SIGNAL SETTING AND PATHS DESIGN FOR ROAD SUPPLY
MANAGEMENT IN EVACUATION CONDITIONS
Filippo A. Marcianò, Giuseppe Musolino
Antonio Polimeni, Agata Quattrone, Antonino Vitetta
Mediterranea University of Reggio Calabria
Dept. of Computer Science, Mathematics, Electronics and Transportation
alessandro.marciano@unirc.it, giuseppe.musolino@unirc.it
antonio.polimeni@unirc.it, agata.quattrone@unirc.it, vitetta@unirc.it
Abstract
In this paper a system of models for signal setting and paths design in
evacuation conditions is proposed. The system of models is developed in
order to respond to the necessity to integrate the design models present in
literature with traffic assignment models, taking into account the effects of
variation of supply and demand in terms of the signal setting and path choice.
1
INTRODUCTION
Transportation systems analysis and planning in emergency conditions
implies the necessity to tackle several issues. Among the others, the design of
traffic signals in junctions and the design of paths for emergency vehicles (e.g.
ambulances, civil protection vehicles, ....) on a road transportation network
have become increasingly relevant.
Nowadays signal setting is considered an effective strategy to increase
network capacity and to mitigate congestion phenomena. Current signal
setting design models and procedures do not provide solutions that take into
account users behaviour at path choice level in response to system
modifications. Few papers on signal setting design models present in
literature take into account users behaviour in response to signal setting
parameters modifications. Moreover, there are no specifications for road
transport systems in evacuation conditions: signal plans are empirically
defined or are defined by means of methods originally concieved to operate in
ordinary conditions.
Path design of emergency vehicles ranges from the design of a single path to
the design of a paths chain (routes design). Route design, commonly named
Vehicle Routing Problem (VRP), is present in literature but few papers present
design models taking into account congested networks.
Generally speaking, models and methods of literature seem not able to face
the VRP in emergency conditions where the assumptions of stationariety do
not hold, due to the relevant changes arising in supply and demand within the
reference period. The above changes affect the path choice dimension and,
therefore, the vehicle routing one, as a vehicle route is the result of a
combination of different paths.
From the above considerations, it emerged the necessity to integrate the
design models present in literature with traffic assignment models, in order to
take into account the effects of variation of supply and demand into the
vehicle routing definition.
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The main research advancements presented in the paper concern the design
models and procedures, which are able to optimize signal setting parameters
and emergency vehicles routes taking into account the travel demand flows
simulated according to a behavioural approach. The models could be
considered as the the core of a Decision Support System (DSS) for the realtime management of intelligent signalized road intersection networks.
The paper is articulated as follow. In section 2 the simulation and design
models are reported. In section 3 a system of design models is proposed.
Finally, in section 4 an application to a real case is reported.
2
LITERATURE REVIEW
The section reports a state of the art concerning simulation models (section
2.1) and design models (section 2.2).
The network design problem in transportation system analysis may be treated
using two different approaches: what if and what to (Cantarella et al., 2006). In
both cases travel demand and assignment models are given. In the what if
approach a specific supply configuration is also given. Hence, link flows can
be calculated as well as indicators of performance and impacts which are
useful to evaluate the current solution. By contrast, in the what to approach
(figure 1), there is a supply design model which generates and evaluates
supply configurations by using information (costs, performances and impacts)
from previous explored solutions, considering given objectives and constraints
(external and technical).
Figure 1 What to and what if approaches in transport network design
2.1
Performances and simulation
Traffic Assignment (TA) models simulate the interaction between travel
demand and transport supply. These models allow to calculate travel costs
and flows for each link of the network.
TA models are generally subdivided into Static (STA) and Dynamic (DTA)
models. In congested networks, STA models simulate a transport system in
stationary conditions, where link (or path) flows and costs are mutually
consistent. This condition is valid if travel demand, path choices and transport
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supply are constant in a reference period of time. Outputs are the link flow
vector and the link cost vector.
DTA models remove stationary assumptions, allowing transport system
evolution to be represented as in the case of emergency conditions when
travel demand peaks, temporary capacity variations, temporary oversaturation of supply elements, queue formation and dispersion occur. DTA
models, in their turn, may be classified into macroscopic, mesoscopic and
microscopic, according to the link flow representation, which may be
continuous or discrete, and to cost functions, which may be aggregate or
disaggregate.
DTA models for emergency conditions started to be developed in USA after
the partial meltdown of the reactor at the Three Mile Island nuclear power
plant in 1979. In the 1980s a first generation of models for supporting
evacuation planning was developed. After 9/11, great efforts were made not
only to adapt existing DSS but also to develop dedicated DSS to simulate
transportation systems in order to support evacuation planning.
Research on DTA models during the last two decades has been continuously
advanced, which has led to a large number of DSS being implemented to
support operative transport planning in ordinary conditions. Among the others,
it is worth recalling MITSIM (MIT, 2002), PARAMICS (Quadstone, 2009),
AIMSUN (TSS, 1999), TransModeler (Caliper, 2006), DYNASMART
(Mahmassani et al., 2004) and DYNAMEQ (INRO, 2006).
The literature presents some papers concerning applications of DTA models
in emergency conditions which may be classified according to three purposes
which are demand management, network design and simulation of an
evacuation plan.
Demand management applications concern departure time definition in order
to reduce congestion phenomena and minimize evacuation time. Several
demand time profiles were defined, simulated through microscopic (Mitchell
and Radwan, 2006) or mesoscopic (Sbayti and Mahmassani, 2006) DTA
models and compared with a simultaneous departures scenarios. Evacuation
demand scheduling is also treated with macroscopic models (Velonà and
Vitetta, 2003, Liu Yue et al., 2008). KLD analyzed demand management for
evacuation of nuclear plants (Goldblatt and Lieberman, 1993) and an arms
depot (Goldblatt, 1996). A specific line of research concerns the simulation of
interactions and activity (or trip) chains of household during an evacuation
(Murray-Tuite and Mahmassani, 2003).
Network design applications concern path optimization and management in
emergency conditions (Russo and Vitetta, 2000). As regards path optimization
design, there are several applications related both to buildings with
microscopic (Sisiopiku et al., 2004) or mesoscopic (Di Gangi and Velonà,
2007) approaches, and urban areas with microscopic (Yuan et al., 2006) or
mesoscopic approaches (Cova and Johnson, 2003). Some papers focused on
supply management through operations like contraflow (Tuydes and
Ziliaskopoulos, 2004; Theodoulou and Wolshon, 2004) and ramp metering
(Gomes and May, 2004) in order to improve network capacity during
evacuation.
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2.2
Design models
2.2.1 Signal Setting design models
The signal setting problem considers at least one of the following design
variables:
 green time on each access and cycle time durations, with exogenous
stages;
 green time and schedule (initial instants of green times and green time on
each access) and cycle time durations;
 offset between each couple of adjacent intersections.
Signal setting design models may be classified according to two criteria
(Cantarella e Vitetta, 2010).
The first is connected to the intersections which may be: isolated, interacting
along an arteria or on a network. The second concerns the signal setting
strategies (or signal setting design parameters), which may be based on
 flows, with two main objectives
 minimization of total delay;
 maximization of capacity factor;
 arrival times.
The strategy based on flows may have two objectives:
 minimization of total delay, with fixed or variable cycle time duration;
green timing setting has been faced with convex optimization techniques
in SIGSET model (Allsop, 1971); green timing setting and scheduling
has been faced with discrete (or non linear) optimization techniques,
adopted in SICCO model (Improta and Cantarella, 1984; Cantarella and
Improta, 1988);
 maximization of capacity factor, given a cycle time duration; green timing
setting with some restrictive assumptions on the structure of the stages
has firstly studied in Webster models (Webster, 1958; Webster and
Cobbe,1966; Cantarella and Improta, 1988); later it has been studied
with linear optimization techniques in SIGCAP model (Allsop, 1976)and
further developed in several models like SIDRA (Akcelik and Besley,
1992) and OSCADY (Burrow, 1987); green timing setting and scheduling
has been faced with discrete (or non linear) optimization techniques, as
in SICCO model (Improta and Cantarella, 1984; Cantarella and Improta,
1988).
The methods based on arrival times can be semi-attuated or totally attuated.
The semi-attuated regulation has fixed scheduling and green timing setting
can be modified in relation to the users arrival. The totally attuated regulation
has green timing setting and scheduling which are variable in relation to users
arrival.
2.2.2 Vehicle Routing Problem
The Vehicle Routing Problem (VRP) regards the necessity to visit a certain
number of nodes according to a given sequence, leaving from an origin and
returning to it with respect to some constraints (i.e. number of users to visit
and their localization, number of vehicles and their capacity, ...) optimizing an
Objective Function (OF). The OF may be dependent on travel time, monetary
cost or number of vehicles.
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The VRP can be solved with exact algorithms (Qureshi et al., 2009) or
heuristic algorithms (Ando e Taniguchi, 2006). Literature is very large (for an
exhaustive review see Laporte, 2007; Gendreau et al., 2008). The problem
generally concerns a fleet of vehicles that has to distribute a quantity of freight
to a number of clients (retailers, …) departing from an origin (depot),
optimizing travel time, distance, number of vehicles.
VRP can be extended to emergency vehicles (ambulances and so on) to
optimize their routes or their relocation (when vehicles do not return to the
origin point). Two separate cases can be considered: ordinary conditions and
emergency conditions (in a disaster scenario).
In ordinary conditions, Gendreau et al. (1997, 2001, 2006) propose a method
for the relocation of emergency vehicles in order to maximize demand served
and covered area. Rajagopalan et al. (2008) propose a model to determine
the minimum number of ambulance and their location to satisfy a given
demand for each time interval. A review on models concerning location and
relocation of ambulances, is reported in Brotcorne et al. (2003). Yang et al.
(2005) consider a fleet of vehicles that operate according to its current
position on the network, in order to maximize the covered area and, in the
case that a vehicle covers a given zone, assigning a sequence of nodes to be
visit according to users characteristics.
In emergency conditions, we can distinguish two user-oriented approaches:
the first one is related to road user (i.e. car drivers) and the second one is
related to the operators (i.e. ambulance drivers). For the first approach,
Takahashi et al. (2005) propose a model that simulates users path choice
behaviour when, due to a calamitous event, the road network has limited
accessibility. The model estimates the variation of costs incurred by users
who are forced to modify their path choice. For the second approach, Araz et
al. (2007) optimize a fleet of emergency vehicles (ambulances and anti-fire
vehicles), so as to minimize travel time and maximize covered area and
number of users to be saved. Liu et al. (2007) propose a VRP to minimize
demand not satisfied and time delays when it is necessary to distribute
medical supplies and to respond at a large-scale attack. Shen et al. (2007)
propose a VRP to support the case of a large scale bioterrorism attack. The
proposed model consists of two stages: planning (routes are generated in
advance for any emergency) and operation (taking into account information
gathered in emergency conditions, appropriate changes to the routes
determined in the planning stage will executed). Vitetta et al. (2007/b, 2008/b,
2009/b) and Polimeni et al. (2010) propose a methodology for routing and
dispatching of emergency vehicles in a disaster scenario. The problem is
solved according the criteria of distance between an emergency vehicle and
the user to be saved of users health conditions.
3
SYSTEM OF MODELS
The system of models proposed, based on what to approach, is composed of
three levels (figure 2), each of which is linked to the internal level, every level
provides some outputs. The analysis may stop at any level depending on the
type of output needed. In particular, at the first level not-congested transport
costs are provided, the output are the system performances; at the second
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level TA allows to simulate the system; at the third level vehicle routing (routes
design) and signal setting allows to design the system.
Costs
Performances
Traffic Assignment
Simulation
Vehicle Routing
Signal Setting
Design
Figure 2. System of models proposed: three levels structure
The proposed system of models may be applied both in ordinary and
emergency conditions. The difference between the two conditions (ordinary
and emergency) is the modification of equations linking the problem variables.
These equations allow to take account changes in the transport system (i.e.
changes in supply and demand) in term of supply performances and users
behaviours due to emergency occurrence.
Travel demand (Russo and Chilà, 2008; 2009) is specified in term of two main
components:
 ordinary demand dOt, average demand flows in time slice t; the element
dOt,r is ordinary demand flow value related to the o/d pair r;
 emergency demand dEt, represented by users present in the
evacuation area in slice time t; the element dEt,r is the emergency
demand value related to the o/d pair r.
Emergency demand can be divided in two sub-components:
 not-controlled travel demand, dE,NCt, that is the sum of users who
wish to evacuate from a given area and operators that intervene for
supporting people and save valuable goods without any real-time
information about transport system conditions;
 controlled travel demand, dE,Ct, which is represented by operators
that intervene for supporting people and save valuable goods with
real-time information about transport system conditions.
3.1
Performances and simulation
In this section models and procedures to design transport supply elements
and to simulate transport system performances are analysed.
The following symbols are used:
 d, travel demand vector;
 ft, time-dependent link flow vector;
 , links-paths incidence matrix;
 ct, time-dependent link cost vector;
 c*t, equilibrium link cost vector at time t;
TA models (figure 3) have the following inputs:
 a supply model, simulating network performances;
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 a demand model, simulating users behaviour.
and they produces as outputs:
 link flows;
 link performances (travel costs).
Figure 3 Traffic Assignment model
3.1.1 Signal setting
The proposed signal setting design model of signalized intersections in a road
network is defined as an optimization problem (design model) subjected to
equilibrium constraints; in other words, travel demand flows must be
consistent with travel times generated by signal setting parameters. The
design model generates and simulates potential solutions for the optimization
of an objective function; solutions generation is executed by a solution
generator procedure, while users behaviour (path choice) is simulated through
a simulation procedure. The design model is solved by means of a heuristic
genetic algorithm, while the simulation is executed by means of a dynamic
within-day procedure with stochastic path choice model.
The simulation procedure has a bi-level structure (figure 4): the first level is
represented by a system of static stocastic traffic assignment models that
allow to estimate the origin-destination path choice probabilities on the first kpaths of minimum congested costs on every origin-destination couple; the
second level is represented by a system of dynamic models that allow to
estimate the temporal profile of in-flows and out-flows to and from different
accesses and, therefore, to estimate the total delay on the network.
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

IMPLICT SUE
cSUE
y
K-PATHS
GENERATOR
k –paths
c
EXPLICIT SUE
gk
pk
d
DISPERSION
MODEL
l
sAT
C
GLOBAL
DELAY
RT
Figure 4 Signal setting design model: simulation
procedure
The simulation procedure is composed by the following modelling elements:
 an implicit Stocastic User Equilibrium (SUE) model with implicit path
enumeration, that provides an estimation of congested link costs vector,
cSUE;
 a k-paths generator, that provides the first k-paths of minimum congested
costs on every origin-destination couple;
 an explicit Stocastic User Equilibrium (SUE) model with explicit
enumeration of the first k-paths of minimum congested costs, which
provides an estimation of path choice probability vector, pk, according to
the equilibrium constraint;
 a dispersion model (aggregate link cost functions) that allows to estimate
the temporal profile of in-flows and out-flows to and from different
accesses and, therefore, the vector of queue lenghts on links, lC;
 a global delay model for the estimation of the delay on the network, RT.
3.1.2 Vehicle routing
Simulation for VRP provides paths and path costs to reach weak users. Paths
are elements which are involved in the route design process (a route is a
sequence paths, the design procedure is presented in section 3.2.2).
Travel demand characteristics introduced above allow to consider two TA
models to simulate demand-supply (Vitetta et al., 2007/a, Vitetta et al.,
2008/a; Vitetta et al., 2009/a, Marcianò et al. 2010) interaction: the first one is
the user equilibrium TA model in which demand, path and link flows are
mutually consistent with costs that they generate; the second one is the
system optimum TA model, based on second principle of Wardrop1.Travel
demand components, dOt and dE,NCt, are assigned to the network according to
user equilibrium approach: they can be considered as one user category and
we consider the vector dt = dOt + dE,NCt. Travel demand component, dE,Ct, is
assigned to the network according to system optimum approach. It is worth
noting that demand dE,Ct is lower than dt and with another level of magnitude;
1
The condition under which the total cost in the network is minimum as expressed by the second principle of
Wardrop is know as System Optimum (SO) (Cascetta, 2009).
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for this reason we can assume that the choices of users moving with the EU
hypothesis are not affected by users who move with the SO hypothesis
3.2
Design
In this section procedures proposed for signal setting and vehicle routing
design are proposed.
3.2.1 Signal setting
This section presents the general procedure for signal setting design.
The basic hypotesis are:
 all intersections of the network have a common cycle time duration or an
its sub-multiple in order to ensure the coordination among signal plans in
successive cycles;
 entering flows in the network are known and concentrated in some source
nodes called origin centroids (the destinations are known);
 exiting flows from the network are concentrated in some sink nodes called
destination centroids;
 users choose paths according to behavioural rules.
The design procedure (figure 5), based on a what-to approach, has a multilevel structure that generates and simulates potential solutions in order to
optimize an objective function.


Design model
c
y
d
sAT
y
Solution
generator
Simulation
y*
RT
Figure 5 Components, inputs and parameters of the
signal setting design procedure
The inputs of the procedure are the elements of the transport system and, in
particular, the travel demand (vector of demand flows, d), the transport supply
(vector of link costs on non-congested network, c, and vector of saturation
flows on each access, sAT), the initial configuration of signal setting
parametres (vector, y). The output is the configuration of signal setting
parameters (vector of solutions at equilibrium, y*) that optimizes the objective
function. The parameters are represented by the matrix of network topology,
, and a vector of transport models paramaters, .
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The design model is described below in terms of variables, objective function
and constraints.
Variables
The assumption that all intesections of the network have a common cycle time
duration (or an its sub-multiple) implies the design of the following variables:
 a common duration of basic cycle for all intersections;
 a sub-multiple of the basic cycle for each intersection;
 green time duration with initial istant of green time, final istant of amber
time.
As the amber time duration is not dependent from other design variables, so it
is exogenous, the independent variables for each access a of an intersection,
is every couple of the following variables.
The number of offsets to be designed (both absolute and related to each
couple of intersections), depends on the duration of the basic cycle and it is
equal to the number of signalized intersections less one.
Objective function
The objective function is defined as the global delay on the network, R T,
calculated as the sum of delays on all accesses of the network.
Matematically, the design problem may be formalized as follows:
Objective: min RT(y, f(y))
with
RT(y, f(y)) = i = 1 … |I|j = 1 … |Ai| RTj(y, f(y))
where
RTj, total delay of vehicles on the access j belonging to the set of accesses (of
numerosity Ai) that converges into the intersection i;
f, link flows functions vector, which depend on the signal setting parameters at
equilibrium;
|I|, is the cardinality of the set of intersections belonging to the network.
Constraints
The objective function is subjected to the following constraints:
 equilibrium constraint, that is given by the vector of link flows at
equilibrium, f, that reproduces itself, according to the assignment model:
f(y) = Δ(y)P(- Δ(y)Tc(f(y))) dE,NC(g(f(y))

where
P, probability path choice functions matrix;
c, link cost functions vector;
d, demand functions vector;
g, path cost functions vector;
technical constraints
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

every set of signalized intersections that are object of cycle
coordination must have the same cycle time duration, or equal to an its
integer sub-multiples;
 for each access of an intersection the relationships between red, green
and cycle times must hold;
 for each intersection the absolute offset must lie between 0 and the
duration of the basic cycle;
external constraints
 for each intersection the duration of every green phase must be greater
or equal to a minimum value;
 the duration of the basic cycle must lie between a minimum and a
maximum value.
3.2.2 Vehicle routing
A what to model is considered in order to design the paths for emergency
vehicles, (Russo and Vitetta, 2003; Cantarella and Vitetta, 2006). The what to
approach is proposed to define optimal emergency vehicle distribution, in
terms of vehicle number, weak users sequence to be visited and hence
paths/routes design to optimize an objective function (i.e. minimizing travel
time and/or maximizing network reliability). What to models allow interventions
on the some supply characteristics (number of vehicles, position of the refuge
areas), according to some constraints (number of persons to be saved and
sites to be left in). The models and the algorithms specified and calibrated in
ordinary conditions cannot be applied in emergency conditions without new
specifications and calibrations (Russo and Vitetta, 2003 and 2006).
Few works (Russo and Vitetta, 2003; Sumalee et al., 2006) are present in the
case in which the transport system conditions are modified due an
approaching disaster.
The optimization problem in such case could be placed in the following terms:
 Objective: minimize the emergency vehicle travel time.
 Variable: paths/routes.
 Constraints: supply constraints, demand constraints, behavioural
constraints, vehicles availability, other constraints.
Routes design can be approached considering all paths between all o/d pairs,
which, in this case, are represented by refuge area and weak users home
(One-to-One Problem) and then searching the path combination that
optimizes the objective function (Many-to-One Problem).
One to One Problem
The one to one approach gives the probability of every path being chosen,
from those perceived as admissible, between each origin to each destination.
Starting from the assumption that just a subset of all the possible topological
paths (choice set) between an origin and destination is actually perceived by
users, the path search problem in the one-to-one approach, has been treated
explicitly by distinguishing two different phases:
1. generation of a choice set, that explicitly identifies the possible
alternatives;
2. path choice among the alternatives belonging to the choice set.
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In the emergency vehicles case, the path design can be defined as a System
Optimum (SO) problem (figure 6). Indeed, considering that the emergency
vehicles flow is much less than the total flow, the link costs (which depend on
the total flow) can be considered not dependent by the controlled emergency
vehicles flow.
The problem can be formulated as the minimization of the total cost of
controlled emergency vehicles:
f*E,Ct = argmin ctT(f*t)  fE,Ct
subject to:
iFSs fE,Ct,i + Is = iBSs fE,Ct,i + Os for each node s
were:
ct, link costs vector in the slice time t, with ct,i the cost on the link i;
fE,Ct emergency vehicle flow vector in the slice time t, with fE,Ct,i emergency
vehicle flow on the link i;
f*t flow vector in the slice time t, with f*t,i the flow on the link i;
FSs is the Forward Star of the node s (the set of exit links from node s);
BSs is the Backward Star of the node s (the set of entry links into node s);
Os =r dE,Ct,r for each O/D pair r, whit origin s;
Is = r dE,Ct,r for each O/D pair r, whit destination s.
Whit this notation, if s is not an origin of O/D pair, Os is equal to zero; if s is not
a destination of O/D pair Is is equal to zero.
Note the emergency vehicles demand vector, the SO give as output the
emergency vehicles flow for each path and, implicitly, the paths followed for
the controlled vehicles. The constraint establish the flow conservation: users
flows cannot be created or dispersed at any node of the network except
origin/destination node.
Figure 6 System Optimum approach for path optimization
Many to One Problem
Concerning the many to one approach (Vitetta et al., 2007b) problem can be
formulated as a VRP. The VRP regards the necessity to visit a certain number
of nodes in a given sequence (named route), leaving from an origin and
returning to it, with the respect of some constraints (i.e. number of users to
visit and their localization, number of vehicles and their capacity, and so on);
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the aim is to optimize an Objective Function (OF). The OF can depend on
travel time, monetary cost or a their combination.
As for path optimization, the VRP can be formulated as an optimum problem
(figure 7). The objective is to calculate the vehicle routes minimizing a cost
function which takes into account the problem characteristics and constraints.
Figure 7 Approach for routes optimization
The VRP formulation can be expressed as:
minimize 1T• •gE,Ct
subject to:
capacity constraints (for each vehicle i the capacity bE,Ci cannot be violated);
congruence constraints (an user can not be reached more than once, all
vehicle return to the starting point);
time windows constraints.
Considering the following variables is the route-path incidence matrix, with
xk,equal to 1 if the path k belong to route , zero otherwise; 1 is an unit
vector that has a number of rows equals to the number of routes; gE,Ct
emergency vehicle minimum path costs vector in the slice time t, with gE,Ct,k the
cost for emergency vehicle on the path k.
4
APPLICATION
An application has been executed on the experimental evacuation test site
defined in SICURO, with the objectives to validate the design model, through
observed data and results from a what-if modelling approach, and to minimize
evacuation times operating on signal setting design of a network of
intersections.
The design model has been applied on the transport system of the central
area of Melito di Porto Salvo (figure 8), which is a town in the south of Italy.
The municipality has an area of 35.30 km2, 10483 inhabitants and 2432
employees.
An incident was reproduced with a simulation in reality and it concerned an
heavy vehicle with leaking hazardous goods inside the urban area during the
morning period of an average working-day.
4.1
Signal setting
The design model has been applied cosidering two signal setting scenarios:
 (current) scenario, where signal setting parameters were defined in order
to reproduce the existing priority rules at the intersections (that are were all
not-signalized);
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
design scenario, where traffic signals operate with the configuration of
signal setting parameters provided as output of the design model, y*.
The results obtained running the design model for the two signal setting
scenarios are presented and discusses below in terms of a set of indicators
belonging to three classes (see Russo and Rindone, 2010):
 demand-supply interaction
 global delay of vehicles on the network;
 evacuation time;
 transport system evolution during evacuation
 temporal profile of vehicles approaching the refuge area;
 link and node
 temporal profiles of vehicular flows on each access of the intersection.
Figure 8 Graph, traffic signals and weak users location.
The simulation model, devolopped in this work and used inside the design
model, allowed to estimate a global delay of vehicles on the network of 52312
[vehic h] and an vacuation time of 33 [min] in the current scenario. In the
design scenario, the estimated global delay was 18118 [veic h], with a
reduction of 71% in relation to current scenario, and the estimated evacuation
time was 25 [min], with a reduction of 24% (table 1).
The number of vehicles approaching the refuge area on each five-minutes
time slice for the two signal setting scenarios is plotted in figure 9. The plots
show that, during the first ten minutes, a larger number of vehicles
approached the refuge area in the current scenario than in the design one,
due to lower waiting times at nodes. Afterwards, the increasing evacuation
demand caused a decay of network performances in the current scenario, due
© Association for European Transport and contributors 2010
14
to an increment of congestion levels. In the design scenario, signal settings
parameters, optimized according to the increasing vehicular flows, allow to a
larger number of vehicles to reach the refuge area, with a subsequent
reduction of evacuation time.
Table 1 – Signal setting scenarios: demand-supply interaction indicators.
Indicators
Scenario
Current
Design
Global delay [vehic h]


Evacuation time [min]
33
25
– 24%
52312
18118
- 65%
 = (Xcurrent-Xdesign)/Xcurrent
90
current
80
design
70
[vehicle]
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
Time [min]
Figure 9 Signal setting scenarios: number of vehicles approaching
the refuge area.
In order to show the potentialities of the simulation procedure, which
incorporates a dynamic supply-demand interaction model, as an example, the
estimated temporal profiles of vehicular flows at node 12 of the network (see
figure 8) are plotted in figure 10. Further comments about estimated temporal
profiles of vehicular flows on the network are reported in Marcianò (2010).
The estimated variation of evacuation time between signal setting scenarios
was compared with the one estimated between two network topology
scenarios, previously defined in SICURO and simulated through a what-if
model (see Vitetta et al. 2008; Vitetta et al. 2009). The two network topology
scenarios are:
 current scenario, where the network topology was the one operating in
ordinary condition, with intersections regulated through priority rules;
 design scenario where network topology was modified in order to prevent
historical travel demand only from crossing the evacuation area (see
Marcianò, 2010) .
Evacuation time in the network topology design scenario is reduced of 14%.
This reduced variation, compared to the one between signal setting scenarios,
indicates that (design) interventions on signal setting parameters could be
more effective than interventions on network topology in reducing evacuation
time for this specific experimental evacuation test site.
© Association for European Transport and contributors 2010
15
3000
[veic/h]
2500
0
50
100
150
200
250
300
[sec]
Vehicular flow at stop line
Exiting vehicular flow
Saturation flow
Figure 10 - Signal setting scenarios: temporal profiles of vehicular
flows at node 12
4.2
Vehicle Routing Problem
The above-proposed VRP simulation was applied to generate the paths
actually observed during evacuation simulation and the best paths to reduce
evacuation time by testing different scenarios (in terms of number of
emergency vehicles, siting of refuge areas, different configurations of the
reserved network). During evacuation simulation the paths chosen by an
ambulance driver were monitored using an on-board GPS and video-cameras
deployed on the network. It was assumed that five weak users must be
rescued, their residences are marked on the network with the letters A -E
(figure 8). It is also assumed that only one emergency vehicle of with a 3-user
capacity is used to rescue all the weak users. The ambulance observed took
five weak users along two routes: on the first route two users (A and C) are
rescued; on the second route three users (B-D-E).
In this phase the criteria considered for path generation is the minimum travel
time.
In table 2 we report the evacuation time for each weak user (A-E) and each
generated route with the many-to-one approach (proposed procedure).
Table 2 - Results obtained for the many-to-one approach
Proposed procedure
Total
Route Observed
Sequence
R1-E-A-B-R1
R1-C-D-R1
R1-C-A-R1
R1-E-D-B-R1
Total
t [sec]
1293
982
2275
1390
1494
2884
Table 2 shows that the paths generated with the proposed procedure reduce
the evacuation times with respect to those observed (with a gain of 21% in the
travel time). The first differs from the second both in terms of sequence. This
highlights the efficiency of proposed procedures in order to plan better weak
user evacuation.
© Association for European Transport and contributors 2010
16
5
CONCLUSION
A system of models and procedures for signal setting and path/routes design
on a road network has been applied on a real experimental evacuation test
site with the objectives to validate the modelling components and to minimize
evacuation times.
The simulations showed remarkable reductions in terms of total delay of
vehicles on the network and of evacuation time in the signal setting design
scenario, emphasized by the small dimensions of the network with few paths
alternatives.
The comparison with network topology scenarios indicates that interventions
on signal setting parameters could be more effective than interventions on
network topology for the examined experimental evacuation test site.
Further research concerns the development of the system of models in order
to allow an integrated design of signal setting and network topology
parameters and the model validation through the definition of integrated
design scenarios on a real test site in evacuation conditions.
The routes design for emergency vehicles are analysed, both in ordinary
conditions and in emergency conditions. This analysis revealed the necessity
to integrate the traffic assignment models with the design models, in order to
take into account the effects of variation of supply and demand into the
vehicle routing definition. A general framework to link simulation models and
design approach was discussed.
The comparison with observed routes and designed routes indicates that
interventions on route design, under the same resources, could cause a
reduction of evacuation time.
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