Question: Suppose the input traffic to a network node follows a Poisson process with the rate of 210,000 packets/sec. Assume the packet lengths are exponentially distributed

Suppose the input traffic to a network node follows a Poisson process with the rate of 210,000 packets/sec. Assume the packet lengths are exponentially distributed with an average of 1250 bytes, and that the output link data rate is 3 Gbps. Assume the packet processing time is negligible, so the only service time is the transmission (serialization) time of the packet.

(a) Calculate the probabilities that the input queue has 1 packet, 2 packets and 5 packets (excluding the packet that is being transmitted), respectively.

(b) What is the mean number of packets in the system? What is the mean number in the queue?

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