Title
Tail asymptotics of the M/G/∞ model
Author
Mandjes, M.
Zuraniewski, P.W.
Publication year
2011
Abstract
This paper considers the so-called M/G/∞ model: jobs arrive according to a Poisson process with rate λ, and each of them stays in the system during a random amount of time, distributed as a non-negative random variable B; throughout it is assumed that B is light-tailed. With N(t) denoting the number of jobs in the system, the random process A(t) records the load imposed on the system in [0, t], i.e., A(t):= ∫t0 N(s)ds. The main result concerns the tail asymptotics of A(t)/t: we find an explicit function f(·) such that f(t) ∼ IP(A(t)/t > ρ(1+ε). for t large; here ρ: =λ double struck E sign B. A crucial issue is that A(t) does not have i.i.d. increments, which makes direct application of the classical Bahadur-Rao result impossible; instead an adaptation of this result is required. We compare the asymptotics found with the (known) asymptotics for ρ → ∞ (and t fixed). Copyright © Taylor & Francis Group, LLC.
Subject
Communication & Information
PNS - Performance of Networks & Services
TS - Technical Sciences
Informatics
Infinite-servers queues
Large deviations
Tail asymptotics
Poisson distribution
Random processes
Random variables
Asymptotic analysis
To reference this document use:
http://resolver.tudelft.nl/uuid:a86cf94e-d691-4a04-8a03-3d84ac35ec56
DOI
https://doi.org/10.1080/15326349.2011.542730
TNO identifier
427571
ISSN
1532-6349
Source
Stochastic Models, 27 (1), 77-93
Document type
article