At a Chick-fil-A location, there are two drive-through lines, each with one staff member responsible for...

  

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At a Chick-fil-A location, there are two drive-through lines, each with one staff member responsible for taking orders. During lunch hours, an average of 120 customers (cars) arrive per hour, following a homogeneous Poisson process, and they choose one of the two lines. The average time required to place an order in either line is 0.75 minutes. Additionally, the average service time at the drive-thru window is 0.4 minutes. Both the time to place an order and the service time at the drive-through window follow exponential distributions. The system is represented as a queuing network in the figure below. Average service time: 0.75 minutes Arrival rate: 120/hour 0.5 00 O Drive-thru line 1 Oo o Drive-thru line 2 Average service time: 0.4 minutes 00 O Drive-thru window a. Each drive-through line, where customers place orders, can be modeled as a system. A. M/M/1 B. M/M/2 C. M/G/1 D. M/D/1 b. The drive-through window can be modeled as a A. M/M/1 B. G/M/1 _queueing system. C. M/G/1 D. M/D/1 _queueing c. Find the utilization of the staff in each drive-through line and at the drive-through window. d. Find the steady-state average time in queue (W) and in system (W), steady state average number of customers in queue (L) and in system (2) for both drive-through lines and the drive-through window. At a Chick-fil-A location, there are two drive-through lines, each with one staff member responsible for taking orders. During lunch hours, an average of 120 customers (cars) arrive per hour, following a homogeneous Poisson process, and they choose one of the two lines. The average time required to place an order in either line is 0.75 minutes. Additionally, the average service time at the drive-thru window is 0.4 minutes. Both the time to place an order and the service time at the drive-through window follow exponential distributions. The system is represented as a queuing network in the figure below. Average service time: 0.75 minutes Arrival rate: 120/hour 0.5 00 O Drive-thru line 1 Oo o Drive-thru line 2 Average service time: 0.4 minutes 00 O Drive-thru window a. Each drive-through line, where customers place orders, can be modeled as a system. A. M/M/1 B. M/M/2 C. M/G/1 D. M/D/1 b. The drive-through window can be modeled as a A. M/M/1 B. G/M/1 _queueing system. C. M/G/1 D. M/D/1 _queueing c. Find the utilization of the staff in each drive-through line and at the drive-through window. d. Find the steady-state average time in queue (W) and in system (W), steady state average number of customers in queue (L) and in system (2) for both drive-through lines and the drive-through window.