1. (2 Points) Consider a system with single server to serve customers. The customers' arrival rate is 5 per hour and the server's service rate is 10 per hour. If we take a look of the system at several random times, shall we observe a queue of customers in the system? Explain the reason. 2. (2 Points) Consider two systems with single server to serve customers. The following two scenarios describe how the waiting time is affected by variability (in customers' arrival time and service time) and utilization (utilization is the demand rate over capacity rate): Scenario 1: Suppose two systems have the same utilization rate. The system with (High/Low) variability has shorter average waiting time. Scenario 2: Suppose two systems have the same variability. The system with (High/Low) utilization has shorter average waiting time. Hint: use the actual flow time - utilization graph 3. (4 Points) Tony Soprano sits at a table in the back of Irish Lion (a bar & restaurant) waiting for visitors. If the chair opposite Mr. Soprano is occupied, visitors wait at the bar. When the chair becomes free, the next visitor sits down and talks to Mr. Soprano. Visitors arrive randomly at a rate of ten per hour. Once seated, the visitor does not leave until Mr. Soprano has finished the conversation. Mr. Soprano is quite unpredictable. The lengths of his conversations are random, and have a mean time of four minutes. Once the conversation is over, the visitor always leaves the restaurant. Each visitor pays to the bar manager for the time waiting in the bar. The payment rate is $0.8 per minute. On average how much will each visitor pay to the bar manager