On the autocorrelation and spectral functions of queues

1968 ◽  
Vol 5 (2) ◽  
pp. 467-475 ◽  
Author(s):  
John F. Reynolds
Keyword(s):  
Fourier Transform ◽  
Spectral Density ◽  
Autocorrelation Function ◽  
Generating Functions ◽  
Queue Length ◽  
Spectral Functions

This paper considers the autocorrelation function of queue length and the corresponding spectral density (i.e., its Fourier transform). Some general expressions are obtained using generating functions and matrices, and applied to M/M/1 and M[x]/M/∞ queues.

On the autocorrelation and spectral functions of queues

1968 ◽  
Vol 5 (02) ◽  
pp. 467-475 ◽  
Author(s):  
John F. Reynolds
Keyword(s):  
Fourier Transform ◽  
Spectral Density ◽  
Autocorrelation Function ◽  
Generating Functions ◽  
Queue Length ◽  
Spectral Functions

This paper considers the autocorrelation function of queue length and the corresponding spectral density (i.e., its Fourier transform). Some general expressions are obtained using generating functions and matrices, and applied to M/M/1 and M [x]/M/∞ queues.

scholarly journals APPLICATION OF WEIGHTING WINDOWS FOR SPECTRAL DENSITY ESTIMATION

2021 ◽  
Author(s):  
Vera Meerson ◽  
O. Khorolsky
Keyword(s):  
Fourier Transform ◽  
Correlation Function ◽  
Spectral Density ◽  
Density Estimation ◽  
Time Windows ◽  
Spectral Density Estimation ◽  
Important Time

The article discusses the application of some of the most important time windows for spectral density estimation determined by the correlogram method (from correlation function) and the periodogram method (from direct fourier transform).

Design Wind Speeds Using Fast Fourier Transform

2011 ◽  
pp. 1576-1591
Author(s):  
Z.. Ismail ◽  
N. H. Ramli ◽  
Z.. Ibrahim ◽  
T. A. Majid ◽  
G. Sundaraj ◽  
...  
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Spectral Density ◽  
Fast Fourier Transform ◽  
Time Series Data ◽  
Absolute Magnitude ◽  
Stationary Pattern ◽  
Wind Speeds ◽  
Hidden Periodicities ◽  
Using Data

In this chapter, a study on the effects of transforming wind speed data, from a time series domain into a frequency domain via Fast Fourier Transform (FFT), is presented. The wind data is first transformed into a stationary pattern from a non-stationary pattern of time series data using statistical software. This set of time series is then transformed using FFT for the main purpose of the chapter. The analysis is done through MATLAB software, which provides a very useful function in FFT algorithm. Parameters of engineering significance such as hidden periodicities, frequency components, absolute magnitude and phase of the transformed data, power spectral density and cross spectral density can be obtained. Results obtained using data from case studies involving thirty-one weather stations in Malaysia show great potential for application in verifying the current criteria used for design practices.

scholarly journals Characteristics of extreme heavy precipitation events occurring in the area of Cracow (Poland)

2014 ◽  
Vol 9 (No. 4) ◽  
pp. 182-191 ◽  
Author(s):  
A. Walega ◽  
B. Michalec
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Spectral Density ◽  
Autocorrelation Function ◽  
Heavy Precipitation ◽  
Botanical Garden ◽  
Maximum Precipitation ◽  
Density Analysis ◽  
Increasing Precipitation ◽  
Precipitation Events

The variability of extremely heavy precipitation events with duration of 120 min occurring in the area of Cracow, southern Poland was assessed. The analysis was performed using time series of maximum annual precipitation events with durations t = 5, 10, 15, 30, 60, and 120 min, recorded at the Botanical Garden station at the Jagiellonian University in the period of 1906–1990. The periodicity of precipitation was analyzed using the autocorrelation function and Fourier spectral density analysis. The Probable Maximum Precipitation (PMP) was calculated by Hershfield’s statistical method. The analysis of the autocorrelation function of sequences and the Fourier spectral density revealed a clear periodicity of the maximum precipitation. For precipitation with t = 60 min, the maximum values occur every 9 years, but also shorter periods (3-year) may be observed. The PMP values calculated for Cracow differ significantly from the values calculated using the probability distribution, as well as from the ones observed and they increase with increasing precipitation duration. The differences between the PMP and probable as well as observed precipitation tend to decrease with increasing duration of precipitation.

The autocorrelation function of the queue length process for the two-server Poisson queue

1978 ◽  
Vol 15 (02) ◽  
pp. 447-451
Author(s):  
James M. Hill ◽  
Keith P. Tognetti
Keyword(s):  
Autocorrelation Function ◽  
Queue Length ◽  
Laplace Transforms ◽  
Analytical Expression ◽  
Explicit Analytical Expression

Using Laplace transforms an explicit analytical expression is obtained for the autocorrelation function of the number in the system for the two-server Poisson queue. The method employed may be extended to Poisson queues with more than two servers.

scholarly journals Operational behavior of the MAP/G/1 queue under N-policy with a single vacation and set-up

2002 ◽  
Vol 15 (2) ◽  
pp. 151-180
Author(s):  
Ho Woo Lee ◽  
Boo Yong Ahn
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Generating Functions ◽  
Queue Length ◽  
Stieltjes Transform ◽  
Arbitrary Time ◽  
Single Vacation ◽  
Set Up ◽  
Computation Algorithms

This paper considers the MAP/G/1 queue under N-policy with a single vacation and set-up. We derive the vector generating functions of the queue length at an arbitrary time and at departures in decomposed forms. We also derive the Laplace-Stieltjes transform of the waiting time. Computation algorithms for mean performance measures are provided.

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