Problem 5 (16 Marks) A take-out fast food restaurant located in a busy downtown area has one window open from 11:00am to 11:00pm each day. It is found that every 10 minutes (in average), there is a customer coming to the restaurant. The average time to serve a customer (including time to place order, time to get food ready and time to pay the bill) is 4 minutes. It is also observed that both arrival and service processes follow Poison distributions. Use the standard queuing theory models discussed in class to evaluate the situation of the restaurant by calculating: 5.1) the estimated time that the service window is busy serving customers in the 12 hours each day 5.2) the expected time a customer will wait to get served after he/she arrives at the restaurant 5.3) the expected time a customer will spend at the restaurant (including waiting time and the time of being served) after he/she arrives at the restaurant 5.4) the estimated time that there are 2 or more customers in the restaurant in the 12 hours each day 2 You may use the following equations in answering this question. System utilization: p = 2, where 2 is customer arrival rate and u is the service rate. Expected time in queue: Tq = H(1-2) Expected time in system T Probability that there are n customers in the system: P(n) = P(0) x 0)* = (1 - 4)*" 1