questions on Markov chain and queue models

1) In an M/M/1 queue model, with λ=1 / time unit, and μ=2 / time unit, find:
a) P(>3 in the system)
b) mean system time and mean waiting time
c) mean number in system and mean number in queue

2) For the M/M/1 queue model, what service rate is required to ensure that the mean delay is <10 seconds if the arrival rate = 2 jobs per second?

3) For the M/M/1 queue model, what service rate is required to ensure that the mean queue length is <10 jobs if the arrival rate = 2 jobs per second?

4) 50 computers (C1-C50) are connected to the internet via another computer (C0) acting as an edge router. We assume that C1-C50 are generating packets randomly, each at a rate of 1 packet per 1⁄2 millisecond, and that the packet lengths are variable with a mean of 1000bytes. Propose a queue model for the buffer in C0 that holds these packets before they are transmitted to the wider internet. Using an appropriate (perhaps approximate) formula, determine the rate (bits per sec) at which C0 must transmit packets out of its buffer such that the loss probability is kept below 0.001. Assume that the buffer can hold at most 1000 packets.