Hansen's Accessibility Model

• Land-use planning is a complex task where land is allocated among alternative uses in private markets
• Locational decisions from private developers and buyers shape cities.
• Land-use models forecast total activities of an urban area and allocate activities among a predetermined set.

Hansen's Accessibility Model

• Designed to predict population location, with employment being the predominant factor.
• Aij represents the accessibility index of zone i with respect to zone j.
• Ej is total employment
• Dij is the distance between i and j.
• b is an exponent
• The overall accessibility index for zone i is At = Σ (Ej / Dij^b)
• The amount of vacant land suitable for residential use is an additional factor that attracts future population.
• Holding capacity (Hi) refers to this factor of vacant land available for residential use.
• The development potential of zone D₁ is AiHi.
• Population is distributed based on relative development potential (A¡Hi/∑ AiHi).
• Population allocated to zone i is G₁ = Gt (Ai Hi / ∑ AiHi) = Gt (Di / ∑ Di) if total growth in population in a future year is Gt.

Density-Saturation Gradient Method

• First used in Chicago, with three empirical rules:
• Intensity of land use declines as distance of travel time to the CBD increases.
• The ratio of land in use to available land decreases as distance from the CBD increases.
• The proportion of land devoted to land use in an area remains stable.
• dx = d0e-bx is the basic density-distance relationship derived by Clark (1951).
• dₓ is population density at distance x from the city center.
• d₀ is central density as extrapolated into the CBD of the city.
• b is the density gradient or slope factor.
• HCᵢ = Pi + Vᵢd is how holding capacity is calculated.
• HCᵢ = holding capacity of zone i
• Pᵢ = existing residential population of zone
• Vᵢ = vacant, available, and suitable land in zone i
• d = anticipated average density at which all future residential development will occur.
• Percentage population saturation of zone i = (Population of zone i / Holding capacity of zone i) x 100

Operational Land-Use Models

• Developed by Putman (1983), forecasts residents and workplaces
• The theoretical base is N₁ = ΣEᵢPi/j
• N₁ represents persons living in zone i
• Eⱼ represents persons working in zone j
• Pᵢ/ⱼ represents the probability that a person working in j would choose to live in zone i.
• Pᵢ/ⱼ = f(Cᵢ,ⱼ)
• Cᵢ,ⱼ is the cost of time of travel between zones i and j.
• α is a cost sensitivity parameter.

Four Step Transportation Model

• Trip Generation/Attraction estimates the volume of trips generated.
• Trip Distribution splits the volume of travel between zones.
• Modal Choice describes travel by each mode
• Traffic Assignment describes the volume of vehicles on each transit/road.
• Four Step Methodology moves from Trip Generation to Trip Distribution to Modal Choice before Traffic Assignment

Trip Generation

• Trip Generation determines the frequency of origin or destination trips by zone, broken down by purpose based on land use or household demographics.
• Trip Production determines population, number of students at resident place, and number of workers at resident place, etc.
• Trip Attraction determines number of employees by industrial sector and working place as well as the number of schools or student enrollment and floor area by business type, etc.
• Can be calculated by looking at three factors
• Intensity of land use
• Socio-economic characteristics
• Availability of transport

Definitions

• Home based (HB) trip is when the trip maker's home is the origin OR the destination of the journey
• Home-based work (HBW) trip is when the purpose is to go from home to work or vice versa
• Home-based other (HBO) trip is when the purpose is to go from home to other locations like shopping, school or theater
• A Non-Home based (NHB) trip is when neither end of the journey is at home.
• Origin is where a travel journey starts
• Destination is where a travel journey ends

Estimating Trips

• Trip generation quantifies the relationship between urban activity and travel and converts measures of urban activity into numbers of trips.
• Production signifies a zone's ability to generate trip ends.
• Attraction relates to a zone's ability to generate trip ends
• Methods for estimating the number of trips produced:
• Growth Factor Modeling
• Category analysis
• Simple and Multiple Classification Analysis
• Trip rates (using ITE's trip generation rates)
• Regression Models

Growth Factor Modeling

• The technique is applied to predict the future number of journeys: Ti = Fiti, where T₁ and t₁ are future and current trips in zone i
• F₁ is a growth factor.
• Normally the F; factor is related to variables like population (P), income (I) and car ownership (C) in a function such as: F₁ = f (Pa, la, Ca)/f (Pc, Ic, Cc)

Multiple Classification Analysis

• An alternative method to define classes and test the resulting cross-classification to provide a procedure for variable selection and classification by creating cross-classification tables that count number of trips

Regression Analysis

• Sample data should include Independent variable: HH Income, Cars Owned, Motorcycle Owned
• From which conclusions Dependent variable: HH Trips can be drawn

Trip Distribution

• Trip Distribution - matching of origin and destination of trip and future OD
• Is the volume of travel predicted from zone to zone
• Uses Growth factor and distribution models

Growth Factor

• Used when forecasting for the near future
• the distribution of future trips from a given origin zone is proportional to the present trip distribution
• this future distribution is modified by the growth factor of the zone
• Has two key components
• Origin trips
• Destination trips
• The formula is: ijf = ijo Σ Oki Dkj / Σ OijDoji
• O and Oº = origin trips
• D and Dº = destination trips
• ij and ij0 = area trips