Question

All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 2.5 passengers per minute. On Monday morning the arrival rate is 3 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution.

Note: Use P₀ values from Table 11.4 to answer the questions below.

1. Suppose two of the three screening stations are open on Monday morning. Compute the operating characteristics for the screening facility.
   
   Round your answer to four decimal places.
   
   P₀ =
   
   Round your answers to two decimal places.
   
   L_q =
   
   L =
   
   W_q =  min
   
   W =  min
   
   Round your answer to four decimal places.
   
   P_w =
   
2. Because of space considerations, the facility manager's goal is to limit the average number of passengers waiting in line to 10 or fewer. Will the two-screening-station system be able to meet the manager’s goal?
   
   Yes
   
3. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places.
   
   min

Answer 1

Solution:-

Given that

Here.

Number of channels open = 2

Average service rate () = 2.5 passengers per minute

Average arrival rate () = 3 passengers per minute.

Suppose two of the three screening stations are open on Monday morning. Compute the operating characteristics for the screening facility.

The operating characteristics are as given below.

1) probability that there are zero people in the system.

=0.25

2) Average number of people in system,

(Note: values might differ slightly due to rounding off)

3) Calculate average time a unit spends in the waiting line,

min

4) Calculate average time number of people or units in line waiting for service,

min

5) Calculate average time a person spends in queue,

min

B) Because of space considerations, the facility manager's goal is to limit the average number of passengers waiting in line to 10 or fewer. Will the two-screening-station system be able to meet the manager’s goal?

The facility manager wants to limit the average number of passenger waiting in line to less than or equal to 10. In the two-screening station system the average number of people waiting in line is 0.675: which is less than 10. Hence, the two-screening station system will be able to meet the manager's goal.

C)  What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places.

The average time required for a passenger to pass through security screening is 0.625 min

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