Graph Convergence for Monotone Functions on the Circle

2020 ◽  
pp. 297-316
Author(s):  
Frank Rhodes ◽  
Christopher L. Thompson
1976 ◽  
Vol 1 (1) ◽  
pp. 44
Author(s):  
Foran
Keyword(s):  

2007 ◽  
Vol 44 (02) ◽  
pp. 306-320
Author(s):  
Marc Lelarge

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.


2013 ◽  
Vol 405 (1) ◽  
pp. 156-172 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Vladimir D. Stepanov
Keyword(s):  

1972 ◽  
Vol 76 (2) ◽  
pp. 135-137 ◽  
Author(s):  
Togo Nishiura ◽  
Franz Schnitzer
Keyword(s):  

1939 ◽  
Vol 61 (4) ◽  
pp. 941
Author(s):  
G. Baley Price
Keyword(s):  

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