning

confidence: 99%

On a unifying product form framework for redundancy models

Ayesta

Bodas

Verloop

2019

SIGMETRICS Perform. Eval. Rev.

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“…The Markov process defined by the system state c is irreducible. The results of [12] show that this process is quasi-reversible, with stationary distribution…”

Section: Stationary Distributionmentioning

confidence: 96%

“…Additionally, the total service rate µ(I(c)) is independent of the arrival order of jobs. The corresponding queueing model is an order-independent (OI) queue [3,12]. An example is shown in Figure 4 for the configuration of Figure 2.…”

Section: Job Schedulingmentioning

confidence: 99%

Dynamic Load Balancing with Tokens

Comte¹

2018

2018 IFIP Networking Conference (IFIP Networking) and Workshops

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Efficiently exploiting the resources of data centers is a complex task that requires efficient and reliable load balancing and resource allocation algorithms. The former are in charge of assigning jobs to servers upon their arrival in the system, while the latter are responsible for sharing server resources between their assigned jobs. These algorithms should take account of various constraints, such as data locality, that restrict the feasible job assignments. In this paper, we propose a token-based mechanism that efficiently balances load between servers without requiring any knowledge on job arrival rates and server capacities. Assuming a balanced fair sharing of the server resources, we show that the resulting dynamic load balancing is insensitive to the job size distribution. Its performance is compared to that obtained under the best static load balancing and in an ideal system that would constantly optimize the resource utilization. * c IFIP, 2018. This is the author's version of the work. It is posted here by permission of IFIP for your personal use. Not for redistribution. The definitive version will be published in IFIP NETWORKING 2018 proceedings.

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“…Aggregate state As in [16], we consider the number of jobs of each class in the queue, independently of their arrival order. We denote by x = (x 1 , .…”

Section: A Multi-server Queuementioning

confidence: 99%

Balanced fair resource sharing in computer clusters

Bonald

Comte

2017

Performance Evaluation

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We represent a computer cluster as a multi-server queue with some arbitrary graph of compatibilities between jobs and servers. Each server processes its jobs sequentially in FCFS order. The service rate of a job at any given time is the sum of the service rates of all servers processing this job. We show that the corresponding queue is quasi-reversible and use this property to design a scheduling algorithm achieving balanced fair sharing of the computing resources.

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Order Independent Queues

Cited by 23 publications

References 23 publications

On a unifying product form framework for redundancy models

On a unifying product form framework for redundancy models

Dynamic Load Balancing with Tokens

Balanced fair resource sharing in computer clusters

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