200 nodes are connected to a 1,500-meter length of coaxial cable. Using some protocol, each node can transmit 50 frames/second, where the average frame length is 2,000 bits. The transmission rate at each node is 100 Mbps (where 1 Mbps = 1,000,000 bps). What is the efficiency of this protocol?
To find the efficiency of this protocol, we need to calculate the total data rate and compare it to the actual transmitted data.
First, let's calculate the total data rate of all the nodes combined.
Total data rate = Number of nodes * Transmission rate per node
Total data rate = 200 nodes * 100 Mbps
Total data rate = 20,000 Mbps
Next, let's calculate the total amount of data that can be transmitted per second.
Total transmitted data = Transmission rate per node * Number of nodes * Average frame length
Total transmitted data = 100 Mbps * 200 nodes * 2000 bits
Total transmitted data = 4,000,000,000 bits
Now, let's calculate the efficiency of the protocol.
Efficiency = Total transmitted data / Total data rate
Efficiency = 4,000,000,000 bits / 20,000 Mbps
Efficiency = 4,000,000,000 bits / 20,000,000,000 bits
Now we can simplify the calculation:
Efficiency = 0.2
Therefore, the efficiency of this protocol is 0.2 or 20%.