- Tail asymptotics of the M/G/∞ model
- Stochastic Models
- Volume | Issue number
- 27 | 1
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
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., . The main result concerns the tail asymptotics of A(t)/t: we find an explicit function f(·) such that
for t large; here ϱ: = λB. 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).
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