The average daily number of passengers in TErminal 3 of Logan airport is 10200, and 12% of them arrive to the terminal during 5-6am. Suppose now that 30% of these passengers are enrolled in TSA's Pre-check program. These passengers line up in a separate queue and go through separate security screening lanes called Pre-check lanes for faster security screening. Non pRe-Check passengers go through a different queue and security screening lanes. A pre-check lane is always staffed with 4 TSA Officers and can process 250 passengers per hour with the coefficient of variation of the processing time 1 and the coefficient of variation of the inter-arrival time 1.

1) To ensure that the Pre-check queue is stable, what is the least-cost lane opening and staffing plan for the 5-6am period? (recall that it cost $30 per TSA per hour and $40 per hour to operate a lane.)

2) what is the Average waiting time of a passenger in the pre-check queue?

3) what is the average queue length?