Question Content Area

Problem 11-19 (Algorithmic)

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 passengers per minute. On Monday morning the arrival rate is 4.8 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 2 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning.

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

1. The facility manager's goal is to limit the average number of passengers waiting in line to 14 or fewer. How many screening stations must be open in order to satisfy the manager's goal? Having 3 station(s) open satisfies the manager's goal to limit the average number of passengers in the waiting line to at most 14.
2. What is the average time required for a passenger to pass through security screening? Round your answer to two decimal places. W=

TABLE 11.4 VALUES OF P, FOR MULTIPLE-SERVER WAITING LINES WITH POISSON ARRIVALS AND EXPONENTIAL SERVICE TIMES Number of Servers (k) Ratio A/u 2 3 4 5 0.15 0.8605 0.8607 0.8607 0.8607 0.20 0.8182 0.8187 0.8187 0.8187 0.25 0.7778 0.7788 0.7788 0.7788 0.30 0.7391 0.7407 0.7408 0.7408 0.35 0.7021 0.7046 0.7047 0.7047 0.40 0.6667 0.6701 0.6703 0.6703 0.45 0.6327 0.6373 0.6376 0.6376 0.50 0.6000 0.6061 0.6065 0.6065 0.55 0.5686 0.5763 0.5769 0.5769 0.60 0.5385 0.5479 0.5487 0.5488 0.65 0.5094 0.5209 0.5219 0.5220 0.70 0.4815 0.4952 0.4965 0.4966 0.75 0.4545 0.4706 0.4722 0.4724 0.80 0.4286 0.4472 0.4491 0.4493 0.85 0.4035 0.4248 0.4271 0.4274 0.90 0.3793 0.4035 0.4062 0.4065 0.95 0.3559 0.3831 0.3863 0.3867 1.00 0.3333 0.3636 0.3673 0.3678 1.20 0.2500 0.2941 0.3002 0.3011 1.40 0.1765 0.2360 0.2449 0.2463 1.60 0.1111 0.1872 0.1993 0.2014 1.80 0.0526 0.1460 0.1616 0.1646 2.00 0.1111 0.1304 0.1343 2.20 0.08 15 0.1046 0.1094 2.40 0.0562 0.0831 0.0889 2.60 0.0345 0.0651 0.0721 2.80 0.0160 0.0521 0.0581 3.00 0.0377 0.0466 3.20 0.0273 0.0372 3.40 0.0186 0.0293 3.60 0.0113 0.0228 3.80 0.0051 0.0174 4.00 0.0130 4.20 0.0093 4.40 0.0063 4.60 0.0038 4.80 0.0017