Ethernet Performance

Ethernet is a set of technologies and protocols that are used primarily in LANs. The performance of Ethernet is analyzed by computing the channel efficiency under different load conditions, particularly focusing on how stations contend for access to the shared medium.

Channel Acquisition Probability

Let us assume an Ethernet network has k stations and each station transmits with a probability p during a contention slot. Let A be the probability that some station successfully acquires the channel in a given slot:

A = kp (1?p)^(k?1)

The value of A is maximized when p = 1/k. If there can be innumerable stations connected to the Ethernet network (k ? ?), the maximum value of A approaches 1/e ? 0.368.

Contention Period Analysis

Let Q be the probability that the contention period has exactly j slots (j?1 collisions followed by one successful transmission):

Q = A (1?A)^(j?1)

The mean number of slots per contention period M is calculated as:

M = 1/A

Given that ? is the propagation time, each slot has duration 2?. Hence the mean contention interval w will be 2?/A.

Channel Efficiency

Let P be the time in seconds for a frame to propagate across the network. The channel efficiency when multiple stations contend for transmission is:

Efficiency = P / (P + (2?/A))

In terms of frame length F, cable length L, signal propagation speed c, and contention slots per frame e, the channel efficiency becomes:

Efficiency = 1 / (1 + 2eLc/(FB))

Key Performance Factors

Conclusion

Ethernet performance is determined by the balance between successful transmissions and collision overhead. Maximum theoretical efficiency approaches 37% under optimal conditions, with longer frames and shorter cables improving performance in contention-based scenarios.