Side_1_360

The Idleand Readstates are stochastic states.
The state sojourn times of these two states are
sampled from a probability density distribution.
Each user that starts to download a file enters the
Downloadcommunication state. A pointer to the
interface module that handles the communica-
tion stream is added to the identity vector of
Download, Idownload. When the file, and all its
content (text, images, applets), is downloaded,
the interface module closes the connection and
removes itself from Idownloadand the user returns
to the Readstate. The modelling framework
enables the (random) setting of an upper limit
of the download time, the impatience factor.
This factor allows the connection to be closed
before the entire web page is downloaded.

The parameters of the state model are extracted
from the work described in [Vic98] where an
aggregated stream of HTTP connections was
separated and broken into web sessions.

• Time sequence of file downloads– The Idle
  state uses the web session separator criterion
  as the expected sojourn time
  TIdle~ neg.exp. (γ) ; 1 / γ= 30 ⋅60 = 1800[sec.].


• Time between requests– Within a web session
  the mean time between requests is

–

X42.8

[sec.] with a coefficient of variation equal to

S/

–

X= 2.9. This means that the Read state in

the overall model is not negative exponential

distributed (in that case the S/

–

X= 1). This

state is therefore substituted by a hyper-expo-

nential distribution with 4 branches, each with

different time constants. The parameters are

determined to fit the truncated-Pareto model

used in [Vic98].

Substituting the Readstate with four sub-states
to model the hyper exponential distribution, the
complete model and the model parameters are
given in Figure 8.

2.2.2.2 The Voice Model
The voice model that is described does not
include control traffic, i.e. call set-up and dis-
connection signalling. The VoIP model uses a
simplified model of a telephony user. The media
stream is uni-directional, i.e. the A and B parties
are included in the same model but no synchro-
nisation (two-way communication) between the
two parties exists.

The user behaviour model consists of two states
as illustrated in Figure 9:

• Idle:A source generates three calls per hour
  and each call is generated according to a
  Poisson process;
  
  
  • Connect:The call duration time follows a
    negative exponential distribution with average
    of three minutes.
  
  
  
  

2.2.2.3 The Complete and Combined Model

The two models can be combined on one

machine by running either

• two processes,one with FTP and one with
  voice; or


• one processwhere the user behaviour state
  description is combined into one model.

In the current case, the simplest, and probably

the most efficient approach is to run two pro-

cesses. Even so, this section will look at a com-

Figure 10 Model with two

interface modules

Stocastic State Space Comm. State Space

λf

FTP

pα (1-p)α

Idle Read Download

Figure 8 The overall model of

a web or FTP client

Stochastic State Space Comm. State Space

λv

VoIP or CBR

α

Idle Send

Comm. State Space

Stochastic State Space Comm. State Space

λf

FTP

pα 1 (1-p)α 1

Read Download

VoIP / CBR

Connect

Idle

λv αv

Figure 9 The model of a voice

source without call signalling