fluctuation bounds
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2020 ◽  
Vol 10 (3) ◽  
pp. 223-250
Author(s):  
Arsalan Sharifnassab ◽  
John N. Tsitsiklis ◽  
S. Jamaloddin Golestani

We consider a multihop switched network operating under a max-weight scheduling policy and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under non-Markovian arrivals and, for the case of independent and identically distributed arrivals, an additive SSC result over an exponential time scale.


2014 ◽  
Vol 156 (2) ◽  
pp. 221-238 ◽  
Author(s):  
L. -P. Arguin ◽  
C. M. Newman ◽  
D. L. Stein ◽  
J. Wehr

2012 ◽  
Vol 147 (1) ◽  
pp. 35-62
Author(s):  
Márton Balázs ◽  
Júlia Komjáthy ◽  
Timo Seppäläinen
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2012 ◽  
Vol 48 (1) ◽  
pp. 151-187 ◽  
Author(s):  
Márton Balázs ◽  
Júlia Komjáthy ◽  
Timo Seppäläinen

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