1.231J/16.781J/ESD.224J Fall 2004 ASSIGNMENT # 3 (Out: October 10, 2004; due: November 9, 2004) Problem 1 (20 points) [Section 23.5 in the textbook provides the background needed to answer this question.] Assume that demand for the runway system at an airport is 100 movements per hour throughout the busy hours of a particular busy day (06:00-21:00), except for the period 10:00 – 14:00 when it is 70 movements per hour. Suppose that, on that day, the airport capacity was 120 movements per hour until 07:00. However, due to a weather front, the capacity was only 60 movements per hour between 07:00 and 10:00. From 10:00 to 12:00 the capacity increased to 80 movements per hour and, finally, at 12:00, the capacity went back to 120 movements per hour where it stayed for the rest of the day. (a) (10 points) Under the usual assumptions described in Section 23.5 of the textbook and assuming no flight cancellations, draw carefully the cumulative diagram for the number of demands as a function of time and the number of aircraft serviced at the runway system as a function of time. Begin your picture at 6 a.m. (b) (5 points) What is the total amount of delay suffered by all aircraft during that day? (c) (5 points) What is the longest delay suffered by any aircraft during this day? Problem 2 (16 points) Suppose that an airport has a maximum throughput capacity of 100 movements per hour in good weather which prevails about 80% of the time and of 60 movements per hour in poor weather (about 20% of the time). To estimate delays at this airport, Consultant A has computed an expected capacity of 92 per hour [= (.8)x(100) + (.2)x(60)] for the airport. He has then obtained delay estimates through a computer-based queuing model that uses as inputs the daily demand profile at the airport and an airport capacity of 92 per hour. Consultant B has used the same computer model as A with the same daily demand profile as A. However, she has run the model twice, once for a capacity of 100 per hour and then for a capacity of 60 per hour. She then took the weighted average of the delays computed through the two runs by multiplying the delays obtained from the first run by 0.8 and those from the second by 0.2. (a) (8 points) Whose consultant’s approach is more correct and why? Please explain with reference to Figure 11.3 or 11.4 in the textbook. (b) (4 points) Whose consultant’s delay estimates will be higher? (c) (4 points) Irrespective of your answers to (a) and (b), would you use the same daily demand profile for good-weather days and poor-weather days?Problem 3 (20 points) Please do Exercise 3 in Chapter 12. [Note: You need not read Chapter 12 to do this problem. All you will need is the equation for the waiting time in a M/G/1 queueing system, which was discussed in class and which is presented as Equation 23.10 in the textbook and discussed in the textbook. Please also make sure to read the note at the end of the problem, which gives you the value of the variance of the service times.]The material in Chapter 10, i.e., the simple model for computing separations between consecutive landings on a runway, is sufficient.] Problem 4 (20 points) In this problem you are asked to estimate the Practical Annual Capacity (in terms of air traffic movements, ATM) of a major US airport, JFK International, New York City. The intent of the problem is to motivate some thinking about the complex considerations that make this question difficult to address. All thoughtful, well-reasoned answers will receive full credit. There is no single correct answer to this question. JFK is still the major international airport on the East Coast of the US, although its relative importance as an international gateway has been declining over the years. The airport has a runway capacity of 88-98 ATM per hour in VMC and 71 in IMC according to the 2001 “benchmarks” study of the FAA (http://www.faa.gov/events/benchmarks). These capacities refer to the “most commonly used” configurations under VMC and IMC respectively. In 2002, the monthly number of ATM in thousands was as given in the Table below. Domestic International Total January 13.2 8.1 21.2 February 12.5 7.4 20.0 March 14.5 8.4 22.9 April 14.7 8.3 23.1 May 15.0 8.7 23.7 June 15.4 9.1 24.5 July 16.4 10.1 26.4 August 16.7 10.2 26.9 September 15.6 9.1 24.8 October 16.3 9.2 25.4 November 15.2 8.8 24.0 December 15.4 9.4 24.8 Total 180.9 106.8 287.7 On the domestic side, conventional scheduled passenger flights constituted about 63% of the total, commuter flights by smaller regional aircraft 25%, all-cargo flights 6% and general aviation flights (business and pleasure) 6%. On the international side, the corresponding percentages were: conventional scheduled passenger flights 82%; all-cargo13%; commuter (to/from Canada) 3%; and charter 2%. Please note that the share of domestic flights at JFK has increased markedly in recent years, largely due to the growing presence of jetBlue at that airport. Note, as well, that JFK experienced a strong decline in total ATMs in 2001 and beyond, from about 350,000 in 1999 to the 287,700 shown in the Table above. However, traffic has grown at a healthy pace so far in 2004. Problem 5 (24 points) Please do Exercise 1 of Chapter 13 of the de Neufville/Odoni book. Do NOT answer part d) of this problem. [Please note: You need not read Chapter 13 to do this problem. The material in Chapter 10, i.e., the simple model for computing separations between consecutive landings on a runway, is