Modelling Approach and Framework

The modelling of airline operational responses to environmental constraints requires the development of an integrated framework that captures the key effects of each relevant element of the air transport system. This can be done by maximising airline profits using an objective function that incorporates models of each relevant element of the air transport system. The effects of competition can be captured by simulating a strategic game between airlines, with each airline’s profit maximised in each stage of the game, iterating until a game theoretical equilibrium is reached that specifies the key operational characteristics of each airline, i.e., the flight network, flight frequencies, and aircraft sizes operated.

In order to identify these key airline operational characteristics, the decision variables in each airline objective function are specified as the airline flight segment frequencies by aircraft size class, and passenger itinerary demand, which defines flight network operated. Other variables in the air transport system, including passenger city-pair demand, average fares, travel times, flight delays and operating costs define the cost and revenue terms that are inputs to the objective function. The modelling of these variables can therefore be extracted from the objective function, making it easier to solve, and allowing more advanced modelling of each variable, to better reflect system behaviour. Each of these variables is, however, a function of flight segment frequency and passenger itinerary demand, i.e., the decision variables. All variables can be determined using an iterative framework in which each variable is updated according to the results of the profit maximisation. The profit maximisation is then run with updated values of each variable, until convergence to an equilibrium solution. This iterative approach can be incorporated into the iterative approach required to solve the strategic game between airlines, described in the previous paragraph.

Chapter 4

The modelling framework for the Airline Response Model is presented in Figure 4-1. A series of network optimisation models determine the key operational characteristics of each airline, which are input into the strategic game simulation between competing airlines. The strategic game is simulated using a system flight frequency calculator and an iterative framework (indicated by the decision node for convergence and the feedback loop to the right of the models, i.e., the dotted line). These components constitute the core of the Airline Response Model, which is shown in the red box in Figure 4-1. All the other models serve to generate inputs for the network optimisation models. The models include a flight delay model, operating cost calculators for each airline, a travel time calculator, an average fare model, and a passenger demand model. These models are updated after each iteration of the strategic game. The operation of the Airline Response Model and the interaction between each of its sub-models is described in greater detail below, sequentially from the top of the diagram.

As shown at the top of Figure 4-1, an initial estimate of flight segment frequencies per day is required for each aircraft size class and airport pair simulated. For the base year modelled this may come from historical flight frequency data, while for subsequent years it may come from the results of the previous year’s model run, necessitating a chronological solution to a multi-year forecast, or from traffic forecasts from a different model. With the initial estimate of flight frequencies per day, average flight delays are estimated at each airport according to specified airport capacities. The Delay Calculator developed for this purpose is described in Section 5.2.

Simultaneous to the calculation of flight delays, a Travel Time Calculator estimates nominal travel times by flight segment and O-D city pair as a function of the aircraft types operated, passenger itinerary demand served (from the same source as the initial estimate of flight frequencies, giving information about passenger routing), specified aircraft performance characteristics (such as cruise speed) and flight segment length information. This model is described in Section 5.3.

The estimated flight delays and nominal travel times are inputs to a series of Operating Cost Calculators, which calculate operating costs per flight and per passenger for each airline. Other inputs include specified fuel price, aircraft fuel efficiency, and airline operating costs per hour and per passenger. Different operating costs are calculated for

Modelling Framework

Demand Model

O-D Demand Operating Cost: Airline 1, 2, 3, ...

Average Delay

Travel Time

Segment Flight Frequency by Aircraft Type: System Itinerary Pax Demand: System

Convergence? No Yes

Segment Flight Frequency by Aircraft Type : System Itinerary Pax Demand: System

Operating Cost Calculator: Airline 1

Segment Flight Frequency by Aircraft Type : Airline 1, 2, 3, ... Itinerary Pax Demand: Airline 1, 2, 3, ...

Travel Time Calculator

System Flight Frequency Calculator

Core of the Airline Response Model

Avg. Fare Model

Average Fare

Avg. Operating Cost Calculator

Average Operating Cost Segment Flight Frequency by

Aircraft Type0: System

Itinerary Pax Demand0: System

Airport Capacities

Aircraft Performance Flight Segment Lengths

Population Income Fuel Price Aircraft Fuel Efficiency Airline Operating Costs

Emissions Calculator

System CO2

LTO NOxby Airport

Average Operating Cost0

Average Fare0

Engine Emission Rates

Flight Mission Profiles

Delay Calculator ... 2 3 ... 2 3 Network Optimisation: Airline 1

Chapter 4

different airlines. The Operating Cost Calculator developed is described in Section 5.4. Average O-D operating costs by city pair, across all airlines, are calculated by an Average Operating Cost Calculator according to the operating costs per flight and per passenger of each airline, and initial estimates of flight frequencies and passenger demand. The Average Operating Cost Calculator is also described in Section 5.4.

The estimates of average operating costs are inputs to an Average Fare Model, which estimates average O-D fares by city pair, across all airlines (fares are not calculated for each airline separately). This model, which also takes base year average operating costs and fares as inputs, is described in Section 5.5. Estimated average O-D fares are output to a Passenger Demand Model. In combination with flight delays from the Delay Calculator, average travel times from the Travel Time Calculator, and specified population and income data, the Passenger Demand Module estimates available O-D passenger demand for each city pair modelled. The Passenger Demand Model is described in Section 5.6.

The estimated operating costs, average fares, and passenger demand, along with initial estimates of flight frequencies, are all inputs to the Network Optimisation Models, which calculate the segment flight frequencies and itinerary passenger demand for each airline. Each optimisation is constrained by available O-D passenger demand, available seats by aircraft size class, and a requirement that the same number of each class of aircraft arrive and depart from each airport every day. The Network Optimisation Models are described in Section 5.1. O-D passenger demand is distributed between airlines according to a market share model, which is also described in Section 5.1. Each airline’s market share for each respective O-D market is defined as the ratio of the airline’s flight frequency on that market to the flight frequency offered by all other airlines serving the market. Because the total number of flights offered by all airlines serving each market, calculated by the System Flight Frequency Calculator, depends on the results of each airline network optimisation, the individual airline network optimisations must be run iteratively, with other airline flight frequencies updated each iteration. A game theoretical equilibrium between airlines is reached when the system reaches convergence. The simulation of the strategic game between competing airlines is described in Section 5.7.

Because the Delay Model, Travel Time Calculator, Operating Cost Models, Average Fare Model, and Passenger Demand Model are not integrated within the network

Modelling Framework

optimisations, they are updated in each iteration after segment flight frequencies and itinerary passenger demand are estimated by the Network Optimisation Models, as described above. These models are therefore included in the iteration loop that is required to identify the game theoretical equilibrium.

Emissions levels, particularly in terms of system CO2 and LTO NOx at airports, are

calculated according to equilibrium flight frequencies by aircraft size class, engine emission rates in different phases of flight for the different types of aircraft modelled, and typical flight mission profiles. The Emissions Calculator developed for this purpose is described in Section 5.8.

Application of the Airline Response Model to simulate future aircraft operations requires consideration of how the constraints and inputs to each model may change over time. In many cases this may be defined by the policy scenario run. In the case of airport capacity constraints, the model may be run with exogenously specified airport capacity inputs. Other inputs may come from population, per capita income and oil price projections. All assumptions about inputs, including their development over time, are described in detail in the sections on each sub-model in Chapter 5.