The authors of the original Ethernet
paper [5] gave the following model
to predict the performance of
an ethernet in terms of the percentage of time data packets were
on the net. Let **Q** be the number of systems connected to the net.
**A**, the probability that one system gains exclusive access at any
point in time, is

(**Q** systems have probability of gaining
access at a time when the other **Q - 1** systems, each with
probability ,
decides not to access the net). This definition is used to define
the mean time a station must wait before it gains access. The
time unit, known as a * slot time*, is the amount of time a system
waits before retransmitting when it finds the network busy. The
probability of waiting 0 slots is equal to **A**; the probability of
waiting one slot time is , etc., so the
probability of waiting
exactly **i** slot times is

The mean of the probability distribution
over all **i** gives the expected number of slot times a system will
have to wait before acquiring exclusive access to the ether:

Finally, the efficiency of the network in this model is the
percentage of time there are packets on the net. Let **P** be the
packet size, in bits (the ether is a bit-serial medium), let **C** be
the peak capacity (in bits per second), and let **T** be the length
of a time slot. Then the efficiency of the ethernet is

i.e. the time to send a packet as a fraction of the total time.

(a) Construct a table that gives the efficiency of the ethernet as a
function of the number of systems connected to the net (**Q**) and
average packet size (**P**). Some reasonable values for **C** are
10,000,000 (10 Mbps, true of most current ethernet installations)
or 100,000,000 (100 Mbps for new technology). For the slot time **T**
use 16 microseconds, which is the value used by Metcalfe and
Boggs.

(b) For a given number of systems on the network, is the network more efficient with long packets or short packets? Is this what you would expect?

(c) Is 16 microseconds a reasonable slot time? Explain.

(d) Given the way researchers actually use a local area network, with rlogins from an X terminal to an X client running on a compute server, e-mail, FTP transfers, etc., what do you think the actual distribution of packet sizes will be?

(e) If you have access to a network analyzer, see if you can record some data about packet sizes and efficiency for a segment of your local network. How do the measurements compare to the performance model?