James T. was thinking how to restructure the front desk to reach an optimum level of staff efficiency and guest service. At present, the hotel has five check-in employees on duty, each with a separate waiting line, during peak check-in time of 3:00pm - 5.00 pm Observation of arrivals during this period shows that an average of 90 guests arrive each hour (18 guests on average for each check-in line). It takes an average of 3 minutes for the front-desk employee to register each guest. He thinks two plans for improving guest service by reducing the length of time that guests spend waiting in line. The first proposal would designate one member of the check-in team as a quickservice employee for guests registering under corporate accounts, a market segment that fills about 30% of all occupied rooms. Because corporate guests are preregistered, their registration takes just 2 minutes. With these guests separated from the rest of the customers, the average time for registering a typical guest would climb to 3.6 minutes. Under this plan, non-corporate guests would choose any of the remaining four lines. The second plan is to implement a single-line system. All guests could form a single waiting line to be served by whichever of five employees became available. This option would require sufficient lobby space for what could be a substantial queue. Assume that arrivals are following a Poisson distribution and service times follow an exponential distribution under all scenarios.

1. What is the utilization of each check-in employee under each scenario? Can you please answer in more than one sentence. how we got this answer?

2. Determine the average amount of time that a guest spends checking in. How would this change under each of the stated options?

3. What is the average length of the queue for the proposed single-line system?

4. Which option do you recommend? Why? Please explain more than one sentence.