α-stable limits for multiple channel queues in heavy traffic

• Autorzy: Zbigniew Michna
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60F17: Functional limit theorems; invariance principles
• 60G52: Stable processes
• 60K25: Queueing theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2003
• Tom: 30
• Numer: 1
• Strony: 55-68

Daty

wydano

2003

Twórcy

autor

Zbigniew Michna

• Department of Mathematics, Wrocław University of Economics, Komandorska 118/120, 53-345 Wrocław, Poland

Identyfikatory

DOI

10.4064/am30-1-4