INTRODUCTION
A model which reflects the interactions between several decisions or sub systems, like for example location patterns, trip flows, house prices and trip frequencies, are called integrated models or models for integrated analysis. One of the first models in land use modeling was developed by Lowry (1964) for the Pittsburgh urban region. He distinguished population, service employment and basic employment and these activities correspond to residential, service and industrial land uses. Activities are translated into appropriate land uses by means of land use/activity ratios. The division of employment into service and basic sectors reflects the use of the economic base method to generate service employment and population from basic employment. The Lowry model allocates these activities to the zones according to the potential of the zones. Population is allocated in proportion to the population potential of each zone and service employment in proportion to the employment potential of each zone, subject to capacity constraints on the amount of land use accommodated in each zone. Consistency is secured by feeding back into the model and reiterating the whole allocation procedure until the distribution inputs to the model are coincident with the outputs.
Garin (1966) suggested to replace the potential models by productionconstrained gravity models and substituted another economic base mechanism for the analytic form. Another example is the Projective Land Use Model (PLUM) was designed by Goldner (1971). He replaced potentials by gravity models to allocate land uses.
Perhaps the most widely used model is Integrated Transportation and Land Use Package (ITLUP) (Putman, 1991). In the ITLUP, the land use model was a modification of Goldner’s Version of the GarinLowry model of land use and the network model was a conventional capacityconstrained incremental assignment model (see Mackett (1991) and Wegener (1994) for more extensions on the Lowry model).
Integrated Land Use and Transportation Demand Model (ILUTDM) can be considered
as extensions of the network UserEquilibrium (UE) equivalent mathematical problem
(Zhao, 2002). These extensions can combine various types of land use models
under a general network equilibrium framework to overcome shortcoming of the
traditional four step approach include inconsistency among steps and the lack
of behavioral theory behind the traditional model (Maruyaman and Harata, 2005).
For example, Shen (1997) derived a network equilibrium framework to combine
travel and residential location choices. His model combines the network equilibrium
models with the Disaggregate Residential Allocation Model (DRAM) and is formulated
into convex programming problems. Chu (1999) presented a model based on a UE
framework and a transformed EMPloyment ALlocation (EMPAL) model to jointly determine
employment location and travel choices. DRAM and EMPAL were proposed by Putman
(1991).
Based on the analysis of solution approaches for the original Lowry model and
its generalized versions, Pietrantonio (2001) suggested a framework for the
equivalent optimization approach. Important conclusion of his work was “ there
is no fully Equivalent Minimization Problem (EMP) formulation for the Lowry
model as originally formulated with using unique model”.
As a worth point, the Lowry lineage had its nascence as an outgrowth from conventional models used for transport planning since the sixties.
In this study, based on the previous discussion, we consider the mains selected
features:
• 
The inclusion of network congestion, as the more basic step into the integration
of land use and transport models that were dealt with heuristically into
several models 
• 
The inclusion of network equilibrium framework to combine travel and activity
location choices simultaneously 
• 
The inclusion of the wellknown random utility maximization behavioral
theory 
Considering these features in a unique framework is motivation of developing
a generalized version of the Lowry model in this study. To develop integrated
transportationland use framework, we propose two combined sub models in the
following define:
• 
The Combined Residential activity location choices, trip Distribution,
Mode choices and Route choices model (CRDMR) 
• 
The Combined Service employment location choices, trip Distribution, Mode
choices and Route choices model (CSDMR) 
In the both combined sub models is assumed each individual minimize his or her travel cost and maximize his or her living or service utility.
We reformulate each above combined sub models into EMP form such as the equilibrium conditions on the network and travel demand functions can be derived as the KarushKuhnTucker (KKT) conditions. We extend Evans algorithm (Evans, 1973) and use it to solve the equilibrium problem.
Finally, we develop an ILUTDM based on Lowry linage that contains the economicbase mechanism, the proposed combined sub models and the constraint procedure and their interactions.
MATERIALS AND METHODS
Activity location choice models (residential and employment): Spatial activity location models are concerned with representing people's location decisions in terms of where to live given the place of work, or where to work given the place of residence. These models can be based on the theory of entropy, or on the theory of random utility. Both lead to the same model specifications (Shen, 1997).
Hereto, the selected activity location choice models are simplified form of the DRAM and the EMPAL developed by Putman (1991). Putman models require relatively less data compare to others models and have been tested in many practical applications (Shen, 1997).
Residential location model: The general form of DRAM is given by:
Where:
H_{i,t} 
= 
No. of residents (placeofresidence) in the zone i at time
t 

= 
No. of employees working in the zone j at time t 
u_{i.t1} 
= 
Population/employee ratio in the zone i at time t1 

= 
Residential location attractiveness measures in the zone i at time t1 

= 
Impedance functions for work to home trips at time t 
c_{ij,t} 
= 
Travel cost from the zone i to the zone j at time t 
The attractiveness measure function attempts to express both land use characteristics
and the effect of household to household interaction on the location behaviors
of different household types (Putman, 1991). The multivariate and multiparameter
function comes into the following form:
Where:

= 
Vacant, buildable land in the zone i 

= 
Proportion of buildable land in the zone i that has already been build
on 

= 
Residential land in the zone i 

= 
No. of type n residents residing in the zone i 

= 
Employed residents of the zone i in income group n' at time t1 
m, n, o, p 
= 
Estimated parameters for each group being located 
Because each income group is analyzed independently in the model calibration
process, the model can be expressed as a simple form without the income group,
n, being shown in Eq. 2.
Service employment location model: The general form of this model is
defined as follows:
Where:

= 
Service employment (placeofwork) in the zone j at time t 
v_{i,t1} 
= 
Service employee/population ratio 
The attractiveness measure is given by:
Where:
L_{j} 
= 
Total area of the zone j 
a^{s}, b^{s} 
= 
Estimated parameters 
We assume the zone to zone impedance function is a simple declining exponential
function, therefore:
Where:
θ^{r,s} 
= 
Empirically estimated parameters 
The location models in Eq. 1 and 3 are
essentially a standard singly constrained spatial interaction model augmented
with a multivariate attractiveness term. The length of the interval between
t1 and t is determined on the basis of the hypothesis that the model is intended
to interpret the lagged effect of developments of land use on transportation.
In all previous applications the length of the interval has been 5 years (Shen,
1997). For convenience of the following presentation, we drop the notation of
time t.
Trip distribution and mode choice model: The main purpose of trip distribution
modeling is to distribute the total number of trips originating in each zone
among all possible destination zones which are available. The location models
shown in Equations 1 and 3 are actually
a tripend summation of a zonetozone trip estimation procedure. The model
used to distribute trips between zones is the wellknown standard singly constrained
gravity model as follow:
Where:

= 
No. of trips for homework and homeservices purposes from the origin
zone i to the destination zone j 
φ^{r,s} 
= 
Trip generation rates to convert homework and homeservices activity
flows to trips 
Furthermore, total population in the zone i and employment in the zone
j are:
Both the travel pattern and the activity location are determined from Eq.
6 implicitly. Equation 6 looks quite similar to the logit
destination choice model, in case the logit utility functions is:
Therefore, the model form of Eq. 6 can be explained within the framework of
the random utility theory of users' behavior. The model used to estimate mode
choice behavior is the wellknown nested logit model as shown below (McFadden,
1974):
Where:
Route choice model: In transportation planning practice, the problem
of route choice is traditionally called traffic (or trip) assignment, since
OriginDestination (OD) flows were viewed as being mechanically assigned to
the network. The UserOptimal model (UO) of route choice described in
this section is based on Sheffi’s (1985) notations. Given a network G(N,A)
with N nodes and A links, with a positive monotonically increasing link performance
(travel cost) function c_{a} (f_{a}) of flow f_{a} on
link a &isin: A, the UO trip assignment distributes the fixed demand such
as no individual can improve his/her route choice. The minimization problem
will be:
Subject to:
Where:
The objective function is to minimize the cumulative system travel cost, which
is measured by the sum of the integral in Eq. 13. Condition
14 describes the connection between link flows and path flows, constraint 15
ensures that all demands are distributed on the network and constraint 16 represents
the nonnegativity of the path flows.
To show the equivalency, it should be building the Lagrange function of the
minimization problem and then solving the KKT conditions for the minimization
problem. After solving KKT conditions:
Where:
u_{ijm} 
= 
Minimum travel cost between i and j by mode m 
These equations show that the path flow comes to zero if the associated path travel cost exceeds the minimum travel cost. However, the associated path travel cost is equal to the minimum travel cost, if the path flow is greater than zero.
COMBINED LOCATION, TRIP DISTRIBUTION, MODE AND ROUTE CHOICES MODEL FORMULATION
Overcoming inconsistency among steps leads to the consideration of a combined
location, trip distribution, mode and route choices model (CLDMR) with which
the problems location and travel choices are solved jointly. The proposed CLDMR
is specified as follows:
Where:
η 
= 
Ratio of occupants to vehicles (persons per vehicle) 
In this model Eq. 1928 constitute a
quantitative statement of UE conditions for the CLDMR. Eq. 1920
determine activity location, trip distribution and mode choice model. Equation
2122 assign trips to a transportation network according
to the UE principle. The condition in Eq. 23 means that number
of trips on all paths belong to a given mode’s network and connecting a
given OD pair equal the total trips distributed from i to j by mode m. The condition
in Eq. 24 states that each path flow is non negative nature.
The relationship between path and link flows is defined by Eq.
25.
EQUIVALENT MINIMIZATION PROBLEM
One of the important issues in analyzing the combined model is to drive its
equivalent optimization problem. The idea of the equivalent optimization problem
approach is to construct an intermediate model built around a convenient objective
function and the original constraints (or a subset of them) that would permit
to recover the model Equations from the conditions of optimality of the minimization
or maximization problem (Pietrantonio, 2001). The CLDMR can be formulated as
an EMP:
subject to:
Where:
In this formulation, the objective function (Eq. 29) comprises
into three components. The term, G (T), is a function of distributed
from a given origin i to a given destination j. The second term, H (M), specifies
each term in the set as a function of distributed from a given origin i to a given destination j by mode m. The function
F (f) has as much terms as the number of links in a transportation network.
Each term is a function of the traffic flows over all possible paths that share
a given link a, which implied by the linkpath incidence relationships (Eq.
37).
Equation 30 through 32 are the flow conservation
constraints. Equation 33 is the flow non negativity constraints
required to ensure the solution of the program physically meaningful.
MODEL PROPERTIES AND CALIBRATION
The analyzing combined model need to prove the equivalence between the proposed
combined model and its EMP problem. To proof of the equivalence theorem, we
should establish the theorems of existence, convexity, uniqueness and positivity.
The proofs of the theorems are not considered in this paper. The theorem of
equivalence can be proved based on the Lagrangian equations and the KKT optimality
conditions for the EMP when the Lagrangean function is:
where,
denote, respectively, the dual variables associated with the constraints in
Eq. 3033.
The KKT optimality conditions obtained by taking derivatives of this function
with respect to are:
If we assume and perform a little computational effort, we have Eq. 19
through 22 with defining:
Therefore, we see that the EMP is equivalent to the CLDMR.
The next step is to determine the appropriate values of the parameters in order to apply the model.
The computation process used to produce values of parameter estimation involves using gradientsearch technique with a MaximumLikelihood (ML) criterion, which is used to guide the gradient search direction. The ML method is a standard approach for calibrating the values of the logit choice functions parameters (Boyce and Zhang, 1997). According to the numerical tests, Putman (1991) pointed out the gradient approach can efficiently estimate nine parameters simultaneously.
SOLUTION ALGORITHM
Implementation of the CLDMR requires an algorithm for obtaining solutions for the EMP. Because of the EMP is a convex programming problem with linear constraints, it can be solved efficiently by either Evans or FrankWolfe algorithm. The Evans algorithm is preferred, because; it requires less iteration than the FrankWolfe algorithm in order to obtain suitable solutions. Moreover, each iteration in the Evans algorithm computes an exact solution for the equilibrium conditions, while in the FrankWolfe algorithm; none of the equilibrium conditions are not satisfied until the final convergence (Chu, 1999). The last advantage of the Evans algorithm is an important issue in the largescale network applications, because subject to cost it is often unlikely that either the Evans or the FrankWolfe algorithm will be run again and again to find out exact convergence.
The Evans algorithm applied to the EMP can be summarized as follows (Patriksson, 1994):
Step 0: Initialization
Find an initial feasible solution Set n: = 0.
Step 1: Travel cost update
Set , n: = n+1 and compute minimum cost paths on
the basis of updated link costs, for every OD pair. Compute based
on Eq. 12 as a function of the shortest path costs.
Step 2: Direction finding
• 
Solve a destination and mode choice models as a function of the shortest
path costs 



applying the dimensional balancing method 
• 
Perform an allornothing assignment of demand to
the shortest paths computed with the updated link costs {C_{ma,n}}.
This yields The represent
the auxiliary flow, variables corresponding to
respectively 
Step 3: Convergence check
Compute the Lower Bound (LB), Best Lower Bound (BLB) and Relative Gap then
test for convergence:
Is the Relative Gap <ε? If YES, STOP; otherwise continue.
Step 4: Stepsize determination
Find that
solves
Step 5: Flow update
Revise trip flows as following:
Step 6: Convergence check
Retest the updated value of the objective function for convergence. If the Relative Gap is acceptable, STOP; otherwise go to Step 1.
It should be mentioned that the other convergence criterion is needed for the trip table. For the trip table, we consider a simple criterion, the Total Misplaced Flow (TMF), which is the sum of the absolute differences of zone to zone flows in the main problem solution and sub problem solution. If these two tables are equal, the algorithm has converged with regard to the trip table (Boyce and BarGera, 2006).
RESULTS AND DISCUSSION
Integrated urban land use and transportation demand model: The Lowry lineage has been fertilized, during the years, by the economic approach and the demographic approach that could be seen under the urban economics
and the microsimulation lineage (Pietrantonio, 2001). The efforts driven to integrating these approaches with general network equilibrium framework were successful in a high degree, even without eliminating their identities.
We use the concept of modified GarinLowry model by Berechmann and Small (1988) to develop our proposed model.
Figure 1 shows descriptively the proposed model to demonstrate
the way in which the economicbase mechanism, the equilibrium activity location
and travel choices sub models and the constraint procedure interact.
Table 1 present the general steps of the proposed model in the glimpse.
The input data include zonal levels of basic employment, zonal levels of attractiveness
for residential and service location, network information, estimated parameters
and control parameters of the economicbase mechanism. Based on these inputs,
first, the workers in the basic sector are allocated to residential zones with
using CRDMR model; this is the step 1 in Table 1.
The iterative computational Evans algorithm will continue until a predefined
convergence criterion is satisfied. In this process, after the congested travel
cost has been obtained, the minimumcost path of the network can be determined.
The initial trip distribution and the initial modal split pattern are determined
using the minimumcost path, destination and mode estimated parameters and residential
zonal attractiveness. Then the residential location choice can be directly obtained.

Fig. 1: 
Flowchart of the proposed combined urban land use and transportation demand
model 
Table 1: 
General steps of the proposed model to integrate land use and transportation
demand 

The trips are assigned to the transportation network according to the household
distribution pattern (the demand of traveling work to home) and the travel cost.
The computation will be terminated when an equilibrium travel and residential
location choice pattern is obtained. The main outputs of the CRDMR model are
initial equilibrium travel cost; equilibrium network link flow; equilibrium
trip patterns and equilibrium residential distribution.
Then the incremental residential population and the resulting incremental dependent
service employment based on Eq. 8, 9 are calculated (step
2). This increment of employment is distributed to zones of workplace with using
CSDMR model (step 3).
The iterative computational Evans algorithm will continue until a predefined convergence criterion is satisfied. In the CSDMR model, the preload traffic on the network which obtained from CRDMR model used as an initial feasible solution. These preload traffic volumes are associated with vehicle trips that are on the network but are not contained in the origindestination matrix to be assigned (Caliper Corporation, 2002). The remainder of the Evans algorithm used to CSDMR model is similar to which used to the CRDMR model. The initial equilibrium travel cost; equilibrium network link flow; equilibrium trip patterns and equilibrium employment distribution come into view of the CSDMR model outputs.
After step 3, the corresponding increment in population is derived and distributed to zones of residential location with using CRDMR model (step 1). This entire iterative process continues until the economicbase mechanism converges.
In each iteration, a test is used to ascertain that zonal densities of service
employment and residential population are within preset bounds. If test fall
in:
• 
False: an iterative procedure (internal to the economicbase iterations)
is used to reallocate the latest increments by changing the zonal attraction
parameters 
• 
True: the outputs satisfy all convergence criteria and we find out the
final solution 
The final output of the proposed model includes vectors of residential population and householddependent employment, equilibrium trip pattern (trip tables), vectors of residentialattractor and serviceattractor weights, equilibrium travel cost and equilibrium link flow.
CONCLUSIONS AND MODEL EXTENSIONS
In this study the integrated urban land use and transportation demand model
based on Lowry linage was presented. We considered two combined sub models for
the simultaneous prediction of activity location choices, trip distribution,
mode choices and route choices. Sub models reformulated as an equivalent minimization
problem. We used Evans algorithm to solve both sub models. We applied two sub
models, the economicbase mechanism and the constraint procedure to develop
a suitable framework of integrated land use and transportation demand model.
The proposed model overcomes to three crucial shortcomings in the previous models:
• 
Consider to network congestion 
• 
Consider to equilibrium combined travel and activity location choices
model 
• 
Consider to random utility maximization behavioral theory 
To calibrate the proposed model ML method can be used as standard approach. However the Evans algorithm that we justified to solve sub models converge in less iteration rather than the FrankWolfe algorithm and in each iteration, we have a feasible solution, in contrast it is not true for the FrankWolfe algorithm. Above issues are very important in large scale application.
This research has some potential for future extension. First, there is a need to apply the proposed model to realworld largescale transportation networks, so that the behavioral richness and computational tractability of the model can be empirically verified. Second, it would be very productive to reformulate the model so that it allows interactions among respective modal networks. Third, it is valuable incorporating trip chaining behavior in proposed integrated model.