Simulation Analysis of Evacuation Guidance

Using Dynamic Distributed Signage

Akira Tsurushima

Intelligent Systems Laboratory, SECOM CO., LTD., Japan

Keywords:

Crowd Evacuation, Dynamic Evacuation Guidance, Distributed Problem Solving, Multi-Agent Simulation.

Abstract:

Evacuation guidance systems must be adaptive and distributed in the unstable and harsh environment of dis-

aster evacuation. Numerous dynamic evacuation guidance systems have been proposed and studied; however,

few of them focus on the unstable evacuation environment that makes computer systems unreliable and mal-

functioning. In this study, we introduce a distributed algorithm for a dynamic evacuation guidance system to

ensure safe and efﬁcient evacuation, even in the face of system component failures. The system is designed to

be resilient, allowing it to continue functioning, providing effective evacuation guidance despite partial system

malfunctions. Simulation experiments showed that the distributed system can provide more efﬁcient evacua-

tion guidance than static guidance systems. Furthermore, it correctly guided evacuees in situations where the

target exit changed during the evacuation, showcasing the system’s adaptability and effectiveness in handling

unforeseen challenges, including system failures.

1 INTRODUCTION

Numerous studies have been conducted on crowd

evacuations, and many devices and systems have been

proposed and developed to support efﬁcient evacua-

tion. Several researchers are currently studying dy-

namic evacuation guidance systems that provide ef-

ﬁcient advice on evacuation paths to evacuees con-

sidering the dynamic evacuation environments in real

time. These systems typically include sensors and

interface devices. Sensors are employed to acquire

local information regarding risks and threats, such

as congestion caused by evacuees, smoke, or harm-

ful gases produced by ﬁre or hazard levels owing to

collapsed pathways. Interface devices such as smart-

phones, personal digital assistants (PDAs), and digital

signage are used to advise evacuees about the paths

they should follow.

A dynamic evacuation guidance system must

function effectively in harsh environments that can

damage its components, which is challenging. There-

fore, it is unrealistic to expect that all system compo-

nents will function as intended. For example, the de-

vices, information lines, or sensors may fail, become

disconnected, or generate inaccurate information, re-

spectively. Thus, the system design should allow it to

https://orcid.org/0000-0003-2711-297X

function despite damaged components. Although the

system may not perform perfectly under these condi-

tions, a single point of failure that can cause the entire

system to malfunction should not exist.

Thus, it is important to design dynamic evacua-

tion guidance systems in a decentralized manner to

ensure effective functionality under harsh conditions,

which can prevent a single component or failure from

causing the entire system to malfunction. This type

of system typically has the following two primary ob-

jectives: 1) reducing the total evacuation time by miti-

gating the congestion caused by crowds, and 2) adapt-

ing evacuation routes to the dynamic environment. In

this study, we present a distributed algorithm that uses

only local information for effectively guiding evac-

uees in indoor situations. Assuming that all compo-

nents operate without malfunctions, we focused on

how a distributed system equipped with our algorithm

can efﬁciently guide crowds to achieve these objec-

tives. We did not consider the scenarios in which cer-

tain components of the system may malfunction.

2 RELATED WORK

The intelligent active dynamic signage system

(IADSS) was developed as part of the GETAWAY

project to overcome the many shortcomings of the

Tsurushima, A.

Simulation Analysis of Evacuation Guidance Using Dynamic Distributed Signage.

DOI: 10.5220/0012268100003636

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2024) - Volume 1, pages 179-188

ISBN: 978-989-758-680-4; ISSN: 2184-433X

179

(A) (B)

Figure 1: (A) Example ﬂoor plan. (B) Graphical representation of the ﬂoor plan.

widely used static signage systems for crowd evac-

uation guidance. IADSS was tested at the Sant Cu-

gat Station in Barcelona, Spain with 1356 volunteers,

demonstrating its effectiveness in crowd evacuation

(Galea et al., 2014; Galea et al., 2017). The suc-

cess of this project gained the attention of several re-

searchers, and numerous studies have been conducted

on dynamic evacuation signage systems. Lin et al. in-

vestigated the effectiveness of IADSS on more com-

plex structures by using a ﬁre dynamics simulator

(Lin et al., 2017).

While IADSS was designed to draw the atten-

tion of the evacuees to signage information, studies

have focused on the dynamic pathﬁnding of evac-

uees. Researchers have proposed dynamic route se-

lection techniques, such as a combination of graph-

based route representation, simulation-based evalu-

ation techniques (Cisek and Kapalka, 2014), and

density-based route selection techniques (Bernardini

et al., 2016).

Subsequently, numerous optimization techniques

have been developed for dynamic pathﬁnding evac-

uation, such as the combination of crowd modeling

and artiﬁcial immune system-based route optimiza-

tion (Khalid and Yusof, 2018), shortest pathﬁnding

using the Dijkstra algorithm (Baidal et al., 2020),

and a two-layer approach of dynamic sign assign-

ment and pedestrian assignment (Li et al., 2022). Xue

et. al. proposed a machine-learning technique us-

ing reinforcement learning (DQN) and evaluated its

efﬁciency against the Dijkstra algorithm (Xue et al.,

2021).

Novel approaches have been proposed for imple-

menting dynamic evacuation guidance by using dis-

tributed systems. A congestion-awareness route se-

lection approach using the cell phone of an evacuee

was proposed (Kasai et al., 2017). A distributed tech-

nique using the Bellman-Ford dual subgradient algo-

rithm was developed to guide groups of evacuees to

use their cell phones (Zu and Dai, 2017). Nguyen et.

al. developed an evacuation guidance system that di-

vides a large building into several sections, calculates

the optimal routes for each section, and subsequently

generates the overall evacuation routes by coordinat-

ing these local sub-routes (Nguyen et al., 2022). A

distributed architecture for real-time evacuation guid-

ance that considers envy-freeness was proposed (Lu-

jak et al., 2017). These studies generally focused on

reducing the complexity of computing the global op-

timum and achieving system scalability.

In a pioneering study, Zhao et al. proposed that

each node of the distributed evacuation guidance sys-

tem independently calculates its direction of evacua-

tion and shares this information with its neighboring

nodes to develop the overall evacuation routes (Zhao

et al., 2022). The system does not contain a single

point of failure that controls the entire system, thus

ensuring that it will continue to function despite cer-

tain components failing, which is expected in harsh

environments during disaster evacuation. However, a

detailed algorithm and its analysis were not clearly

presented in their paper, and the performance of the

distributed system was evaluated only in terms of ﬁre

detection time against a theoretical worst-case sce-

nario.

In this study, we formulated a distributed evacua-

tion guidance problem and proposed a distributed al-

gorithm to generate the overall evacuation route. We

also evaluated the performance of the distributed sys-

tem in terms of congestion mitigation and adaptation

to environmental changes using multi-agent simula-

tions.

3 PROBLEM

Fig. 1(A) illustrates the evacuation environment (Tsu-

rushima, 2022a) with the coordinate (x, y) ∈ R

× R

where R

= [−39, 41], R

= [−26, 24], which repre-

sents the positions in the environment used in this

study. The environment consisted of a central core

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

180

(dark gray square), with exits (depicted in blue with

numbers), aisles (white), corners (depicted by num-

bers), and the surrounding space (light gray). Doors

connecting the surrounding space and aisles in the

central core are depicted in yellow, which evacuees

in the surrounding space can use to move to the aisles

and evacuate to the exits. Evacuation signs, which can

advise evacuees regarding the directions for their next

moves, are positioned in front of doors (1, . . . , 10), at

corners (11, . . . , 22), and at two exits (23 and 24). Al-

though not clearly illustrated, the environment con-

tained sensors that indicate the levels of danger, such

as congestion, smoke, or toxic gases produced by ﬁre

in the aisles and spaces near the doors.

Fig. 1(B) presents a graphical representation of

Fig. 1(A). The nodes represent the doors, corners,

and exits. The edges represent the corresponding

aisles or regions in the surrounding space. The nodes

in the ﬁgure also represent the evacuation signs po-

sitioned at the corresponding doors, corners, or ex-

its. These signs and their positions can be interpreted

interchangeably. The red dotted lines represent the

communication channels between the two evacuation

signs. The topologies of the aisles and device con-

nections in the example are the same, which is not re-

quired in general cases. The blue arrows in the ﬁgure

represent the directions of the next moves of the evac-

uees or the directions displayed on evacuation signs.

For example, at door 1, an evacuee has three direction

choices: door 2, door 10, and corner 11; the evacua-

tion sign on door 1 indicates either one of doors 2, 10,

or 11. The danger level in each region can be repre-

sented by the weights of the corresponding edges in

the graph.

Each evacuation sign, which is a computational

process in the system, acquires danger levels on the

edges connecting the adjacent nodes using sensors,

delivers data through communication channels, and

displays the evacuation direction to adjacent nodes.

Every evacuation sign functions autonomously and

independently.

In this study, given the ﬂoor layout illustrated

in Fig. 1, we investigated the generation of efﬁ-

cient evacuation plans for a dynamic evacuation envi-

ronment using independently functioning evacuation

signs. The study had two objectives: 1) to reduce

the total evacuation time by mitigating the congestion

caused by evacuees and 2) adapt to evacuation routes

by considering dynamic environmental hazard levels.

3.1 Formulation

Consider the graph

G = (V,

E,W ) depicted in

Fig. 1(B) with red dotted lines. Nodes V =

{1, 2, . . . , 24} represent evacuation signs, undirected

edges {i, j} ∈

E represent the communication chan-

nel between evacuation signs, and ordered lists W =

, . . . , w

, . . .) represent the weight values w

I (i, j)

given by the corresponding sensors, where I : V ×

V → N maps i, j to index k in an ordered list. The

weighted values represent the cost or level of danger

at the edge if the evacuee uses an edge as part of the

evacuation route; an evacuee should choose an evac-

uation route with a lower cost. w

and w

{i, j}

can be

expressed interchangeably only if there is no confu-

sion. Furthermore, w

{i j}

> 0 and w

{i, j}

= w

{ j,i}

In this study, we made the following assumptions:

G is a connected graph.

2. Any node i ∈ V can communicate with the adja-

cent nodes j ∈ { j ∈ V |{i, j} ∈

E} and the sensors

immediately associate with w

{i, j}

3. All evacuation signs, sensors, and communication

channels function without malfunctions.

1) indicates that any two nodes i and j on

G have

at least one path; i, . . . , j is denoted by (i, j). 2) shows

that i can communicate with the adjacent node

i on

the path (i, j), for example, i,

i, . . . , j, which implies

that i can communicate with any node on path (i, j)

if i is replaced with

i. Node i can also communicate

with any sensor because all the sensors on

G are con-

nected to at least one node on

G and we assume that

all the devices operate without malfunctions from 3).

Accordingly, we make the following assumption:

Assumption 1. Any node i on

G can instantly com-

municate with any other node j and sensor w

{i, j}

Assumption 1 does not hold for real evacuation situa-

tions; however, in this paper, we discuss all the tech-

nical details under this assumption for simplicity.

We now consider a directed graph G = (V, E,W ),

as shown in Fig. 1(B), with blue arrows, where e

∈

E is the directed edge e

= (i, j), which represents a

set of adjacent nodes j, where evacuation sign i can

point out or an evacuee at i can select the next move.

Finally, we introduce a set of exits, V

= {23, 24}.

Given the dynamic nature of the problem stated

in this section, namely E and W continuously vary

and may need to be denoted temporally, for example,

as E(t) and W(t). However, for simplicity, E and W

are considered and treated as static information un-

til Section 5. The dynamic nature of the problem is

examined in Section 6; both E and W are treated as

dynamic information in this section.

Deﬁnition 1. We call G a universal evacuation graph.

The set of nodes on G being pointed out by i, which in-

dicates any possible direction that an evacuee in i can

choose, is denoted by ∆ : V → 2

, j ∈ ∆(i), (i, j) ∈ E.

Simulation Analysis of Evacuation Guidance Using Dynamic Distributed Signage

181

(A)

(B)

Figure 2: (A) Evacuation graph with cycles. (B) Graph rep-

resentation of evacuation graph with cycles.

Deﬁnition 2. We call

G = (V,

W ) a evacuation

graph, where

E = {(i, j) ∈ E} denotes the set of edges

when an evacuation sign i points to an adjacent evac-

uation sign j and a set of corresponding edge weights

W . The evacuation sign indicated by i on

G is denoted

by δ : V → V, (i, δ(i)) ∈

Note that δ(i) ∈ ∆(i).

Corollary 1. Given evacuation graph

E ⊂ E,

W ⊂

W , where |V | − |V

| = |

E| = |

W | and ∀i ∃ j (i ∈ {V \

}, (i, j) ∈

E).

A evacuation graph is a graph in which each evac-

uation sign i advises evacuees to a speciﬁc evac-

uation route by pointing to an adjacent evacuation

sign (node); each evacuation sign points to only one

node. Now, we consider the special case of evacua-

tion graphs.

3.2 Cycle

Deﬁnition 3. We denote

G = (V,

W ), where

E =

{(i, j) ∈

E |

E is acyclic}, an efﬁcient evacuation

graph.

If we denote a tree by T = (V, E,W ), the follow-

ing lemma holds.

Lemma 1. An efﬁcient evacuation graph can be rep-

resented as

G = {T

, . . . , T

}, where T

is a tree with

element V

as its root.

Proof. We divide

G = (V,

W ) into

G =

, . . . , G

}, V = {V

, . . . ,V

E =

{

, . . . ,

}, where

= {(i, j) ∈

E | i, j ∈

}, ∄(i, j) (i ∈ V

, j ∈ V

, m ̸= n) (

W is di-

vided in the same manner as

E). Corollary 1

indicates that |V | − |V

| = |V

| + . . . + |V

| − |V

| =

| − 1 + . . . + |V

| − 1 = |

| + . . . + |

| = |

E|.

Now, we have |

| = |V

| − 1 because |V

| has only

one element of |V

| and

does not have a cycle

(Deﬁnition 3). Therefore, G

= T

= (V

)

represents a tree with element V

as a root.

(A)

(B)

Figure 3: (A) Evacuation graph without cycles. (B) Graph

representation of evacuation graph.

In this section, we discuss how the evacuation

graphs with and without cycles affect the evacuation

guidance results using two examples.

Fig. 2 (B) presents an evacuation graph with two

cycles: 12, 13, 16, 17, 22 and 6, 7 illustrated by red

arrows; blue arrows indicate evacuation routes from

doors to exits. Fig. 2 (A) presents the assignment

of evacuation directions displayed by each evacuation

sign associated with evacuation graph (B) at each lo-

cation in the ﬂoor plan. The dark blue regions in (A)

indicate the regions where trafﬁc jams are caused by

the evacuees when the evacuation simulations were

performed using evacuation graph (B). By comparing

these two ﬁgures, we observed that the congestion of

the evacuees occurs when the cycles are formed in the

evacuation graph.

Fig. 3 (B) depicts an evacuation graph without cy-

cles (efﬁcient evacuation graph). This graph has no

red arrows and consists of two trees whose roots are

exits (Lemma 1). Fig. 3 (A) presents the evacuation

simulation results in the ﬂoor plan corresponding to

efﬁcient evacuation graph (B). There are no dark blue

areas in this ﬁgure, indicating that evacuees did not

cause trafﬁc jams.

According to the simulation results, severe con-

gestion can occur when the evacuation graph includes

cycles. Therefore,

Requirement 1. the formation of cycles in the evac-

uation graph should be avoided in evacuation guid-

ance,

despite the individual evacuation signs independently

generating the evacuation routes using only local in-

formation.

In addition, the cycles on the evacuation graph do

not lead the evacuees to any exits, giving them the im-

pression that the system is inconsistent and resulting

in a loss of conﬁdence in the system. This is another

reason the cycles on the evacuation graph should be

avoided.

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

182

Figure 4: Universal evacuation graph (left). Minimum spanning tree (center). Minimum efﬁcient evacuation graph (right).

3.3 Edge Weight

Considering the universal evacuation graph presented

on the left in Fig. 4, suppose that node 1 is the exit

and the numbers on the edges are the weight values

representing the costs or levels of danger in evac-

uation routes, such as congestion, smoke, or toxic

gases. A route with a lower weight was preferred.

(the center of Fig. 4) is the minimum spanning

tree of the universal evacuation graph, whose weight

∑

= 37. T

(right-hand side of Fig. 4) is an-

other spanning tree of the universal evacuation graph

whose weight is

∑

= 45, which is not the min-

imum. Let us denote the path from i to j on tree

T (i, j), and the total weights of the edges on the path

weight(T (i, j)). Subsequently, ∀i weight(T

(i, 1)) ≥

weight(T

(i, 1)). For example, weight(T

(4, 1)) = 21

and weight(T

(4, 1)) = 20; the latter is smaller than

the values of the former. Thus, to implement an ef-

ﬁcient evacuation guidance we must determine evac-

uation routes consisting of trees with minimum route

weights, as shown for T

in Fig. 4.

We deﬁne the total path weight (TPW ) of tree T

as follows:

Deﬁnition 4. T PW (T ) =

∑

i∈V \{g}

weight(T (i, g)),

where g denotes the exit node of T .

We also deﬁne TPW of the efﬁcient evacuation

graph

G = {T

, T

, . . .} as follows:

Deﬁnition 5. T PW (

G) =

∑

T PW (T

Deﬁnition 6. We call an efﬁcient evacuation graph

with a minimum TPW a minimum efﬁcient evacuation

graph G

∗

Now, we have an evacuation guidance problem,

that is, min T PW (

G) s.t.

G ∈

G, where

G is a set of

efﬁcient evacuation graphs. To implement an efﬁcient

evacuation guidance

Requirement 2. we must ﬁnd the minimum efﬁcient

evacuation graph on a universal evacuation graph.

Algorithm 1: Broadcast.

Local Variable:

W ,

1 Function

Broadcast(o, i, δ(o), t, Ω

, ϒ

2 if

T [o] < t then

T [o] ← t;

E[o] ← δ(o);

5 foreach j ∈ 1, . . . , |Ω

| do

W [Ω

[ j]] ← ϒ

[ j]

7 end

8 foreach a ∈ ∆(i) do

9 Call

Broadcast(o, a, δ(o), t, Ω

, ϒ

)

on node a

10 end

11 end

12 end

4 DISTRIBUTED ALGORITHM

Evacuation guidance systems must operate under ex-

treme conditions where not all components are ex-

pected to function as intended;

Requirement 3. the system should be resilient, have

no single point of failure, and be distributed.

In this section, we present a distributed algorithm

satisfying Requirement 1 – 3 under Assumption 1.

Each universal evacuation graph node is equipped

with the algorithm that repeatedly executes at cer-

tain intervals; the algorithm is distributed but not fully

asynchronous. The proposed algorithm consists of

two steps: 1) Broadcast , which propagates local in-

formation throughout the graph, and 2) UpdateSign ,

which determines the optimal evacuation routes based

on the information provided by Broadcast .

Simulation Analysis of Evacuation Guidance Using Dynamic Distributed Signage

183

4.1 Broadcast

Broadcast collects local information, including the

current pointing direction of node i and the edge

weights obtained from the connected sensors, and dis-

tributes them to all the adjacent nodes. Each node

repeatedly broadcasts this information throughout the

graph, and all the other nodes acquire them to con-

struct a local image of the global graph. We assume

that the times at which the nodes broadcast vary but

all the nodes ﬁnish broadcasting within a certain pe-

riod. At this point, all the nodes have local images

of the global graph

G = (V,

W ). We assume that

each node has local variables

W ,

T , and ∆i.

T is

an ordered list containing the last broadcast reception

times of all the nodes, and

T [i] presents the ith ele-

ment of the ordered list

T . It also has two other or-

dered lists: Ω

to hold the edge indices of

W and

2) ϒ

to maintain their corresponding values, which

contain the local edge weights collected by node i.

Broadcast at node i is presented in Algorithm 1,

where the originator node is indicated by o, the node

id is i, the current direction of the originator is δ(o),

and the time at which the originator sent the broadcast

is t. Broadcast is a simple ﬂooding algorithm that re-

quires 2|

E||V | − |V |

+|V | communications to update

the given value of universal evacuation graph.

4.2 UpdateSign

Algorithm 2: UpdateSign.

Local Variable:

W , δ(i)

1 Function UpdateSign(i):

2 l

∗

← Search(i,

W );

3 (i, next) ← l

∗

[1];

E[i] ← (i, next);

5 if

E include a cycle then

6 call UpdateSign(next) on next;

7 await

E ← UpdateSign(next) from

8 end

9 δ(i) ←

E[i];

10 return

11 end

Given a set of weights

W (t) at any point in time t,

our algorithm generated a series of efﬁcient evacua-

tion graphs and converged to the minimum efﬁcient

evacuation graph as below.

→

→ . . . → G

∗

where T PW (

) ≥ T PW (

n+1

)

→

n+1

demonstrates that by executing the al-

gorithm, node i in

pointing to node j changes its

pointing direction to another node

j, resulting in the

transformation of

into

n+1

, which is also an efﬁ-

cient evacuation graph.

In reality, each node executes its algorithm at dif-

ferent times and the local image varies from node-

to-node because

W represents an evacuation environ-

ment, which is dynamic. UpdateSign at each node

searches for the evacuation routes with a minimum

TPW for different graphs, resulting in inconsistent

evacuation routes which may include cycles. There-

fore, UpdateSign requires a mechanism to break the

cycles when it ﬁnds cycles on the evacuation graph.

Subsequently, we consider the case in which node

i ∈ T

G = {T

, T

} (Lemma 1) changes its point-

ing direction to the other nodes step-by-step. Edge

(i, j) is removed from

G (STEP 1) and a new edge

(i,

j) is added to the resulting graph (STEP 2).

After STEP 1, because the tree has minimal con-

nectivity, T

is split into two trees: T

, which ex-

cludes node i, and T

, which includes node i as its

root.

Theorem 1. A graph consisting of three trees was ob-

tained.

G = {T

, T

} after STEP 1.

By adding a new edge (i,

j) to

G in STEP 2, the

following theorem holds:

Theorem 2. When node i on T

changes its pointing

direction from j to

j, the resulting graph

new

is an

efﬁcient evacuation graph only if

j ∈ T

and

j ∈ T

Proof. In these three cases, a new edge (i,

j) is added

G = {T

, T

} (Theorem 1).

j ∈ T

. Both T

and T

are trees, and the resulting

graph

created by adding an edge from the root of

to any node of T

is also a tree. Therefore,

new

} is an efﬁcient evacuation graph.

j ∈ T

. Both T

and T

are trees and the resulting

graph

created by adding an edge (i,

j) is also a tree.

Therefore,

new

= {

, T

} is an efﬁcient evacuation

graph.

j ∈ T

j is any node on T

except i. One path

exists between i to

j on T

because it is a tree. Thus,

adding a new edge (i,

j) will form a cycle on T

Therefore, G

new

∈ {

G \

G} is not an efﬁcient evac-

uation graph.

Let l

i j

= ((i, i

), (i

, i

), . . . , (i

n−1

, j)) be a path

from node i to node j in graph G. The weight of path

i j

is denoted by weight(l

i j

), given by weight(l

i j

) =

∑

(i, j)∈l

i j

(i j)

, where w

(i j)

∈ W represents the weights

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

184

associated with the edges in W . The path with the

minimum weight is denoted as l

∗

i j

, and its weight as

∗

(i j)

= weight(l

∗

i j

). Let l

∗

, g ∈ V

represent the path

with the minimum TPW from node i to one of the

exits on graph G, and suppose we have a function

Search(i,

W ) that determines l

∗

in graph G with

W .

The distributed algorithm UpdateSign at node i

that converges to G

∗

is given by Algorithm 2. Local

Variable: in Algorithm 2 presents the local variables

available at node i. Node i executes U pdateSign(i)

on itself when it starts the algorithm, and

E returned

by the algorithm contains the updated routes with a

minimum TPW .

5 ANALYSIS

In this section, an analysis of the proposed algorithm

is presented under Assumption 1 assuming that W re-

mains unchanged.

Theorem 3. UpdateSign stops after a ﬁnite number

of steps.

Proof. Under Assupmtion 1, UpdateSign will only

stop if the next node in line 7 of Algorithm 2 does not

return. Suppose Search in line 2 ﬁnds path l

∗

ig1

with

a minimum TPW from node i to exit g1. This occurs

when a certain node j on l

∗

ig1

recursively calls node i

in line 6 of UpdateSign . There are two possible sce-

narios. First, node j ﬁnds the path from j to g1 such

that l

∗

jg1

= ( j, . . . , i, . . . , g1). w

∗

( j,g1)

= w

∗

( j,i)

+ w

∗

(i,g1)

because w

∗

( j,g1)

is a minimum. However, w

∗

(i,g1)

∗

(i, j)

∗

( j,g1)

= w

∗

(i, j)

∗

( j,i)

∗

(i,g1)

, which leads to

∗

(i,g1)

= 2w

∗

(i, j)

+ w

∗

(i,g1)

because w

(i, j)

= w

( j,i)

. This

contrasts with the deﬁnition w

(i, j)

> 0. Second, node

j ﬁnds the path with a minimum TPW from j to g2

such that l

∗

ig2

= ( j, . . . , i, . . . , g2), where g2 is the other

exit. Because l

∗

ig1

= (i, . . . , j, . . . , g1) has the minimum

TPW , w

∗

(i,g1)

= w

∗

(i, j)

+ w

∗

( j,g1)

≤ w

∗

(i,g2)

. However,

node j also has path l

∗

jg2

with a minimum TPW w

∗

( j,g2)

which includes node i; therefore, w

∗

( j,g2)

= w

∗

( j,i)

(i,g2)

≤ w

∗

( j,g1)

. Now, w

∗

(i, j)

+ w

∗

( j,g1)

≤ w

∗

( j,g1)

−

∗

( j,i)

, which leads to w

∗

(i, j)

+ w

∗

( j,i)

≤ 0. This is con-

trary to the deﬁnition w

(i, j)

> 0. Thus, line 7 of Algo-

rithm 2 must return.

Theorem 4. UpdateSign always generates efﬁcient

evacuation graphs.

Proof. Theorem 2 indicates that

E is not an efﬁcient

evacuation graph only if node i points to node j such

that j ∈ T

. However, in this case, line 5 of Al-

gorithm 2 ensures that

E passes recursively to Up-

dateSign on the adjacent node. Theorem 3 indicates

that this recursive call stops after a ﬁnite number of

steps, and

E returns to line 7 in Algorithm 2 and

does not include l

∗

that recursively contains i. Thus,

UpdateSign always generates an efﬁcient evacuation

graph.

Consider a system S in which each evacuation sign

has an UpdateSign and executes it randomly.

Theorem 5. System S generates a series converging

on minimum efﬁcient evacuation graph such that

→

→ . . . → G

∗

where T PW (

) ≥ T PW (

n+1

)

Proof. Consider that node i on T

old

G executes

UpdateSign . We have

G = {T

old

, T

old

, T

} (Theo-

rem 1) and let T

new

be a new tree having node i after

executing UpdateSign . T

new

is generated using the

method given in Cases 1 and 2 in the proof of Theo-

rem 2. First,

j ∈ T

. Let the exits before and after Up-

dateSign be g and ´g, respectively, which differ from

one another. T PW (T

old

(i, g)) ≥ T PW (T

new

(i, ´g)) be-

cause Search in line 2 of UpdateSign determines the

path with the minimum TPW . As both T

old

and T

remain unchanged, and T

old

is a tree with root i, the

following relationships hold for all the nodes k in T

old

except i:

T PW (T

new

(k, ´g))

= TPW (T

new

(k, i)) + T PW (T

new

(i, ´g))

≤ TPW (T

new

(k, i)) + T PW (T

old

(i, g))

= TPW (T

old

(k, i)) + T PW (T

old

(i, g))

= TPW (T

old

(k, g)).

Second,

j ∈ T

old

. In this case, exit g remains un-

changed. T PW (T

old

(i, g)) ≥ T PW(T

new

(i, g)), and

old

and T

also remain unchanged, yielding in the

same manner T PW (T

old

( j, g)) ≥ T PW (T

new

( j, g)).

Therefore, T PW (

old

) ≥ T PW (

new

). Furthermore,

Theorem 4 yields that UpdateSign always generates

efﬁcient evacuation graph, and the series above is ob-

tained.

Theorem 6. UpdateSign is self-stabilizing.

Proof. Suppose that system S begins from an initial

graph with cycles G

init

∈ {

G \

G}. At a certain point,

node i executes UpdateSign in a cycle. Search in line

2 of Algorithm 2 will ﬁnd a path to an exit l

∗

; subse-

quently, line 5 of the algorithm ﬁnds where i denotes

the cycle. It recursively calls UpdateSign on the next

node of l

∗

in line 6. However, this recursive call ter-

minates in a ﬁnite number of steps according to The-

orem 3. At this point, a cycle must be broken owing

Simulation Analysis of Evacuation Guidance Using Dynamic Distributed Signage

185

Figure 5: Mitigating Congestions.

Table 1: Mean evacuation time in Fig. 5.

Scenario 200 400 600 800

23&24 dynamic 117.8 172.0 233.6 290.6

static 116.2 198.1 272.7 345.5

23 dynamic 164.3 238.0 322.3 410.9

static 152.2 251.5 361.4 468.5

24 dynamic 178.8 275.3 377.0 473.0

static 170.4 277.4 384.4 501.2

to Theorem 4; a series from G

init

G is formed. The-

orem 5 ensures that the series never forms a cycle and

generates only efﬁcient evacuation graphs. Thus, Up-

dateSign is self-stabilizing.

The evacuation environment is constantly chang-

ing and evacuees always move to different locations;

thus, W is constantly changing information and it is

usually not possible to obtain a minimum efﬁcient

evacuation graph. Despite considering these facts,

Theorem 4 ensures that UpdateSign always generates

efﬁcient evacuation graphs.

Corollary 2. System S generates a series of efﬁcient

evacuation graphs, despite W being dynamical.

6 EXPERIMENT

Thus far, we have treated E and W as static informa-

tion for simplicity, whereas in real situations they are

dynamic. Both the evacuees and evacuation signs are

autonomous entities that affect one another, compli-

cating the prediction of the overall behavior of the

system, for example, the evacuation may never end

owing to oscillations caused by these two entities. In

this section, we treat E and W as dynamic informa-

tion and evaluate the performance of the dynamic dis-

tributed signage system using multi-agent simulations

(Wilensky, 1999) assimilating real evacuation situa-

tions.

6.1 Mitigating Congestion

Evacuation simulation experiments were conducted

to investigate the effectiveness of the dynamic sig-

nage system in reducing congestion during evacua-

Figure 6: Adapting the Evacuation Route.

Table 2: Mean evacuation time and ratio in Fig. 6.

Scenario 200 400 600 800

23 ratio 0.91 0.94 0.96 0.97

time 201.7 267.7 346.7 443.8

23&24 ratio 0.92 0.95 0.96 0.97

time 162.1 225.2 293.5 372.8

24 ratio 1.00 1.00 1.00 1.00

time 157.1 234.6 306.1 383.4

tions. We highlighted these results by comparing

them with those of a static signage system. To create

congestion during evacuation, evacuation agents were

initially placed in

⃝ and

⃝, as shown in Fig. 1(A);

⃝ and

⃝ were left empty. We also assumed w

{i, j}

d(n − 1) > 0, where d is the length of the edge {i, j}

and n is the number of agents currently on {i, j}.

To illustrate the effects of the dynamic signage

system, we use an agent with a simple random choice

model as follows:

1. When the agent is in the surrounding space, it will

randomly select doors that are visible from its lo-

cation, for example, if the agent is at

⃝, it will

randomly select doors 7–10.

2. When the agent is at a corner in the central core,

it will randomly select a direction, as indicated by

the blue arrows in Fig. 1(B), for example, if the

agent is at corner 12, it will randomly select di-

rections 11, 13, or 22.

3. If the agent is in the central core and there is an

evacuation sign in its ﬁeld of view, the agent will

follow the evacuation sign rather than make a ran-

dom selection.

The results of the three scenarios, including both

available, Exit 23 available, and Exit 24 available, are

shown in the left, center, and right diagrams in Fig. 5,

respectively, and are summarized in Table 1. In this

ﬁgure, the x-axis indicates the number of evacuation

agents, that is, 200, 400, 600, and 800; the y-axis rep-

resents the evacuation time. A total of 100 simula-

tions were conducted for each case. We plotted the

results for the static signage system in green, and the

dynamic signage system in blue.

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

186

6.2 Adapting the Evacuation Route

We also conducted experiments to investigate how the

dynamic signage system adapts evacuation routes to

dynamic environments. In this setting, Exit 23 was

initially the only available exit; however, the available

exit changed to Exit 24 when half of the evacuees ex-

ited. The evacuation graph possessed by each node

changes immediately at this point. We measured the

ratio of agents who evacuated via an available exit;

the agents evacuated via Exit 23 in the ﬁrst half of the

simulation and via Exit 24 in the second half. The

following two other variations of the scenario were

examined: 1) Both exits were initially available, fol-

lowed by Exit 24 being the only available exit. 2)

Exit 24 was initially the only exit available, followed

by both exits becoming available .

The results of the three scenarios are presented in

Fig. 6. The results of the scenarios in which Exits

23, 23&24, and 24 were initially available are shown

in the left, center, and right diagrams of Fig. 6 and the

means of these results are summarized in Table 2.

7 RESULT AND DISCUSSION

Fig. 5 reveals that by comparing the static (green) and

dynamic (blue) evacuation signs, the latter generally

provides a shorter evacuation time, as the blue plots

are below the green plots. However, when the num-

ber of evacuation agents is small (e.g., 200), the static

evacuation signs tend to provide shorter evacuation

times compared with the dynamic evacuation signs,

conﬁrming the effectiveness of the dynamic evacua-

tion signs when the number of evacuees is large and

congestion was anticipated. This suggests that dy-

namic evacuation signs may incur certain costs in

evacuation guidance, such as additional time owing

to collisions and confusion among the evacuees, re-

sulting in longer evacuation times.

Fig. 6 demonstrates that our algorithm could guide

approximately 90% of evacuees to the intended exits,

except when the number of evacuees was small (e.g.,

200). The ﬁgure demonstrates that as the number of

evacuees increases, the proportion of evacuees guided

to the intended exits increases. The diagram on the

right side of Fig. 6, where Exit 24 is ﬁrst available fol-

lowed by both Exits 23 and 24, indicates that nearly

100% of the evacuees were directed to the intended

exit when an available exit was initially limited, af-

ter which all the exits became available. This indi-

cates that unintended steering generally occurs imme-

diately after the available exit changes, which is ow-

ing to the change in the evacuation graph possessed

by each node. This is because it is easier to direct

more evacuees to available exits if the available exit is

initially restricted and the restriction is later removed,

as shown in the right diagram in Fig 6. Theorem 6

also ensures that our algorithm can continue to gener-

ate efﬁcient evacuation graphs despite the subsequent

turbulence caused by the change in efﬁcient evacua-

tion graphs.

In this study, we proposed a distributed algorithm

that provides efﬁcient evacuation guidance to miti-

gate congestion during evacuation and adapts evac-

uation routes based on the changes that occur in evac-

uation environments. One limitation of this algorithm

is that although it is decentralized, it is not fully asyn-

chronous. In actual distributed systems, each device

cannot predict whether the message it sends will be

received by the other device within a certain time, or

in the order in which they were sent. However, the de-

vice cannot predict that the task delegated to the other

device is completed, and whether the results for the

tasks are returned within a certain period. Line 7 of

Algorithm 2 assumes that the UpdateSign on the ad-

jacent node will be completed and its result will be

returned within a certain time, which is not guaran-

teed in real situations, leading to the termination of

the entire process. This is particularly critical if the

system contains faulty devices that are unable to re-

turn responses. Therefore, it is crucial to make this

algorithm asynchronous to address this problem and

analyze how the system performs in faulty environ-

ments.

Other important aspects such as human factors

were not investigated in this study. The human

decision-making process is more complex, mak-

ing evacuation behavior unpredictable, especially

wayﬁnding during evacuations (Lovreglio et al.,

2016; Vizzari et al., 2020; Andresen et al., 2018),

while we employed a simple agent model in the

simulations. Furthermore, the visual functions of

evacuees affect their ability to ﬁnd evacuation signs

(Ding, 2020; Tsurushima, 2021; Tsurushima, 2022b).

Whether people follow an evacuation sign when it

rapidly changes directions is also critical but it has

not been tested thus far. These topics should be inves-

tigated in future studies.

8 CONCLUSION

We proposed a distributed algorithm for a dynamic

evacuation guidance system to mitigate congestion

during evacuation and to advise evacuees on evac-

uation routes that are adaptable to environmental

changes. This system has no central control mech-

Simulation Analysis of Evacuation Guidance Using Dynamic Distributed Signage

187

anism, and the devices equipped with our algorithm

only use local information and communicate with

neighboring devices. Simulation results demonstrated

that the proposed algorithm can provide evacuation

guidance, resulting in a shorter evacuation time com-

pared with static evacuation guidance; furthermore,

approximately 90% of the evacuees were guided to

the intended routes despite the available exits chang-

ing during evacuation.

ACKNOWLEDGMENT

The author would like to thank Mr. Kei Marukawa for

his assistance and helpful discussions.

REFERENCES

Andresen, E., Chraibi, M., and Seyfried, A. (2018). A rep-

resentation of partial spatial knowledge: a cognitive

map approach for evacuation simulations. Transport-

metrica A: Transport Science, 14(5-6):433–467.

Baidal, C., Arreaga, N., and Padilla, V. (2020). Design

and testing of a dynamic reactive signage network to-

wards ﬁre emergency evacuations. International Jour-

nal of Electrical and Computer Engineering (IJECE),

10:5853.

Bernardini, G., Azzolini, M., D’Orazio, M., and

Quagliarini, E. (2016). Intelligent evacuation guid-

ance systems for improving ﬁre safety of Italian-

style historical theatres without altering their archi-

tectural characteristics. Journal of Cultural Heritage,

22:1006–1018.

Cisek, M. and Kapalka, M. (2014). Evacuation route assess-

ment model for optimization of evacuation in build-

ings with active dynamic signage system. Transporta-

tion Research Procedia, 2:541–549.

Ding, N. (2020). The effectiveness of evacuation signs in

buildings based on eye tracking experiment. Natural

Hazards, 103.

Galea, E., Xie, H., Deere, S., Cooney, D., and Filippidis, L.

(2017). Evaluating the effectiveness of an improved

active dynamic signage system using full scale evacu-

ation trials. Fire Safety Journal, 91.

Galea, R. E., Xie, H., and Lawrence, J. P. (2014). Experi-

mental and survey studies on the effectiveness of dy-

namic signage systems. Fire Safety Science, 11:1129–

1143.

Kasai, Y., Sasabe, M., and Kasahara, S. (2017). Congestion-

aware route selection in automatic evacuation guiding

based on cooperation between evacuees and their mo-

bile nodes. EURASIP Journal on Wireless Communi-

cations and Networking, 164.

Khalid, M. N. A. and Yusof, U. K. (2018). Dynamic crowd

evacuation approach for the emergency route planning

problem: Application to case studies. Safety Science,

102:263–274.

Li, M., Xu, C., Xu, Y., Ma, L., and Wei, Y. (2022). Dynamic

sign guidance optimization for crowd evacuation con-

sidering ﬂow equilibrium. Journal of Advanced Trans-

portation, 2022:2555350.

Lin, H.-M., Chen, S.-H., Kao, J., Lee, Y.-M., Lin, C.-

Y., and Hsiao, G. (2017). Applying active dynamic

signage system in complex underground construction.

International Journal of Scientiﬁc & Engineering Re-

search, 8.

Lovreglio, R., Fonzone, A., and dell’Olio, L. (2016). A

mixed logit model for predicting exit choice during

building evacuations. Transaportation Research Part

A: Policy and Practice, 92:59–75.

Lujak, M., Billhardt, H., Dunkel, J., Fern

andez, A., Her-

moso, R., and Ossowski, S. (2017). A distributed ar-

chitecture for real-time evacuation guidance in large

smart buildings. Computer Science and Information

Systems, 14:257–282.

Nguyen, V.-Q., Vu, H.-T., Nguyen, V.-H., and Kim, K.

(2022). A smart evacuation guidance system for large

buildings. Electronics, 11:2938.

Tsurushima, A. (2021). Simulation analysis of tunnel vision

effect in crowd evacuation. In Rutkowski, L., Scherer,

R., Korytkowski, M., Pedryca, W., Tadeusiewicz,

R., and Zurada, J. M., editors, Artiﬁcial Intelligence

and Soft Computing. ICAISC 2021. Lecture Notes in

Computer Science, volume 12854, pages 506–518.

Springer.

Tsurushima, A. (2022a). Efﬁcient crowd evacuation guid-

ance with multiple visual signage using a middle-

range agent model and black-box optimization. In

2022 IEEE International Conference on Systems,

Man, and Cybernetics (SMC), pages 2591–2598.

Tsurushima, A. (2022b). Tunnel vision hypothesis: Cogni-

tive factor affecting crowd evacuation decisions. SN

Computer Science, 3(332).

Vizzari, G., Crociani, L., and Bandini, S. (2020). An agent-

based model for plausible wayﬁnding in pedestrian

simulation. Engineering Applications of Artiﬁcial In-

telligence, 87:103241.

Wilensky, U. (1999). NetLogo. Center for Connected

Learning and Computer-Based Modeling, Northwest-

ern University, Evanston, IL.

Xue, Y., Wu, R., Liu, J., and Xianglong, T. (2021). Crowd

evacuation guidance based on combined action-space

deep reinforcement learning. Algorithms, 14(26).

Zhao, H., Schwabe, A., Schl

aﬂi, F., Thrash, T., Aguilar, L.,

Dubey, R., Karjalainen, J., H

olscher, C., Helbing, D.,

and Schinazi, V. (2022). Fire evacuation supported

by centralized and decentralized visual guidance sys-

tems. Safety Science, 145:105451.

Zu, Y. and Dai, R. (2017). Distributed path planning for

building evacuation guidance. Cyber-Physical Sys-

tems, 3(1-4):1–21.

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

188