Bruton,  M. J. 1970. Chapter 4: Trip Distribution. Introduction to Transportation Planning. Hutchinson Technical Education: London. pp. 97- 129.

Part I: Growth Factor Methods

General Notation and Formula

T_ij²⁰¹⁰ = T stands for flows
                subscript three possibilities
                    ij  = flow from i to j
                    i   = total outflows or inflows i
                        = (blank) totals trips
                superscript three possibilities
                    2010 = year of flow
                    k      = iteration
                    0      = current data
               

T_ij²⁰¹⁰ = T_ij²⁰⁰² * E

T_ij²⁰⁰² = Trips from i to j in 2002

T_ij²⁰¹⁰ = Future Trips i to j in 2010

E        = Growth (Adjustment) Factor

 

• This method can be used to generate trips in both directions (i>j and j>i) usually assume inflows equal outflows in 24hrs.

• Growth can be simple of complex

  • can be based on single factor (population)

  • or combination of factors

    • land use

    • immigration

    • class shifts

    • commuting ease

4 Types of Trip Distribution Growth Factors

1. Uniform Factor

2. Average "    "

3. Fratar

4. Detroit

Uniform Method:  Future Flow = Present x Growth Factor

Givens

T_ij²⁰⁰² =  Today's flows (other ways of writing
                this include (T_ij²⁰⁰² = t_ij = T_ij⁰)

T_i^G     = Trip Generation Output for Future (Trip
                Ends)

Assumption

T_ij²⁰¹⁰  = T_ji²⁰¹⁰    Projected Inflows equal
             Projected Outflows (24hr. model)

Formulas

E = S T_i^G / SS T_ij²⁰⁰²  =  T^G / T²⁰⁰²

T^G  = Total Trips at Future Date

T²⁰⁰² = Total Trips Today

T_ij²⁰¹⁰ = T_ij²⁰⁰² * E

T_ij²⁰¹⁰ = Flow from i to j in future (year 2010)

 

Step 1:  Determine the Uniform Growth Factor

Step 2: Apply factor to all current flows

 

Average Method:  Future Flow = Present x Growth Factor

Givens

T_ij²⁰⁰² =  Today's flows (other ways of writing this include ( t_ij = T_ij⁰) or flows before iterations

T_i^G     = Trip Generation Output for Future (Trip Ends)

a₁, a₂  = Tolerances lower (1) and upper (2)

Assumption

T_ij²⁰¹⁰  = T_ji²⁰¹⁰    Projected Inflows equal
             Projected Outflows (24hr. model)

Formulas

E_i^k-1 = T_i^G / T_i^k-1  = = T_i^G / S T_ij^k-1

T_i^G = Total Trip Generation at i in Future Date

T_i^k-1 = Total Trips for iteration k at i

T_ij^k = T_ij^k-1 * [(E_i^k-1 =E_j^k-1 )/2]

T_ij^k = Flow from i to j for iteration k (represents future)

 

Step 1:  Run Trip Generation Model

Step 2:  Determine first estimate of "Average Growth Factors"

k = 1    E_i^1-1 = T_i^G / T_i^1-1  = T_i^G / T_i²⁰⁰²

Step 3: Apply first set of ave. growth factors to all current flows

            k = 1   T_ij^k = T_ij^k-1 * [(E_i^k-1 + E_j^k-1 )/2]

   T_ij¹ = T_ij⁰ * [(E_i⁰ + E_j⁰ )/2]

Step 4:  Check for closure