α-stable limits for multiple channel queues in heavy traffic

Zbigniew Michna. "α-stable limits for multiple channel queues in heavy traffic." Applicationes Mathematicae 30.1 (2003): 55-68. <http://eudml.org/doc/279107>.

@article{ZbigniewMichna2003,
abstract = {We consider a sequence of renewal processes constructed from a sequence of random variables belonging to the domain of attraction of a stable law (1 < α < 2). We show that this sequence is not tight in the Skorokhod J₁ topology but the convergence of some functionals of it is derived. Using the structure of the sample paths of the renewal process we derive the convergence in the Skorokhod M₁ topology to an α-stable Lévy motion. This example leads to a weaker notion of weak convergence. As an application, we present limit theorems for multiple channel queues in heavy traffic. The convergence of the queue length process to a linear combination of α-stable Lévy motions is derived.},
author = {Zbigniew Michna},
journal = {Applicationes Mathematicae},
keywords = {weak convergence in the sandwich sense; sequence of renewal processes; weak convergence; functional limit theorems; heavy traffic},
language = {eng},
number = {1},
pages = {55-68},
title = {α-stable limits for multiple channel queues in heavy traffic},
url = {http://eudml.org/doc/279107},
volume = {30},
year = {2003},
}

TY - JOUR
AU - Zbigniew Michna
TI - α-stable limits for multiple channel queues in heavy traffic
JO - Applicationes Mathematicae
PY - 2003
VL - 30
IS - 1
SP - 55
EP - 68
AB - We consider a sequence of renewal processes constructed from a sequence of random variables belonging to the domain of attraction of a stable law (1 < α < 2). We show that this sequence is not tight in the Skorokhod J₁ topology but the convergence of some functionals of it is derived. Using the structure of the sample paths of the renewal process we derive the convergence in the Skorokhod M₁ topology to an α-stable Lévy motion. This example leads to a weaker notion of weak convergence. As an application, we present limit theorems for multiple channel queues in heavy traffic. The convergence of the queue length process to a linear combination of α-stable Lévy motions is derived.
LA - eng
KW - weak convergence in the sandwich sense; sequence of renewal processes; weak convergence; functional limit theorems; heavy traffic
UR - http://eudml.org/doc/279107
ER -