Access Type

Open Access Dissertation

Date of Award

January 2010

Degree Type


Degree Name



Electrical and Computer Engineering

First Advisor

Cheng-Zhong Xu








August 2010

Advisor: Dr. Cheng-Zhong Xu

Major: Computer Engineering

Degree: Doctor of Philosophy

Internet traffic often exhibits a structure with rich high-order statistical properties like selfsimilarity

and long-range dependency (LRD). This greatly complicates the problem of

server performance modeling and optimization. On the other hand, popularity of Internet

has created numerous client-server or peer-to-peer applications, with most of them,

such as online payment, purchasing, trading, searching, publishing and media streaming,

being timing sensitive and/or financially critical. The scheduling policy in Internet servers

is playing central role in satisfying service level agreement (SLA) and achieving savings

and efficiency in operations. The increasing popularity of high-volume performance critical

Internet applications is a challenge for servers to provide individual response-time guarantees.

Existing tools like queuing models in most cases only hold in mean value analysis

under the assumption of simplified traffic structures.

Considering the fact that most Internet applications can tolerate a small percentage of

deadline misses, we define a decay function model characterizes the relationship between

the request delay constraint, deadline misses, and server capacity in a transfer function

based filter system. The model is general for any time-series based or measurement based

processes. Within the model framework, a relationship between server capacity, scheduling

policy, and service deadline is established in formalism. Time-invariant (non-adaptive)

resource allocation policies are design and analyzed in the time domain. For an important

class of fixed-time allocation policies, optimality conditions with respect to the correlation

of input traffic are established. The upper bound for server capacity and service level are derived

with general Chebshev's inequality, and extended to tighter boundaries for unimodal

distributions by using VysochanskiPetunin's inequality.

For traffic with strong LRD, a design and analysis of the decay function model is done

in the frequency domain. Most Internet traffic has monotonically decreasing strength of

variation functions over frequency. For this type of input traffic, it is proved that optimal

schedulers must have a convex structure. Uniform resource allocation is an extreme case

of the convexity and is proved to be optimal for Poisson traffic. With an integration of

the convex-structural principle, an enhance GPS policy improves the service quality significantly.

Furthermore, it is shown that the presence of LRD in the input traffic results

in shift of variation strength from high frequency to lower frequency bands, leading to a

degradation of the service quality.

The model is also extended to support server with different deadlines, and to derive

an optimal time-variant (adaptive) resource allocation policy that minimizes server load

variances and server resource demands. Simulation results show time-variant scheduling

algorithm indeed outperforms time-invariant optimal decay function scheduler.

Internet traffic has two major dynamic factors, the distribution of request size and the

correlation of request arrival process. When applying decay function model as scheduler

to random point process, corresponding two influences for server workload process is revealed

as, first, sizing factor--interaction between request size distribution and scheduling

functions, second, correlation factor--interaction between power spectrum of arrival process

and scheduling function. For the second factor, it is known from this thesis that convex

scheduling function will minimize its impact over server workload. Under the assumption

of homogeneous scheduling function for all requests, it shows that uniform scheduling is

optimal for the sizing factor. Further more, by analyzing the impact from queueing delay

to scheduling function, it shows that queueing larger tasks vs. smaller ones leads to less

reduction in sizing factor, but at the benefit of more decreasing in correlation factor in the

server workload process. This shows the origin of optimality of shortest remain processing

time (SRPT) scheduler.