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Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue [PDF]

Queueing Systems, 2006
This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not ...
Hans Van Den Berg, Richard J Boucherie, Van Den Berg Hans   +2 more
exaly   +3 more sources

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Sojourn Times of Brownian Sheet

Periodica Mathematica Hungarica, 2000
The distribution of \(\int_{[0,1]^2} v(B_s) \, ds\) is given if \(v=1_{[0, \infty)}\), \(v=1_{[-1,1]}\) and \(v=1_{(-\infty,1)}\).
Davar Khoshnevisan, Robin Pemantle
openaire   +1 more source

Wafer Sojourn Time Fluctuation Analysis of Time-Constrained Dual-Arm Cluster Tools With Wafer Revisiting and Activity Time Variation

IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018
A robotic cluster tool involves many activities whose time is subject to some disturbance, thus leading to the activity time variation. It results in wafer sojourn time fluctuation in a process module, which may in turn violate wafer residency time ...
Yan Qiao, Naiqi Wu, Fajun Yang
exaly   +2 more sources

Sojourn Time Minimization of Successful Jobs

ACM SIGMETRICS Performance Evaluation Review, 2022
Due to a growing interest in deep learning applications [5], compute-intensive and long-running (hours to days) training jobs have become a significant component of datacenter workloads. A large fraction of these jobs is often exploratory, with the goal of determining the best model structure (e.g., the number of layers and channels in a convolutional ...
Yuan Yao, Marco Paolieri, Leana Golubchik   +2 more
openaire   +1 more source

On the average sojourn time under M/M/1/SRPT

Operations Research Letters, 2005
We study an M/M/1 queueing system under the shortest remaining processing time (SRPT) policy. We show that the average sojourn time varies as Theta((mu(1-rho)ln(e/(1-rho)))(-1)), where rho is the system load.
Nikhil Bansal
exaly   +2 more sources

Sojourn Times in Queueing Networks

Mathematics of Operations Research, 1982
We consider a queueing network with types of customers. Poisson arrivals, type dependent routing and state dependent service. A number of stochastic aspects relating to sojourn times are investigated. Included are limiting state distributions imbedded at customer move times, mean sojourn times, and sojourn time distributions along overtake-free paths.
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Interpolation Approximations of Sojourn Time Distributions

Operations Research, 1991
We present a method for approximating sojourn time distributions in open queueing systems based on light and heavy traffic limits. The method is consistent with and generalizes the interpolation approximations for moments previously presented by M. I. Reiman and B. Simon.
Philip J. Fleming, Burton Simon
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Sojourn times in closed queueing networks

Advances in Applied Probability, 1983
This paper obtains the stationary joint distribution of a customer's sojourn times along an overtake-free path in a closed multiclass Jackson network. The distribution has a simple representation in terms of the product form distribution for the state of the network at an arrival instant.
Kelly, FP, Pollett, PK
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On a Sojourn Time Problem

Theory of Probability & Its Applications, 1958
Let $\{ \xi (t),0 \leqq t < \infty \} $ be a probability process such that the variable $\xi (t)$ takes on the two values 0 and 1. Let $\xi _1 ,\eta _1 ,\xi _2 ,\eta _2 , \cdots $ be the intervals of time, passed successively in states 0 and 1.
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The Distribution of the Sojourn Time for the Brownian Excursion

Methodology And Computing In Applied Probability, 1999
Let \(\{B(t ...
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