Asymptotic analysis of multiple class queueing networks

A class of hierarchical queueing networks and their analysis

Queueing networks are an adequate model type for the analysis of complex system behavior. Most of the more realistic models are rather complex and do not fall into the easy solvable class of product form networks. Those models have to be analyzed by numerical solution of the underlying Markov chain and/or approximation techniques including simulation. In this paper a class of hierarchically str...

Using ODEs from PEPA models to derive asymptotic solutions for a class of closed queueing networks

In this paper a class of closed queueing network is modelled in the Markovian process algebra PEPA. It is shown that a fluid flow approximation using ordinary differential equations (ODEs) gives rise to well known asymptotic results. This result gives context to the use of a fluid flow approximation and is potentially useful in cases where the model is not obviously a closed queueing network. T...

Stability of Single Class Queueing Networks

Asymptotic Analysis of Queueing Systems with Reneging: A Survey of Results for FIFO, Single Class Models

In this paper, we survey results for the GI/GI/N + GI queueing model. Our focus is on finding situations in which simple performance measure approximations can be developed. To do this, we study the behavior of the GI/GI/N + GI queue in the conventional heavy traffic and Halfin-Whitt limit regimes, and we also discuss the overloaded regime in which there is a single server as well as the overlo...

Discrete Time Analysis of Multi-Server Queueing System with Multiple Working Vacations and Reneging of Customers‎

This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customer...