scholarly journals Fluid limits for networks with bandwidth sharing and general document size distributions

2009 ◽  
Vol 19 (1) ◽  
pp. 243-280 ◽  
Author(s):  
H. Christian Gromoll ◽  
Ruth J. Williams
Keyword(s):  
Size Distributions ◽  
Bandwidth Sharing ◽  
Fluid Limits

scholarly journals Stability of a Subcritical Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

2020 ◽  
Vol 10 (3) ◽  
pp. 251-273
Author(s):  
Yingjia Fu ◽  
Ruth J. Williams
Keyword(s):  
Lyapunov Function ◽  
Fluid Model ◽  
Model Solution ◽  
Size Distributions ◽  
File Size ◽  
Bandwidth Sharing ◽  
Initial State ◽  
Model Solutions ◽  
Slight Generalization ◽  
Subcritical Fluid

This work concerns the asymptotic behavior of solutions to a (strictly) subcritical fluid model for a data communication network, where file sizes are generally distributed and the network operates under a fair bandwidth-sharing policy. Here we consider fair bandwidth-sharing policies that are a slight generalization of the [Formula: see text]-fair policies introduced by Mo and Walrand [Mo J, Walrand J (2000) Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networks 8(5):556–567.]. Since the year 2000, it has been a standing problem to prove stability of the data communications network model of Massoulié and Roberts [Massoulié L, Roberts J (2000) Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems 15(1):185–201.], with general file sizes and operating under fair bandwidth sharing policies, when the offered load is less than capacity (subcritical conditions). A crucial step in an approach to this problem is to prove stability of subcritical fluid model solutions. In 2012, Paganini et al. [Paganini F, Tang A, Ferragut A, Andrew LLH (2012) Network stability under alpha fair bandwidth allocation with general file size distribution. IEEE Trans. Automatic Control 57(3):579–591.] introduced a Lyapunov function for this purpose and gave an argument, assuming that fluid model solutions are sufficiently smooth in time and space that they are strong solutions of a partial differential equation and assuming that no fluid level on any route touches zero before all route levels reach zero. The aim of the current paper is to prove stability of the subcritical fluid model without these strong assumptions. Starting with a slight generalization of the Lyapunov function proposed by Paganini et al., assuming that each component of the initial state of a measure-valued fluid model solution, as well as the file size distributions, have no atoms and have finite first moments, we prove absolute continuity in time of the composition of the Lyapunov function with any subcritical fluid model solution and describe the associated density. We use this to prove that the Lyapunov function composed with such a subcritical fluid model solution converges to zero as time goes to infinity. This implies that each component of the measure-valued fluid model solution converges vaguely on [Formula: see text] to the zero measure as time goes to infinity. Under the further assumption that the file size distributions have finite pth moments for some p > 1 and that each component of the initial state of the fluid model solution has finite pth moment, it is proved that the fluid model solution reaches the measure with all components equal to the zero measure in finite time and that the time to reach this zero state has a uniform bound for all fluid model solutions having a uniform bound on the initial total mass and the pth moment of each component of the initial state. In contrast to the analysis of Paganini et al., we do not need their strong smoothness assumptions on fluid model solutions and we rigorously treat the realistic, but singular situation, where the fluid level on some routes becomes zero, whereas other route levels remain positive.

Fluid Limits for Bandwidth-Sharing Networks in Overload

2014 ◽  
Vol 39 (2) ◽  
pp. 533-560 ◽  
Author(s):  
Sem Borst ◽  
Regina Egorova ◽  
Bert Zwart
Keyword(s):  
Bandwidth Sharing ◽  
Fluid Limits

scholarly journals Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints

2014 ◽  
Vol 39 (3) ◽  
pp. 746-774 ◽  
Author(s):  
Maria Remerova ◽  
Josh Reed ◽  
Bert Zwart
Keyword(s):  
Bandwidth Sharing ◽  
Fluid Limits ◽  
Rate Constraints

254. A Comparison of the Particle Size Distributions for Aerosols Generated During Wet Grinding and Dry Deburring of Beryllium

1999 ◽  
Author(s):  
K.K. Ellis ◽  
R. Buchan ◽  
M. Hoover ◽  
J. Martyny ◽  
B. Bucher-Bartleson ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Wet Grinding

DROPLET SIZE DISTRIBUTIONS OF ADJUVANT-AMENDED SPRAYS FROM AN AIR-ASSISTED FIVE-PORT PWM NOZZLE

2011 ◽  
Vol 21 (3) ◽  
pp. 263-274 ◽  
Author(s):  
Jiabing Gu ◽  
Heping Zhu ◽  
Weimin Ding ◽  
Hong Young Jeon
Keyword(s):  
Droplet Size ◽  
Size Distributions ◽  
Droplet Size Distributions
Sign in / Sign up

Export Citation Format

Share Document