We need to plan our travel to reach Washington D.C. (Reagan National Airport) departing from EH. There are a couple options one could consider:
1. Take the Metro to Madison Dane County Regional (MSN) airport and fly to Reagan (DCA) airport through Chicago O’Hare (ORD) airport
2. Drive to Madison Dane County Regional (MSN) airport and fly to Reagan (DCA) airport through Chicago O’Hare (ORD) airport
3. Walk to Chazen Museum to catch the Bucky Bus shuttle to O’Hare (ORD) airport and fly to Reagan (DCA) airport.
4. 4. Drive to O’Hare (ORD) airport and fly to Reagan (DCA) airport.

Bus Route A to North Transfer Point leaves from EH every 30 minutes beginning at 6 AM till 6 PM. TT reliability for Route A is as follows:

Route A TT (mins)	Probability
25	0.45
28	0.30
33	0.25

Bus Route B from North Transfer Point to the Airport leaves every 30 minutes beginning at 6 AM till 6 PM. TT reliability for Route B is as follows:

Route B TT (mins)	Probability
12	0.65
15	0.25
20	0.10

Need to reach the airport 45 minutes before scheduled departure, otherwise one cannot board the flight. Airline Schedule and associated TT reliability for MSN to ORD is as follows:

Flight	Departure Time	Time to ORD (h:mm)	Probability
Badger 2376	10 AM	0:50	0.30
		1:00	0.20
		1:15	0.40
		Infinity	0.10
Badger 1204	1 PM	0:55	0.30
		1:00	0.25
		1:20	0.40
		Infinity	0.05
Badger 9042	4 PM	1:00	0.20
		1:10	0.20
		1:20	0.50
		infinity	0.10

Airline Schedule and associated TT reliability for ORD to DCA is as follows:

Flight	Departure Time	Time to DCA (h:mm)	Probability
Badger 761	11:30 AM	1:50	0.35
		2:00	0.40
		2:15	0.24
		Infinity	0.01
Badger 204	2:45 PM	1:55	0.10
		2:00	0.20
		2:20	0.69
		Infinity	0.01
Badger 423	5:30 PM	2:00	0.05
		2:10	0.35
		3:15	0.59
		infinity	0.01

Walk time to Chazen Museum from EH:

Walk time to Chazen (mins)	Probability
10	0.30
12	0.40
15	0.30

Bucky Bus shuttle leaves from Chazen Museum every 1.5 hours beginning at 6 AM till 6 PM.

Travel time to Badger Airline terminal at O’Hare airport:

Bucky Shuttle Departure Time	TT to ORD (h:mm)	Probability
12 PM and Before	2:45	0.30
	3:00	0.40
	3:30	0.30
After 12 PM	3:00	0.20
	3:20	0.50
	3:45	0.30

Drive time from EH to Madison airport is as follows:

Departure Time	TT to MSN (mins)	Probability
8 AM - 9 AM	25	0.15
	30	0.55
	40	0.30
9 AM – 4 PM	20	0.20
	25	0.60
	30	0.20

Drive time from EH to O’Hare is as follows:

Departure Time	Drive time to ORD (h:mm)	Probability
7 AM – 12 PM	2:30	0.30
	2:40	0.40
	3:00	0.30
After 12 PM	2:45	0.20
	3:10	0.50
	3:30	0.30

Notes/Assumptions:

• All bus/flight departures are on time.
• Instantaneous transfer at the Metro Transit transfer point.
• Need to reach the airport 45 minutes before scheduled departure, otherwise one would not be able to check-in, clear security and board the flight in time.
• Add 10 mins for parking at MSN airport and reaching the check-in counter. For ORD add 20 mins.
• Need 30 mins gap between landing at ORD and getting to another flight at ORD. Otherwise you cannot make it to the next flight.
• Assume if a flight is missed, you are guaranteed a seat in the next flight out.
• Assume zero walking time to bus stop at EH/parking ramp at EH.
• Assume that once you reach Chazen you are on the Bucky Shuttle.
• Please note we are in Central Time and DCA is in Eastern Time.

Questions:

1. Please develop the probability distribution functions for each of the four travel options if one were to leave EH at 8:30 AM. Compare the expected, 95th percentile travel times under each option.
2. For each of the four travel options, what is the latest one can leave from EH to reach DCA by 9 PM with 95% probability?