Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data
Utilization data are defined as the time series data consisting of time fractions of busy periods in fixed time intervals and are practically used to represent server conditions, such as CPU utilization. In general, it is more challenging to estimate the model parameters from the utilization data si...
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doaj-0859af2a35cf49aba78848e5f2fafc862021-03-29T22:49:13ZengIEEEIEEE Access2169-35362019-01-017426644267110.1109/ACCESS.2019.29067968672563Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization DataChen Li0https://orcid.org/0000-0002-8784-8148Hiroyuki Okamura1Tadashi Dohi2Department of Information Engineering, Graduate School of Engineering, Social Computing Laboratory, Hiroshima University, Higashihiroshima, JapanDepartment of Information Engineering, Graduate School of Engineering, Dependable Systems Laboratory, Hiroshima University, Higashihiroshima, JapanDepartment of Information Engineering, Graduate School of Engineering, Dependable Systems Laboratory, Hiroshima University, Higashihiroshima, JapanUtilization data are defined as the time series data consisting of time fractions of busy periods in fixed time intervals and are practically used to represent server conditions, such as CPU utilization. In general, it is more challenging to estimate the model parameters from the utilization data since we do not know the exact job arrival time and the service time from the utilization data. In this paper, we consider an approach to estimate the model parameters from the utilization data by assuming a few model assumptions. In particular, we suppose an M<sub>t</sub>/M/1/K queueing system whose job arrival follows a Non-homogeneous Poisson Process (NHPP) and propose a parameter estimation method for the NHPP approximately from the utilization data based on the maximum likelihood estimation (MLE) via the expectation maximization (EM) algorithm. In numerical experiments, we generate the simulated utilization data of an M<sub>t</sub>/M/1/K queueing system and investigate the effectiveness of our method. Also, we use the real CPU utilization data to exhibit the performance evaluation.https://ieeexplore.ieee.org/document/8672563/Queueing systemstime intervalsutilization dataEM algorithm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Chen Li Hiroyuki Okamura Tadashi Dohi |
spellingShingle |
Chen Li Hiroyuki Okamura Tadashi Dohi Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data IEEE Access Queueing systems time intervals utilization data EM algorithm |
author_facet |
Chen Li Hiroyuki Okamura Tadashi Dohi |
author_sort |
Chen Li |
title |
Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data |
title_short |
Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data |
title_full |
Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data |
title_fullStr |
Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data |
title_full_unstemmed |
Parameter Estimation of <inline-formula> <tex-math notation="LaTeX">$M_{t}/M/1/K$ </tex-math></inline-formula> Queueing Systems With Utilization Data |
title_sort |
parameter estimation of <inline-formula> <tex-math notation="latex">$m_{t}/m/1/k$ </tex-math></inline-formula> queueing systems with utilization data |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2019-01-01 |
description |
Utilization data are defined as the time series data consisting of time fractions of busy periods in fixed time intervals and are practically used to represent server conditions, such as CPU utilization. In general, it is more challenging to estimate the model parameters from the utilization data since we do not know the exact job arrival time and the service time from the utilization data. In this paper, we consider an approach to estimate the model parameters from the utilization data by assuming a few model assumptions. In particular, we suppose an M<sub>t</sub>/M/1/K queueing system whose job arrival follows a Non-homogeneous Poisson Process (NHPP) and propose a parameter estimation method for the NHPP approximately from the utilization data based on the maximum likelihood estimation (MLE) via the expectation maximization (EM) algorithm. In numerical experiments, we generate the simulated utilization data of an M<sub>t</sub>/M/1/K queueing system and investigate the effectiveness of our method. Also, we use the real CPU utilization data to exhibit the performance evaluation. |
topic |
Queueing systems time intervals utilization data EM algorithm |
url |
https://ieeexplore.ieee.org/document/8672563/ |
work_keys_str_mv |
AT chenli parameterestimationofinlineformulatexmathnotationlatexmtm1ktexmathinlineformulaqueueingsystemswithutilizationdata AT hiroyukiokamura parameterestimationofinlineformulatexmathnotationlatexmtm1ktexmathinlineformulaqueueingsystemswithutilizationdata AT tadashidohi parameterestimationofinlineformulatexmathnotationlatexmtm1ktexmathinlineformulaqueueingsystemswithutilizationdata |
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1724190749093789696 |