Absolutely Monotone Functions

1954 ◽  
Vol 60 (3) ◽  
pp. 467 ◽  
Author(s):  
Brockway McMillan



1982 ◽  
Vol 25 (2) ◽  
pp. 143-148 ◽  
Author(s):  
Arvind Mahajan ◽  
Dieter K. Ross

AbstractThe solutions of a certain class of first order linear differential equations are shown to be either completely or absolutely monotone depending on the nature of its coefficients. This is a simple theorem which is used to deduce a number of new and interesting results dealing with the complete and absolute monotonicity of functions. In particular, a partial answer is supplied to a question posed by Askey and Pollard: “When is completely monotone?”



1969 ◽  
Vol 7 (2) ◽  
pp. 137-146 ◽  
Author(s):  
D. Amir ◽  
Z. Ziegler


1994 ◽  
Vol 79 (2) ◽  
pp. 199-221
Author(s):  
E. Lapidot


1965 ◽  
Vol 3 (3) ◽  
pp. 173-180 ◽  
Author(s):  
Samuel Karlin ◽  
Zvi Ziegler




1993 ◽  
Vol 19 (1) ◽  
pp. 44
Author(s):  
Brown ◽  
Darji
Keyword(s):  


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.



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