scholarly journals Tail Asymptotics for Monotone-Separable Networks

2007 ◽  
Vol 44 (02) ◽  
pp. 306-320
Author(s):  
Marc Lelarge
Keyword(s):  
Queueing Network ◽  
Network Models ◽  
Moment Generating Function ◽  
Stochastic Petri Nets ◽  
Arrival Process ◽  
Polling Systems ◽  
Tail Asymptotics ◽  
State Variables ◽  
Monotone Functions ◽  
Jackson Networks

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.

Elevator-type polling systems (abstract)

1992 ◽  
Vol 20 (1) ◽  
pp. 255-257 ◽  
Author(s):  
Ruth Shoham ◽  
Uri Yechiali
Keyword(s):  
Polling Systems

scholarly journals Critical random walks on two-dimensional complexes with applications to polling systems

2003 ◽  
Vol 13 (4) ◽  
pp. 1399-1422 ◽  
Author(s):  
M. V. Menshikov ◽  
I. M. MacPhee
Keyword(s):  
Random Walks ◽  
Polling Systems ◽  
Two Dimensional

scholarly journals Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle

1995 ◽  
Vol 5 (3) ◽  
pp. 681-719 ◽  
Author(s):  
E. G. Coffman ◽  
A. A. Puhalskii ◽  
M. I. Reiman
Keyword(s):  
Heavy Traffic ◽  
Polling Systems ◽  
Averaging Principle ◽  
Switchover Times
Sign in / Sign up

Export Citation Format

Share Document