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

1978 ◽  
Vol 15 (2) ◽  
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.

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.

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.

ENTANGLEMENT AND AUTOCORRELATION FUNCTION IN SEMICONDUCTOR MICROCAVITIES

2010 ◽  
Vol 24 (29) ◽  
pp. 5653-5662 ◽  
Author(s):  
H. ELEUCH
Keyword(s):  
Quantum Well ◽  
Strong Coupling ◽  
Autocorrelation Function ◽  
Entangled State ◽  
Strong Coupling Regime ◽  
Analytical Expression ◽  
Nonstationary Regime ◽  
Semiconductor Quantum Well ◽  
Semiconductor Microcavities

The autocorrelation function of the light emitted by a microcavity containing a semiconductor quantum well in the nonstationary regime is investigated. An analytical expression in the weak pumping and strong coupling regime is derived. Furthermore, it is shown that the initial entangled state can be deduced from the nonstationary autocorrelation function.

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.

Explicit Analytical Expression for Solar Flux Distribution on an Undeflected Absorber Tube of Parabolic Trough Concentrator Considering Sun-Shape and Optical Errors

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sourav Khanna ◽  
Vashi Sharma
Keyword(s):  
Flux Distribution ◽  
Computational Effort ◽  
Solar Flux ◽  
Outer Diameter ◽  
Parabolic Trough ◽  
Analytical Expression ◽  
Explicit Analytical Expression ◽  
Aperture Width ◽  
Design Calculations ◽  
Circumferential Nonuniformity

The absorber tube of the parabolic trough receives the concentrated sun-rays only on the portion facing the reflector. It leads to nonuniformity in the temperature of absorber tube. Thus, the material of tube expands differentially and the tube experiences compression and tension in its different parts. It leads to bending of the tube and the glass cover can be broken. The bending can be reduced by (i) reducing the circumferential nonuniformity in absorber's temperature (using material of high thermal conductivity) and (ii) reducing the nonuniformity in solar flux distribution (using appropriate rim angle of trough). In most of the available studies, Monte Carlo Ray Tracing software has been used to calculate the distribution of solar flux and few studies have used analytical approach. In the present work, an explicit analytical expression is derived for finding the distribution of solar flux accounting for the sun-shape and optical errors. Using it, the design calculations can be carried out in significantly lesser time and lesser computational effort. The explicit expression is also useful in validating the results computed by softwares. The methodology has been verified with the already reported results. The effects of optical errors, rim angle, and aperture width of trough on the solar flux distribution and total flux availability for absorber tube have also been studied. From the calculations, it is found that for Schott 2008 PTR70 receiver (absorber tube with 70 mm outer diameter), 126 deg, 135 deg, and 139 deg, respectively, are the appropriate rim angles corresponding to minimum circumferential nonuniformity in solar flux distribution for 3 m, 6 m, and 9 m aperture width of trough. However, 72 deg, 100 deg, and 112 deg, respectively, are the appropriate rim angles corresponding to the maximum solar flux at absorber tube for 3 m, 6 m, and 9 m aperture width of trough. Considering both the circumferential nonuniformity and the total solar flux availability, 100 deg, 120 deg, and 130 deg, respectively, are the best rim angles.

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