Consider a communication link between two nodes, A and B. The bit rate of the channel is 10,000,000 bits per second. Packets arriving at the channel are placed in a queue until they are transmitted. (Assume the number of buffers in the queue is infinite.) Assume packet lengths (including headers) are exponentially distributed, with a mean packet length of 5000 bits. Assume packet arrivals are Poisson at a mean rate of 1800 packets per second.

Assume that router A has just finished transmitting a packet and that the queue currently holds 5 packets. What is the probability that none of these packets will be transmitted completely in a period of 1 millisecond (0.001 seconds)? Show your work.

Imagine that we partition the channel into 4 subchannels, each with a bit rate of 2.5 Mbps (2,500,000 bits per second) and each with its own queue. Assume that arriving packets are randomly placed in one of the 4 outgoing queues. Compute the average time (T 0 ) that a packet spends in this system (both in the queue and being transmitted). Show your work.