Title page for ETD etd-12042006-061411

Type of Document

Dissertation

Author

Lin, Chuan ,

Author's Email Address

chuanlin76@gmail.com

URN

etd-12042006-061411

Title

HEAVY TRAFFIC AND MARKOV MODULATED MODELS FOR WIRELESS QUEUEING SYSTEMS AND NUMERICAL METHODS FOR ASSOCIATED RESOURCE ALLOCATION PROBLEMS

Degree

PhD

Graduate Program

Operations Research

Advisory Committee

Advisor Name	Title
Robert Buche	Committee Chair
Ito, Kazufumi	Committee Member
Pang, Tao	Committee Member
Tran, Hien	Committee Member

Keywords

Markov modulated
Multi-completely S
Markov chain approximation
Heavy traffic

Date of Defense

2006-12-01

Availability

unrestricted

Abstract

This dissertation is concerned with heavy traffic and Markov modulated diffusion models
that are applied to resource allocation problems in wireless communication system and
the numerical analysis for their associated continuous time stochastic control problems.
To be specific, the heavy traffic model is a two-dimensional stochastic differential equation
with reflection (SDER), and the other model is a second-order Markov modulated diffusion
process.
With the proliferation of wireless applications having large capacity requirements, such
as multimedia, internet, gaming, etc., and the limitations of realizing spectral efficiency
gains, wireless queueing systems will be operating a near-capacity levels, so called ?Heavy
traffic?. Under this assumption, SDER has been developed as an approximation model
for a multi-buffer and various channel state wireless communication system. Building on
the seminal work of Buche and Kushner [13], we study how the reflection process can af-
fect the solution of the SDER and the resource (reserve power) allocation theoretically and
numerically. We have shown that Multi-Completely
S is a necessary condition for the exis-
tence and uniqueness for the SDER instead of the well known Completely
S in the wireline
system [69]. The whole resource (reserve transmission power) allocation is modeled as
a stochastic control problem subject to the SDER. Using Markov Chain Approximation
(MCA) method [51], various effects of factors, especially the reflection processes (nominal
power reallocation) are studied via numerical experiments. After optimal control policies
are obtained via MCA method under an appropriate grid size setting, Monte Carlo and real
time simulation experiments are done using heavy traffic policies v.s. heuristic wedge con-
trol policies. The performance of heavy traffic policies is better than that of wedge policies
under various traffic patterns including aggregated ON/OFF process (Long Range Depen-
dence & Heavy Tailed) which is an active research area in mathematical and engineering
communities.
Usually, the common objective of power control problem in mobile system is to min-
imize power consumption while maintaining the signal-to-interference-plus-noise ratio (SINR) above a predesigned threshold determined by the QoS requirement ( [88], [30]).
Static or quasi static channel gain is assumed (i.e., for most of the users, the channel
gains remain approximately constant over sufficiently long periods of time). But we pro-
pose a queue-based power control model where the channel gain process is modeled by a
finite-state continuous-time Markov chain and embedded explicitly in the queue dynam-
ics. Relatively few wireless power control literatures take a queue-based approach. In [16]
Chisci and his coworkers introduce Queue-Based Distributed Power Control algorithm but
the queue dynamics are described by a discrete-time system in quasi-static channel gain
environment. Buche and Kushner [13] study the forward-link queueing system with time-
varying channels using a heavy traffic method. A limit queueing model is obtained by weak
convergence methods, where an ?averaging? occurs through taking the limit, the channel
process is modelled in the prelimit process, however the channel process does not appear
explicitly in the limit model due to the averaging. Huang and his coworkers [36] propose
a reverse-link stochastic control framework, in their case, the channel gain (power attenu-
ation process) is described by a stochastic differential equation, the control objective is to
try to minimize the total transmission power as well as maintain acceptable levels for the
SINR. We consider queue dynamics described by a continuous time Markov-modulated
diffusion process due to the time-varying channel gains. Furthermore, we model the affect
of the SINR on the queue dynamics through a bit error rate (BER) function. Similarly, we
discusse the associated power allocation problem in a stochastic control framework, the
corresponding HJB function is derived and numerical method is discussed.

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