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 3.5 passengers per minute. On Monday morning the arrival rate is 4.9 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. Note: Use Po values from Table 11.4 to answer the questions below. a. 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. Por Round your answers to two decimal places. L= Warmin W= min Round your answer to four decimal places. Pw = 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? c. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places. min

Answer 1

a = 49,4²3.5 ²3 9. on Monday morning a serening station are open de ser s! 1-lu) 4:0 911 1-4V 22.176470 - 0.1765 2067 4.9 * 3,5 5! (1-3) 20.1165x (%5), 07 sooth by 2177-0.792 la comte = 0.1765 x 1.4), 2 013 2. mga Kast = 1.3453 foto Contes L² Lat Malan Elovne 1 1.3453 + 4.2 - 2.7453 ~ 9.744 3.5 319 = 0.27450.27 4.92 We Wq + r = 0.2745 + 1/5 = 0.5602 ~ 0.56 Pwet- Po-Pi-P2 21-0-17849 – (Ma) po co fin ( 21-0.17647 - 1.4x0.17647 – 1.42 0.17647 L' if osnss! z 0.40353 ~ 0.4035 47 - -0.17647 21 -0.17 00/74

B) Lq = 1.34 < 10 , So two screening station will be able to meet the manager's goal.

C) Average time required for a passanger to pass through the security screening = W = 0.56 min