Asymptotic relations in queueing theory

On asymptotic accuracy in queueing theory

Recently results have shown that a single server queue Poisson Pareto Burst Process input has a tail which is bounded by hyperbolic functions. We show that the hyperbolic upper and lower bounds for this system can be very misleading, that this hyperbolic tail result is relevant only from a certain threshold onwards, and the magnitude of this threshold may be very large. We also show that any hy...

Queueing Theory

Queueing Theory

A queue is a waiting line (like customers waiting at a supermarket checkout counter); queueing theory is the mathematical theory of waiting lines. More generally, queueing theory is concerned with the mathematical modeling and analysis of systems that provide service to random demands. A queueing model is an abstract description of such a system. Typically, a queueing model represents (1) the s...

On asymptotic accuracy in queueing theory - the tale of the misleading tail

Recently results have shown that a single server queue Poisson Pareto Burst Process input has a tail which is bounded by hyperbolic functions. We show that the hyperbolic upper and lower bounds for this system can be very misleading, that this hyperbolic tail result is relevant only from a certain threshold onwards, and the magnitude of this threshold may be very large. We also show that any hy...

Asymptotic Relations for Partitions

Asymptotic relations are obtained for the number PA(n) of partitions of the integer n into summands from a set A of integers. The set A is subject to certain conditions; however the only arithmetic condition is that A have property Pk of Bateman and Erdös. A conjecture of Bateman and Erdös concerning the *th differences of p^(n) may be verified using these asymptotic relations. 1. Let A = {a0, ...