Steady-state two-dimensional diffusion of a radioactive impurity in a channel with sorbing walls

1988 ◽  
Vol 55 (6) ◽  
pp. 1385-1388
Author(s):  
O. V. Ivanov ◽  
V. D. Akin'shin ◽  
V. D. Seleznev
Keyword(s):  
Steady State ◽  
Two Dimensional ◽  
Radioactive Impurity ◽  
Dimensional Diffusion

Steady state in two-dimensional diffusion-controlled reactions

1997 ◽  
Vol 89 (1-2) ◽  
pp. 369-377
Author(s):  
C. A. Condat ◽  
G. J. Sibona ◽  
C. E. Budde
Keyword(s):  
Steady State ◽  
Two Dimensional ◽  
Dimensional Diffusion ◽  
Diffusion Controlled

scholarly journals Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime

2020 ◽  
Vol 45 (3) ◽  
pp. 1069-1103
Author(s):  
Anton Braverman
Keyword(s):  
Steady State ◽  
Diffusion Limit ◽  
Fluid Limit ◽  
Time Intervals ◽  
Dimensional Diffusion ◽  
Queue Model ◽  
Join The Shortest Queue ◽  
Shortest Queue ◽  
Process Level ◽  
General Tool

This paper studies the steady-state properties of the join-the-shortest-queue model in the Halfin–Whitt regime. We focus on the process tracking the number of idle servers and the number of servers with nonempty buffers. Recently, Eschenfeldt and Gamarnik proved that a scaled version of this process converges, over finite time intervals, to a two-dimensional diffusion limit as the number of servers goes to infinity. In this paper, we prove that the diffusion limit is exponentially ergodic and that the diffusion scaled sequence of the steady-state number of idle servers and nonempty buffers is tight. Combined with the process-level convergence proved by Eschenfeldt and Gamarnik, our results imply convergence of steady-state distributions. The methodology used is the generator expansion framework based on Stein’s method, also referred to as the drift-based fluid limit Lyapunov function approach in Stolyar. One technical contribution to the framework is to show how it can be used as a general tool to establish exponential ergodicity.

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