Tail asymptotics of the M/G/∞ model
article
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.
Topics
TNO Identifier
427571
ISSN
15326349
Source
Stochastic Models, 27(1), pp. 77-93.
Pages
77-93
Files
To receive the publication files, please send an e-mail request to TNO Repository.