Asymptotics for transient and stationary probabilities for finite and infinite buffer discrete time queues

Asymptotics for transient and stationary probabilities for finite and infinite buffer discrete time queues

0.00 Avg rating0 Votes
Article ID: iaor20002502
Country: United States
Volume: 26
Issue: 1/2
Start Page Number: 1
End Page Number: 22
Publication Date: Oct 1997
Journal: Queueing Systems
Authors: ,
Keywords: GI/G/1 queues
Abstract:

Consider a discrete time queue with independent, identically distributed arrivals (see the generalisation below) and a single server with a buffer length m. Let Tm be the first time an overflow occurs. We obtain asymptotic rate of growth of moments and distributions of Tm as m → ∞. We also show that under general conditions, the overflow epochs converge to a compound Poisson process. Furthermore, we show that the results for the overflow epochs are qualitatively as well as quantitatively different form the excursion process of an infinite buffer queue studied in continuous time in the literature. Asymptotic results for several other characteristics of the loss process are also studied, e.g., exponential decay of the probability of no loss (for a fixed buffer length) in time [0, n], as n → ∞, total number of packets lost in [0, n], maximum run of loss states in [0, n]. We also study tails of stationary distributions. All results extend to the multiserver case and most to a Markov modulated arrival process.

Reviews

Required fields are marked *. Your email address will not be published.