Brownian Control Problems for a Multiclass M/M/1 Queueing Problem with Model Uncertainty

Brownian Approximations of Multiclass Open-Queueing Networks

Simplified Control Problems for Multiclass Many-Server Queueing Systems

We consider scheduling and routing control problems for queueing models with I customer classes and J server pools, each consisting of many statistically identical, exponential servers. Customers require a single service that can be performed by a server from one of the pools; the service rate is ij ≥ 0, which depends on the customer’s class i and the server’s pool j , and customers can abandon...

Nonexistence of Brownian models for certain multiclass queueing networks

It has been demonstrated that Brownian models are effective for approximate analysis of queueing networks, particularly when no explicit analytical methods are available [3,4,1]. In 1988 Harrison [2] proposed Brownian models as approximations for multiclass open queueing networks. That work was expanded by Harrison and Nguyen in two recent papers [3,4] with the aim of developing a systematic me...

A Brownian control problem for a simple queueing system in the Halfin-Whitt regime

We consider a formal di4usion limit for a control problem of a multi-type multi-server queueing system, in the regime proposed by Hal*n and Whitt. This takes the form of a control problem where the dynamics are driven by a Brownian motion. In one dimension, a pathwise minimum is obtained and is characterized as the solution to a stochastic di4erential equation. The pathwise solution to a specia...

Robust Fluid Control of Multiclass Queueing Networks

This thesis applies recent advances in the field of robust optimization to the optimal control of multiclass queueing networks. We develop models that take into account the uncertainty of interarrival and service time in multiclass queueing network problems without assuming a specific probability distribution, while remaining highly tractable and providing insight into the corresponding optimal...