6
Traffic Models
you’ve got a source
LEVELS OF TRAFFIC BEHAVIOUR
So, what kind of traffic behaviour are we interested in for ATM, or IP? In
Chapter 3 we looked at the flow of calls in a circuit-switched telephony
network, and in Chapter 4 we extended this to consider the flow of
cells through an ATM buffer. In both cases, the time between ‘arrivals’
(whether calls or cells) was given by a negative exponential distribution:
that is to say, arrivals formed a Poisson process. But although the same
source model is used, different types of behaviour are being modelled.
In the first case the behaviour concerns the use made of the telephony
service by customers – in terms of how often the service is used, and
for how long. In the second case, the focus is at the level below the call
time scale, i.e. the characteristic behaviour of the service as a flow of cells
or, indeed, packets. Figure 6.1 distinguishes these two different types of
behaviour by considering four different time scales of activity:
ž calendar: daily, weekly and seasonal variations
ž connection: set-up and clear events delimit the connection duration,
which is typically in the range 100 to 1000 seconds
ž burst: the behaviour of a transmitting user, characterized as a cell (or
packet) flow rate, over an interval during which that rate is assumed
constant. For telephony, the talk-spurt on/off characteristics have
durations ranging from a fraction of a second to a few seconds. In IP,
similar time scales apply to packet flows.
ž cell/packet: the behaviour of cell or packet generation at the lowest
level, concerned with the time interval between arrivals (e.g. multiples
of 2.831
µ
s at 155.52 Mbit/s in ATM)
Introduction to IP and ATM Design Performance: With Applications Analysis Software,

information about typical service mixes – how much voice, video and
data traffic is being transported on any link (which would be obtained
from a study of service use).
TIMING INFORMATION IN SOURCE MODELS
A source model describes how traffic, whether cells, bursts or connections,
emanates from a user. As we have already seen, the same source model
can be applied to different time scales of activity, but the Poisson process
is not the only one used for ATM or IP. Source models may be classified in
a variety of ways: continuous time or discrete time, inter-arrival time or
counting process, state-based or distribution-based, and we will consider
some of these in the rest of this chapter. It is worth noting that some
models are associated with a particular queue modelling method, an
example being fluid flow analysis.
A distinguishing feature of source models is the way the timing
information is presented. Figure 6.2 shows the three different ways in
the context of an example ATM cell stream: as the number of cell slots
between arrivals (the inter-arrival times are 5, 7, 3 and 5 slots in this
TIME BETWEEN ARRIVALS
83
20% of cell slot rate
Cells in block of 25 cell slots
12 345
5735
Cell slots between arrivals
Time
Figure 6.2. Timing Information for an Example ATM Cell Stream
example); as a count of the number of arrivals within a specified period
(here, it is 5 cells in 25 cell slots); and as a cell rate, which in this case is
20% of the cell slot rate.
TIME BETWEEN ARRIVALS

2
Figure 6.3. The Memoryless Property of the Negative Exponential Distribution
84
TRAFFIC MODELS
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