Contents Telektronikk - Telenor

Since the calculated delays are those of
the M/M/1 sojourn times, node processing
times and link propagation delays
should be added to give complete results.
18 Local area networks
Up till now the traffic system description
and analysis has assumed very simple
methods of access to the available
servers. That is assured by having only
one access point at each end of a link.
Simultaneous occupation from both ends
is resolved before any user information is
transmitted. Competition for resources is
resolved by rejection of attempts or by
queuing. In multi-access systems competition
can be handled by means of polling
by a control node, by handing over sending
permission (token) from node to
node, or simply by trying and (if necessary)
repeating.
18.1 The ALOHA principle
The simplest assumption for transmission
over a common channel, whether it is a
frequency band for radio transmission or
a local bus, is the one called ALOHA.
The normal Poisson case of an unlimited
number of independent sources each with
an infinitesimal call rate to give a resulting
finite total call rate is assumed. Each
transmission is assumed to last one time
unit. There is a common control node to
detect collisions between transmissions,
and all sources have the same delay to
the control node. Collisions result in
retransmissions. At very low offered
rates, collisions are very unlikely, and
throughput will be equal to offered traffic.
With growing call rates the number
of collisions will increase, thus increasing
the number of retransmissions, and
after passing a maximum the throughput
will decrease with increasing call rate,
until virtually nothing is let through.
When one packet is being transmitted, a
packet from another station will partially
overlap if transmission starts within a
time window twice the packet length.
A simple deduction leads to the formula
for throughput
S = Ge –2G (106)
where G = number of transmitted packets
per time unit. That includes primary
transmissions and retransmissions as
well. We see that S' = dS/dG = e –2G (1 –
2G) = 1 for G = 0, and S' = 0 for G = 0.5
and G = ∞.
Thus, Smax = 0.5/e = 0.18.
An improvement is obtained by synchronising
transmission in time slots to give
slotted ALOHA. Thus collisions only
happen in complete overlaps, and the
critical period is one time unit instead of
two, to give
S = Ge –G (107)
with Smax = 1/e = 0.37 for G = 1.
18.2 The CSMA/CD principle
The ALOHA analysis can be modified
by taking into account delays. When the
simple form is used, it can be supported
by the fact that it has been used mostly
with low rate radio transmission, where
the propagation delay is short compared
with the packet transmission time
(a = Tp /Tt 0.9, whereas
CSMA/CD would experience congestion
at a much lower point.
Tp
1
=
a(a +
N
1
N )
19 Mixed traffic and high
capacity systems
The main focus of the article has been
basic traffic relations and models based
initially on telephone traffic relations.
However, also data traffic has been discussed,
and the distinct burstiness of such
traffic has been pointed out. (See for
instance Figure 10.) There is far less
knowledge available on real data traffic
than that of telephone traffic. The two
main reasons for this are 1) the long tradition
(~ 90 years) of studies, and 2) the
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