Data packets arrive (with Poisson distribution) to a pool of 2 modems with the arrival rate of 20 packets per second (lambda=20 packets/second), and the packet lengths are exponentially distributed with mean length 1000 bits per packet. Each modem has a service rate 10 kbits/s (kilobits per second). First, assume that there are no buffers (or queues) in the system, and hence, packets that find all modems reserved get blocked. a) Draw the state diagram of the system with the corresponding transition rates. b) Obtain the steady state probabilities by using the state diagram. c) What is the probability that a connection attempt fails due to blocking? d) What is the average waiting time spent in the system? Now, assume that we include a buffer with a maximum size of 2. (i.e. the system is now of type M/M/2/4). e) Recalculate the parameters asked in parts c), d). f) Comment on the change in both blocking probability and average waiting time when we insert a buffer into the system. Explain the change (i.e. why there is an increase or decrease) in each case.