Question No. 1: Consider an M/M/1/2 queueing system in which each customer ac- cepted into the system brings in a profit of $5 and each customer rejected results in a loss of $1. Find the arrival rate at which the system breaks even. Question No. 2: Suppose that two types of customers arrive at a queueing system according to independent Poisson process of rate Both types of customers require exponentially distributed service times of rate u. Type 1 customers are always accepted into the system, but type 2 customers are turned away when the total number of customers in the system exceeds K. (a) Sketch the state transition diagram with total number of customers. (b) Find the steady state PMF. Question No. 3: Consider the M/M/1/B queue with the departure probability of 0.2. In order to limit the packet loss probability to 0.05 and the load factor to 0.5, how much the buffer size should be? Also find all the performance metrics of the queue