Question 1. (100 points) Consider a queueing system with two paralel servers and a single waiting line: customers join a single line if both servers are busy. They eventually serviced by the first free server. If a customer arrives while both servers are idle, he/she then prefers server 1 (who happens to work faster). The times between arrivals and the service time distributions of the servers are given as the following: Time between Arrivals (min.) Probability Service time for Server 1 Probability Service time for Server 2 Probability 1 0.25 2 0.30 3 $0.35 2 0.40 3 0.28 4 0.25 3 0.20 4 0.25 5 0.20 4 0.15 5 0.17 6 0.20 Random Numbers 26 98 90 26 42 74 5 68 22 48 for Arrival Random Numbers for Service Time 95 21 51 92 89 38 84 61 50 49 a. (90 points) By using the above random numbers for inter-arrival and service time, create a hand simulation table that shows the operation of the system for 10 new customers. The first of the 10 new customers arrives at a time determined at random. Start the simulation with one customer being served in server 1, and assume that his/her service time is 3 minutes. b. (10 points) What is the probability that a customer has to wait in the queue? In your calculation, exclude the customer being served in server 1 at the beginning of the simulation.