1. Consider a service system where arrivals tend to get discouraged as the number of cus- tomers in the system increases: (we observe this effect in the arrival rates) 1 lo = = 1, 11 1 2 12 1 13 3 4 and lk = 0 for k = 4,5, ... customers/min. There are two identical servers in this system; each server's service time is an exponen- tially distributed random variable with rate u = customers/min. For the queueing system, (a) (5 points) Construct the state transition rate diagram. (b) (10 points) Determine the steady-state probabilities. (c) (5 points) Determine the expected number of customers in system (d) (5 points) Determine the effective arrival rate (e) (5 points) Determine the expected system time