You are opening a new gym where members must check in their workout each day when they arrive. The arrival of members is estimated to be 6 minutes apart and follow a Poisson distribution. The service time to enter the information is estimated to average 9.6 minutes per transaction and follow an exponential distribution. To handle the demand you have installed two check in kiosks. You are designing the queue and are trying to decide if you should have everyone join one queue and then go to the first open kiosk or have two queues (one for each kiosk).
1. (4 pts) What would be the average wait time of the system with one queue and two servers?
2. Assuming that arrivals in each individual queue would be 12 minutes apart, what would be the average wait time of the system with two individual queues?
3. Which system do you recommend they install?