Waiting time distributions for closed M/M/N processor sharing queues

Braband, Jens

doi:10.1007/bf01150417

Cited by 9 publications

(7 citation statements)

References 11 publications

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“…Figure 9 illustrates the transient behaviors p i (t), i = 0, 1, 2, 3 of the CIMS without Bernoulli feedbacks. We can see that the transient solution of the CIMS without Bernoulli feedbacks tends to its steady-state solution ( 1 4 , 3 16 , 9 64 , 27 256 , . .…”

Section: Numerical Examplesmentioning

confidence: 93%

“…The inverse Laplace transform method and the generation function method are two common methods to solve the transient behavior of the finite buffer. Braband [3] presented transient solutions for a mathematical model of statistical multiplexing by inverse Laplace transform method. In Sharma et al [33], the transient analysis of a single server Markovian queueing model having customers impatience with threshold is performed by using probability generating function technique.…”

Section: Introductionmentioning

confidence: 99%

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Transient analysis of a single server queueing system with infinite buffer

Huo

Chen

et al. 2021

RAIRO-Oper. Res.

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As a typical single server queueing system, computer integrated manufacturing system (CIMS) has been widely used in the field of intelligent manufacturing. Howerve, how to derive its instantaneous index is still an imporant issue. This paper investigates the transient behavior of the CIMS with spectral method. By constructing an asymptotic system and analyzing the spectral distribution, we derive the explicit transient solution of the asymptotic system. Trottter-Kato theorem is used to prove that the transient solution of the CIMS is just the limitation of explicit transient solution of the asymptotic system. At the end of the paper, numerical examples are shown to illustrate the effectiveness of the proposed approximation.

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Section: Numerical Examplesmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Transient analysis of a single server queueing system with infinite buffer

Huo

Chen

et al. 2021

RAIRO-Oper. Res.

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“…Second, as shown in the remainder of this section, it allows us to use formal models from queuing theory to reason about the load that the application is subjected to. 11 By construction, closed-loop workload generators cannot significantly overload the system under test, because load generators will wait until they have received a response before issuing a new request. However, precisely this property makes them useful in determining the maximum service handling capacity of the system under test.…”

Section: Performance and Load Dimensioningmentioning

confidence: 99%

Impact of etcd deployment on Kubernetes, Istio, and application performance

et al. 2020

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Summary This experience article describes lessons learned as we conducted experiments in a Kubernetes‐based environment, the most notable of which was that the performance of both the Kubernetes control plane and the deployed application depends strongly and in unexpected ways on the performance of the etcd database. The article contains (a) detailed descriptions of how networking with and without Istio works in Kubernetes, based on the Flannel Container Networking Interface (CNI) provider in VXLAN mode with IP Virtual Server (IPVS)‐backed Kubernetes Services, (b) a comprehensive discussion about how to conduct load and performance testing using a closed‐loop workload generator, and (c) an open source experiment framework useful for executing experiments in a shared cloud environment and exploring the resulting data. It also shows that statistical analysis may reveal the data resulting from such experiments to be misleading even when careful preparations are made, and that nondeterministic behavior stemming from etcd can affect both the platform as a whole and the deployed application. Finally, it is demonstrated that using high‐performance backing storage for etcd can reduce the occurrence of such nondeterministic behaviors by a statistically significant (P < .05) margin. The implication of this experience article is that systems researchers studying the performance of applications deployed on Kubernetes cannot simply consider their specific application to be under test. Instead, the particularities of the underlying Kubernetes and cloud platform must be taken into account, in particular because their performance can impact that of etcd.

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“…Hence, a key component of our analysis is the numerical inversion of Laplace transforms, drawing on Abate and Whitt [4], [5]; see Abate, Choudhury and Whitt [1] for a review. Numerical transform inversion was previously applied to PS queues by Braband [6], but not for the purpose of realtime prediction. We show that the conditional mean can indeed be very efficiently computed by numerical transform inversion.…”

Section: Introductionmentioning

confidence: 99%