A statistical multiplexer is used to buffer large data files prior to transmission. The arrival rate of files is λ files/sec. The average file length is 40,000 bytes. Assume the inter-arrival times and file lengths are exponentially distributed. The link speed is 1 Mbits/sec.
A design objective is that total delay (queuing + service time) must be no more than 500 ms.
(a) Find the maximum arrival rate, λmax, under this delay constraint.
(b) Using the maximum arrival rate from part (a), find the probability that there is a file currently in
service and none waiting in the buffer.