Airports have always faced the problem of long waiting lines and waiting times at security gates. Waiting lines can be as long as hundreds of yards and waiting times can sometimes be hours. In their efforts to reduce waiting lines and times, or at least to not have them become longer as airline demand increases, airports have analyzed their existing security systems and sought quantitative solutions. One of the key components of any effort to operationally improve airport security procedures is forecasting passenger arrivals at security checkpoints to determine how many security checkpoints and staff are needed. At Berry International Airport (BEI), security analysts would like to forecast passenger arrivals for next July, the airport's busiest travel month of the year, for the purpose of determining how many security checkpoints they should staff during the month so that waiting lines and times will not be excessively long. Demand for airline travel has generally been increasing during the past 3 years. There are two main concourses at BEI, North and South, each serving different airlines. The attached table shows passenger arrivals at the South concourse for 10 days (selected randomly) in 2-hour segments from 4:00 a.m. to 10:00 p.m. for the month of July for the past 3 years.

Part (a) Develop a forecast for daily passenger arrivals at the South concourse at BEI for each time period for one day in July of year 4.

Part (b) Use the forecast developed to perform this type of waiting line analysis to determine how many security checkpoints are needed during each time segment. Assume that as passengers arrive at the South concourse security gate, they join a single line to have their boarding pass and identification checked at one of several stations. When passengers leave these stations, they again form a single line and are approximately equally distributed among the security checkpoints by security personnel before going through the various detection machines. For July the airport plans to staff six security checkpoints for each 2-hour time segment from 4:00 a.m. to 6:00 p.m., and then three checkpoints from 6:00 p.m. to 8:00 p.m., and two check- points from 8:00 p.m. to 10:00 p.m. Assume that the arrival rate at this point in the security system is Poisson distributed, with the forecasted passenger arrivals developed in Part (a) as the mean arrival rate. Further, assume that service times are exponentially distributed with a mean of 11.6 seconds. Determine whether the number of security checkpoints the airport plans to use for each 2-hour time segment is sufficient to keep passengers moving freely through the security system without excessive delays. The airport wants to keep the average time of a passenger in the system to be less than 5 minutes. If the planned system is not likely to be sufficient, determine the number of checkpoints that would be needed for each 2-hour segment in order for passengers to move quickly through the security checkpoints without excessive waiting times (the average time in the system to be less than 5 minutes).

	Day	4-6 AM	6-8 AM	8-10 AM	10-noon	noon-2 PM	2-4 PM	4-6 PM	6-8 PM	8-10 PM
Year One	1	2400	2700	3200	1400	1700	1800	1600	800	200
Year One	2	1900	2500	3100	1600	1800	2000	1800	900	300
Year One	3	2300	3100	2500	1500	1500	1800	1900	1100	200
Year One	4	2200	3200	3100	2200	1900	2400	2100	1200	400
Year One	5	2400	3300	3400	1700	2200	2100	2000	1000	600
Year One	6	2600	2800	3500	1500	1700	1900	1500	1100	300
Year One	7	1900	2800	3100	1200	1500	2000	1400	900	400
Year One	8	2000	2700	2500	1500	2000	2300	1900	1000	200
Year One	9	2400	3200	3600	1600	2100	2500	1800	1400	200
Year One	10	2600	3300	3100	200	2500	2600	2400	1100	400
Year Two	11	3100	3900	4100	2200	2600	2300	2500	1100	300
Year Two	12	2800	3400	3900	1900	2100	2500	2000	1200	300
Year Two	13	2700	3800	4300	2100	2400	2400	2400	1200	400
Year Two	14	2400	3500	4100	2400	3000	3200	2600	1200	700
Year Two	15	3300	3700	4000	2600	2600	2700	2900	1000	300
Year Two	16	3500	4000	3800	2300	2700	3100	3000	900	200
Year Two	17	2900	4100	3900	2400	3000	3200	2500	1100	500
Year Two	18	3400	3800	4200	2000	2500	3000	2200	1000	300
Year Two	19	3600	3600	4000	2300	2600	2800	2600	1200	200
Year Two	20	3700	3700	4000	2200	2600	2700	2400	1200	200
Year Three	21	4400	4400	4500	2600	3300	3400	3000	1200	400
Year Three	22	4200	4500	4300	2500	3400	3600	3100	1400	300
Year Three	23	4500	4500	4700	2700	3400	3500	2900	1200	300
Year Three	24	4600	4600	4600	2500	3200	3500	2800	1300	300
Year Three	25	4500	4300	4400	2900	3300	3300	3300	1500	400
Year Three	26	4200	4300	4500	3000	4000	3400	3000	1500	600
Year Three	27	4500	4500	5100	3300	4000	3700	3100	1200	300
Year Three	28	4300	4200	4300	2800	3500	4000	3300	1100	400
Year Three	29	4900	4100	4200	3100	3600	3900	3400	1400	500
Year Three	30	4700	4500	4100	3000	4000	3700	3400	1200	500