# Average waiting time for constant-length messages

I. Messages arrive at random to be sent across a communications link with a data rate of 9600 bps. The link is 70% utilized, and the average message length is 1000 octets. Determine the average waiting time for constant-length messages and for exponentially distributed length messages

II. Messages arrive at a switching center for a particular outgoing communications line in a Poisson manner with a mean arrival rate of 180 messages per hour. Message length is distributed exponentially with a mean length of 14,400 characters. Line speed is 9600 bps.

What is the mean waiting time in the switching center?

III+IV. Consider a bus LAN with a number of equally spaced stations with a data rate of 10 Mbps and a bus length of 1 km.

a. What is the mean time to send a frame of 1000 bits to another station, measured from the beginning of transmission to the end of reception? Assume a propagation speed of 200m/sec.

b. If two stations begin to transmit at exactly the same time, their packets will interfere with each other. If each transmitting station monitors the bus during transmission, how long before it notices interference, in second? In bit times?

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#### Solution Summary

Average waiting time for constant-length messages and for exponentially distributed length messages, Mean waiting time in the switching center, Mean time to send a frame