Commuting –defined as the daily travelling for employment purposes– has gradually intensified in the last decades. At the heart of today’s working life, the multivariate commuting is of great importance for every sustainable policy. Thus, the objective of this paper is to examine, using the latest available census data, commuting flows in Greece at relatively fine unit scales (Local Administrative Unit - LAU1). For this purpose, the gravity model is used, as is the radiation model, which recently was introduced in the approach of transportation fluxes. Both the methodology and the results are compared. Consequently, this paper aims not only to approach the commuting patterns in Greece, but also to conclude whether the radiation model is a good alternative to the use of gravity models in spatial interaction analysis.

1. 3rd Conference on Sustainable Urban Mobility
26-27 May, 2016, Volos, Greece
Gravity vs Radiation model: two
approaches on commuting in Greece
Maria Stefanouli
Serafeim Polyzos

2. Introduction
Commuting: the daily travelling for work beyond the administrative unit
Multivariate
commuting
Economic
factors
Social
factors
Geopolitical
factors
A variety of models has been
developed with the aim of modelling
and analyzing commuting flows
most popular: gravity models
new: radiation models

3. A Greece-wide view of commuting
2001
Low out-commuting intensity e.g. Grevena, Komotini, Tripoli, islands
• Remote areas
• Mountainous areas
• Areas with special geomorphology
• Areas with highly developed primary sector of the economy

4. A Greece-wide view of commuting
2001
High out-commuting intensity in municipalities close to urban centres
(Athens, Thessaloniki)

5. A Greece-wide view of commuting
2001
The
commuting
intensity
increased in
a decade
Mean Travel Time
(one-way) (min)
Mean Travel Distance
(one-way) (km)
All municipalities 23,99 19,29
Cities 29,61 25,21

6. Gravity model vs Radiation model
𝐆𝐞𝐧𝐞𝐫𝐚𝐥 𝐟𝐨𝐫𝐦 Tij =
f Pi g(Pj
d(cij
β
Extended form Tij = a Pi
β1
Pj
β2
d(t ij
β
Ki
γ
Gravity model: is based on Newton’s physical law
The interaction between two regions is proportionally a result of a parameter, for
example the municipality size, and inverse proportionally result of some power
law of the distance
dij
Pi
Pj

7. Gravity model vs Radiation model
Gravity model: is based on Newton’s physical law
Drawbacks
• The fitting parameters can vary significantly
even within a data set
• It not always easy to calibrate all the parameters
of a gravity model
• Little emphasis on social aspects
• Gravity models for commuting flows in
heterogeneous population groups can be
subject to serious misspecifications
• The used geographical subdivision in the origin
zone and the destination zone omits other
catchment centers

8. Tij = Ti
PiPj
Pi + Sij (Pi + Pj + Sij
Gravity model vs Radiation model
Radiation model: is rooted in diffusion dynamics
The equation relates the origin
population, the destination
population and the total
population in the circle with center
the origin and radius the distance
between the origin and the
destination. Finally, the commuters
from origin (i) to destination (j) are
calculated as a part of the total
out-commuters of origin
rij
Pi
Pj

9. Gravity model vs Radiation model
Cost-based radiation model: it is supposed that the employees choose the
workplace which has the lowest travel cost. They use as travel cost measure the
path length and also the travel time.
By using travel time tij as a search
criterion instead of Euclidean
distance, the model is more realistic,
since it takes into account the
geographical heterogeneity of areas

10. Data & Methodology
Parameters in the
extended model
Symbol Expected behaviour
Gross Domestic Product
per capita
GDPi,j
rural commuting increases eventually, while urban
commuting distances increase
Participation of the
secondary sector at the
GDP
Bsectori,j
the higher the participation of the secondary sector is,
the lower the potential of long distance commutes is
Participation of the
tertiary sector at the GDP
Csectori,j
the higher of the participation of the tertiary sector is,
the higher the potential of long distance commutes is
Commuting flow pattern is estimated using
1. Standard gravity model
2. Extended gravity model
3. Modified radiation model

11. Data & Methodology
The commuting data of the
research derives from the official
Census conducted by the National
Statistical Service in 2011 and
refers spatially to the Greek
municipalities

12. Results
𝐒𝐭𝐚𝐧𝐝𝐚𝐫𝐝 𝐆𝐫𝐚𝐯𝐢𝐭𝐲 𝐦𝐨𝐝𝐞𝐥: Tij = 0,04289 ∙ Pi
0,709
∙ Pj
0,726
∙ d(t ij
−2,214
Extended Gravity model:
Tij = 0,5461 ∙ Pi
0,776
∙ Pj
0,616
∙ d(t ij
−2,139
∙ GDPi
−0.920
∙ GDPj
0.716
∙ Csectorj
0.917
• All coefficients are significant (p < 0,05)
• Only the participation of the tertiary sector at the GDP of the city destination
was found statistically significant
• The standard model shows that the power of the population in the city of
destination is greater than the one of the population in the city of origin, in
contrast with the extended model
• A high GDP and the participation of the tertiary sector at the GDP of the city of
destination pull commuters
• A high GDP in the city of origin reduces the out-commuters

13. Results
Radiation model
Standard gravity
model
Extended gravity
model
R2 0,54 0,85 0,87
RNWP 0,158 0,621 0,694
SRMSE 7,789 7,646 8,958
RMSE 274,216 269,204 315,368
• The relative number of wrong predictions (RNWP) is much better for the
modified radiation model
• The values of the other measures are quite the same for all of the three
models
• By including economic coefficients in the gravity model - worse fitting

14. Results
The dashed line (y=x) in each diagram shows where the model meets the
real data, and the dispersion of each model.
The dispersion seems larger in the radiation model.

15. Conclusions
Commuting is of central interest to geographers, policy makers, transport planners
and economists alike
Understanding commuter flows in large transportation networks is an
ongoing challenge due to the complex nature
The findings show that the distance constitutes an impediment for
commuting, while the developed economic fundamentals pull incommuters
The radiation model describes the commuting pattern adequately but
because of its parameter-free nature there are concerns on its capability to
describe the multivariate motivations of commuters
Future research should focus on application in heterogeneous population groups
and on investigation of the applicability of radiation models in commuting
research

16. If you are interested to read the whole paper you can find and download it
here:
https://doi.org/10.1016/j.trpro.2017.05.069
as well as other related papers here:
https://www.researchgate.net/profile/Maria_Stefanouli/publications