The effective bandwidth problem revisited

Abstract

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.

arXiv comment29 pages, 11pt, Final version, that will be published as is in Stochastic Models

References in corpus (5)

• Asymptotic Behavior of the Number of Lost Messages
• Asymptotic analysis of the GI/M/1/n loss system as n increases to infinity
• A Large Closed Queueing Network Containing Two Types of Node and Multiple Customer Classes: One Bottleneck Station
• Large closed queueing networks in semi-Markov environment and its application
• Asymptotic Analysis of Losses in the $GI/M/m/n$ Queueing System as $n$ Increases to Infinity

Cited by in corpus (1)

• Takacs' asymptotic theorem and its applications: A survey