The authors of the original Ethernet paper  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?