IEEE Circuits and Systems Magazine - Q4 2019 - 61

connectivity pattern, indicating that in a small portion of the network, the hub nodes are well connected. Furthermore, the evaluated node weight showed
positive correlation with the corresponding degree,
weighted degree, and number of routes along a node
(R), indicating that the stations carrying maximum
load are always well connected [26].
vi)	A simple and realistic routing algorithm called
passenger intuitive logic (PIL) was used by Wu
et al. [32] to study the passenger flow in metro networks. The passengers' intuitive strategy of choosing routes, including minimizing the number of
hops traversed and the number of transfers made,
formed the basis of the routing algorithm used in
the study. In the study, Wu et al. combined the use
of shortest path (SP) and minimum transfer path
(MTP) to determine the routes chosen by passengers. Here, MTP corresponds to the route that has
the least number of transfer times, i.e.,

employed the SUMO (Simulation of Urban Mobility)
simulator to validate the time efficiency for a single route using the synthetic mobility trace which
yielded a better estimation of time efficiency.
	  SUMO is a microscopic multi-modal traffic simulator which allows the user to explicitly control
the behavior of each vehicle [65]. To conduct the
simulation, we first build the road network topology by importing the actual road topology including information on road junctions, bus stops,
POIs, and traffic lights according to Openstreetmap [66], as shown in Fig. 8(a). Then, the routes
for buses are set up according to the actual time
table, and other generic vehicles are set up using
Activitygen, an activity-based traffic generator
[67]. Finally, results are extracted from the SUMO

1

	

2 2
(cl - p) 2
o
PMTP = c 1 - f2 m e 1 2

p

m th

where f ! [0, m th], cl ! [0, p]; and PSP = 1 - PMTP
(23)
	where PMTP is the probability of taking a minimum
transfer path, and PSP is the probability of taking
a shortest path. Simulation results for the Beijing,
Tokyo, Hong Kong, and London metro systems
offer insightful observations on the relationship
between the topological structure of metro networks and traffic flow [32].
vii)	Topological efficiency of traffic networks has traditionally been evaluated in terms of the number of
hops as given by
hG =

1
/ 1 (24)
N (N - 1) i ! j d ij

	where dij is the shortest distance path between
nodes i and j. In a recent work [13], we proposed
an alternative approach to measure the network
efficiency in terms of time rather than distance
since the time metric is more naturally used by
passengers, i.e.,
	

h G, t =

1
N (N - 1)

/

i = 1...n - 1
j = i + 1....n

d ij
(25)
v ij

	where dij is the total number of hops between nodes
i and j, N is the network size, and vij is the maximum
velocity attained along every hop with the shortest
path between nodes i and j [13]. Due to the constraint in obtaining real-world data of vij in (25), we
FOURTH QUARTER 2019 		

50
45
40
Vmax (km/h)

	

(a)
Dependency of Vmax to wi_norm

35
30
25
20
15
10
5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
wi_norm
Vmax (Empirical Result)
Vmax (Simulation Result)
(b)

Figure 8. (a) Snapshot of the SUMO simulator; and (b) comparison of the simulation and empirical results for the dependency of vehicular speed on node weight.

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