Robert Utes needs to decide where to get a haircut. He has narrowed the choice down to two local hair salons – Large Hair Salon (LHS) and Small Hair Cutters (SHC).
During busy periods, a new customer walks into LHS every 15 minutes on average, with a standard deviation of 15 minutes. At SHC, a customer walks in every hour on average, with a standard deviation of 1 hour. LHS has a staff of 4 barbers, while SHC has 1 barber. The average service time at both salons is 30 minutes, with a standard deviation of 30 minutes.
1. If Robert walks into LHS during a busy period, how long must he wait in line (in minutes) before he receives a haircut? (Only include the waiting time, not any service time)
2. What is the total average flow time (in minutes) of LHS, which includes both the waiting time and the time in service?
3. How many customers, on average will be in LHS, including both customers waiting in line and customers being served?
4. What is the average number of customers in service (excluding those that are waiting in line) in LHS?
5. If Robert goes to SHC, how long (in minutes) must he wait in line before his haircut starts?
6. LHS will buy out SHC. LHS will then close SHC’s operations and serve all customers, including existing SHC customers, at the LHS location only. Assuming that the previous traffic of SHC customers now flows to the LHS location, what is the new inter-arrival time (in minutes) at LHS?