Consider the following operation across output buffer of a network router that connects to a radio module that forwards (transmits) messages across an outgoing line.
Assume that messages that arrive at the output buffer follow a Poisson message arrival point process.
The time it takes to transmit a message across the outgoing line is assumed to be random and to follow an exponential distribution.
On average, each message contains a total of 6000 bits.
The outgoing messages are transmitted across the line at a rate of R Mbps.
Design the system by selecting, if feasible, the lowest outgoing data rate R and the maximum allowable message arrival rate λ(lambda), so that all the following objectives are met:
*Average message system-size is equal to 8.
*Average message waiting time is not higher than 20 msec.
*More than 80% of the messages experience a waiting time that is not higher than 26 msec.
Then for the system designed calculate the probability that the message waiting time is higher than 30 msec.