Calculating Trip Distribution Using Gravity Model

Introduction

Trip distribution is the second step of conventional four-step transport models. The main purpose of trip distribution modeling is to distribute the total number of trips originating in each zone among all possible destination zones available. As input, it uses a set of zonal trip productions and attractions, and attempts to estimate the way in which the production and attraction will be linked.

The trip distribution model may be expressed in a general form as follows:

T_ij=(fT_i,T_j,F_ij)............(1)

Here Tij is the traffic moving between zones i and j; and Fij is the impedance to travel between i and j and can be represented by travel distance, time, costs, or a combination of them.

The most common form of the gravity model:

Tij =

K Ti Tj

( Fij ) n

.............................. (2)

Where k = socio-economic factor

n = constant power

Gravity models stipulate that the amount of traffic interaction between zone I and zone j is positively related to the product of the amount of traffic in zone I and zone j and inversely related to the impedance of getting from zone i to zone j. The K in equation 2 is a constant used to scale the estimate up or down, and the power n permits the friction or impedance factor to be manipulated in model estimation.

Objectives

In order to fulfill the main purposes of this study, the following objective is taken to conduct the study-

Ø To calculate the number of trips produced in inter-city train services from Khulna city by using the Gravity model.

Methodology

To conduct this study a simple methodology is followed and that is described in bellow.

Table.1: Informations about the Destinations.

a) Data Collection:

The value of the parameters of gravity model is to be collected for calculation of trip distribution. Railway sector is randomly pre-selected for this study. Destination, distances and number of trips produced in those destinations are documented through an interview with station master as secondary data. Collected values are given bellow.

Table.1: Informations about the Destinations

Origin	Destination	Distance (In km.)	Produced trip / day
Khulna Khulna	Noapara	29	100
	Jessore	57	150
	Darshana Halt	124	50
	Chuadanga	139	70
	Poradaha	179	30
	Iswardi	247	30
	Rajshahi	307	270
	Dinajpur	440	110
	Natore	283	95
	Parbotipur	423	25
	Sayedpur	437	235
	Joydebpur	503	190
	Sirajgonj	324	150
	Dhaka	530	220
Total			1725

Source: Field Survey, 2008.

As secondary data, the population of Khulna city and the other destination were collected from the official website of Bangladesh Bureau of Statistics (BBS).

Table.2: Informations about the No. of population of Origin and Destination.

Origin (Khulna City)	Population	Destination	Population
Khulna	2378971	Noapara	250319
		Jessore	2471554
		Darshana Halt	719378
		Chuadanga	1007130
		Poradaha	1740155
		Iswardi	292938
		Rajshahi	2286874
		Dinajpur	2642850
		Natore	1521336
		Parbotipur	325070
		Sayedpur	232209
		Joydebpur	2631891
		Sirajgonj	2693814
		Dhaka	8511228

Source: BBS, 2004.

Map of the Location of the Destinations

Figure: Map of the Location of the Destinations

b) Model Fixation and Calculation:

First a suitable model is established. Then by using necessary computer software Ms Excel results are produced with collected data.

c) Final Report Presentation:

Finally with the analysis, necessary figures and tables a final report was prepared finally.

Model Fixation

As mentioned before gravity model needs a production factor (T_i) of origin which is applied by the population of Khulna and attraction factor (T_j) of destination is applied by population of destination. Value of Friction factor (F_ij) is applied by the distance between origin and destination Value of socio-economic factor K is taken 1 to reduce the complexity of calculation. Value of n (power of friction factor) is taken 2 as default.

So the number of trips from i to j,

=

( Fij ) 2

Calculation

With MSExel value of T_ij is derived. Values are listed bellow.

Population Khulna ( Ti )	Destination	Population (Tj)	Distance (Fij)	Impedance ( Fij ) 2	Predicted Tij
2378971	Noapara	250319	29	841	708087564.5
	Jessore	2471554	57	3249	1809712309
	Darshana Halt	719378	124	15376	111301990.1
	Chuadanga	1007130	139	19321	124006679.9
	Poradaha	1740155	179	32041	129202530.5
	Iswardi	292938	247	61009	11422757.41
	Rajshahi	2286874	307	94249	57723762.87
	Dinajpur	2642850	440	193600	32475534.65
	Natore	1521336	283	80089	45189904.05
	Parbotipur	325070	423	178929	4322005.393
	Sayedpur	232209	437	190969	2892712.833
	Joydebpur	2631891	503	253009	24746915.58
	Sirajgonj	2693814	324	104976	61047338.3
	Dhaka	8511228	530	280900	72082465.6

From these calculated values of Tij and actual number of trips to different destination actual probability and predicted probability is calculated. The bars bellow show their differences

Figure: Actual and predicted probability

From this chart it is clear that predicted probabilities are not applicable due to the desperation from calculated value. So incorporating socio-economic factor K is very essential. Correlation between actual probabilities and predicted probabilities is 0.041. It means a common K is not applicable. So K_ij (socio-economic factor between i and j) have to be applied. But due to the unavailability of sufficient data K_ij is not calculable.

Conclusion

This study is a small afford for trip distribution analysis. A very general gravity model is used to calculate number of trips to different destination. Enormous prediction has been occurred. But the process is in write way.

References

1. D.Meyer, M. and Miller, E. J., 2001: Urban Transportation Planning (P.279).