Heavy Traffic Methods in Wireless Systems: Towards Modeling Heavy Tails and Long Range Dependence

2007 ◽  
pp. 53-74
Author(s):  
Robert T. Buche ◽  
Arka Ghosh ◽  
Vladas Pipiras ◽  
Jim X. Zhang
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Heavy Traffic ◽  
Wireless Systems ◽  
Long Range Dependence

scholarly journals How system performance is affected by the interplay of averages in a fluid queue with long range dependence induced by heavy tails

1999 ◽  
Vol 9 (2) ◽  
pp. 352-375 ◽  
Author(s):  
David Heath ◽  
Sidney Resnick ◽  
Gennady Samorodnitsky
Keyword(s):  
Long Range ◽  
System Performance ◽  
Heavy Tails ◽  
Long Range Dependence ◽  
Fluid Queue

scholarly journals Marcinkiewicz law of large numbers for outer products of heavy-tailed, long-range dependent data

2016 ◽  
Vol 48 (2) ◽  
pp. 349-368
Author(s):  
Michael A. Kouritzin ◽  
Samira Sadeghi
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Law Of Large Numbers ◽  
Nonlinear Function ◽  
Dependent Data ◽  
Long Range Dependence ◽  
Linear Processes ◽  
Strong Law ◽  
Large Numbers ◽  
Heavy Tailed

Abstract The Marcinkiewicz strong law, limn→∞(1 / n1/p)∑k=1n(Dk - D) = 0 almost surely with p ∈ (1, 2), is studied for outer products Dk = {XkX̅kT}, where {Xk} and {X̅k} are both two-sided (multivariate) linear processes (with coefficient matrices (Cl), (C̅l) and independent and identically distributed zero-mean innovations {Ξ} and {Ξ̅}). Matrix sequences Cl and C ̅l can decay slowly enough (as |l| → ∞) that {Xk,X ̅k} have long-range dependence, while {Dk} can have heavy tails. In particular, the heavy-tail and long-range-dependence phenomena for {Dk} are handled simultaneously and a new decoupling property is proved that shows the convergence rate is determined by the worst of the heavy tails or the long-range dependence, but not the combination. The main result is applied to obtain a Marcinkiewicz strong law of large numbers for stochastic approximation, nonlinear function forms, and autocovariances.

Introduction Non-conventional Queueing Models: Heavy Tails, Long-Range Dependence, and Rare Events

2004 ◽  
Vol 46 (1/2) ◽  
pp. 5-7
Author(s):  
Takis Konstantopoulos ◽  
Stan Zachary ◽  
Serguei Foss
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Rare Events ◽  
Long Range Dependence ◽  
Queueing Models

scholarly journals Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models

1998 ◽  
Vol 23 (1) ◽  
pp. 145-165 ◽  
Author(s):  
David Heath ◽  
Sidney Resnick ◽  
Gennady Samorodnitsky
Keyword(s):  
Long Range ◽  
Heavy Tails ◽  
Long Range Dependence ◽  
Fluid Models
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