m odeling of e vacuation p lanning o f b uilding using d ynamic e xits by: prachi garg roll no :...

MODELING OF EVACUATION PLANNING OF BUILDING USING DYNAMIC EXITS

By:Prachi Garg

Roll No : 09305012______________________________________

under the guidance ofProf. N. L. Sarda

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OUTLINE Introduction Literature Survey• Modeling of a building

• Heuristics based method Motivation Evacuation Planning using dynamic Exits• Modeling of Building using Dynamic exits

• Heuristic approach for Dynamic Exits based Evacuation Planning(HDEEP)

Conclusion Future Scope References

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INTRODUCTION

Evacuation as an emergency process can be defined as removal of evacuees from a danger zone to safe place as quickly as possible.

One critical step during evacuation planning is to find the route and scheduled each evacuee.

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OUTLINE

Introduction Literature Survey• Modeling of a building• Heuristics based method

Motivation Evacuation Planning using dynamic Exits• Modeling of Building using Dynamic exits• Heuristic approach for Dynamic Exits based

Evacuation Planning(HDEEP) Conclusion Future Scope References 4

MODELING OF BUILDING

Corridorroom1

room2

room3

room4

Exit

3D Building 5

Geometric Network Model

ex

co1

1

2

3

4co2

In most of the approaches a network is taken as a directed graph

HEURISTIC BASED METHOD

These method do not always generate optimal solution but they have been able to reduce the computational cost dramatically.

A well-known approach is Capacity Constrained Route Planner(CCRP).

Some more faster heuristics were given such as Contraflow Network Recognition, Intelligent Load Reduction, Incremental Data Structure etc. These all heuristics are based on CCRP.

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HEURISTIC BASED METHOD Objective:

Minimize the total evacuation time Minimize the computational cost of producing the evacuation plan.

Input: Evacuation Network with non-negative integer capacity constraints on

nodes and edges, Travel time on edges, Initial capacities of the nodes.

Set of source nodes Set of destination nodes

Constraints: Edge travel time preserves FIFO properties, Limited amount of computer memory

Output: Evacuation plan consisting of routes

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CAPACITY CONSTRAINED ROUTE PLANNER

Finds solution which is near to optimal. Models capacity as time series, since available

capacity of a node and edge varies with time. Divides the evacuees into multiple groups and

assign a route and time schedule to each group.

Scheduling of groups is done by prioritizing according to group’s destination arrival time.

The quickest route is re-calculated in each iteration based on the available capacity.

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Symbols : G(N,E): A graph G with a set of nodes n∊N and a

set of edges e∊E. S: Set of Sources , S⊆N D: Set of Destinations D⊆N

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Pre-process network: add super source node s0 to network,

link s0 to each source nodes with an edge which

Maximum Edge Capacity() =∞ and Travel time() = 0; (0)

while any source node s ∊ S has evacuee do { (1)

find route R <n0,n1,...,nk> with time schedule <t0,t1,...,tk-1>

using one generalized shortest path search from super source s0 to all destinations,(where s∊S,d∊D,n0=s, nk=d)

such that R has the earliest destination arrival time among routes between all(s,d) pairs,

and Available Edge Capacity(e(ni,ni+1),ti)> 0, ∀i∊{0,1,...,k-1},

and Available Node Capacity(ni+1,ti + Travel time(e(ni,ni+1))) > 0, ∀i∊{0,1,...,k-1} (2)

//Find nearest pair (Source S, Destination D), based on current available capacity of nodes and edges

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flow=min( number of evacuees still at source node s,

Available Edge Capacity(e(ni,ni+1),ti), ∀i{0,1,...,k-1},

Available Node Capacity(ni+1,ti + Travel time(e(ni,ni+1))),∀i∊{0,1,...,k-1};

); (3)

//Compute available flow on shortest route R(S,D)

for i = 0 to k-1 do { (4)

Available Edge Capacity(e(ni,ni+1),ti) reduced by f low; (5)

Available Node Capacity(ni+1,ti + Travel time(e(ni,ni+1))) reduced by flow; (6)// Make reservation of capacity on route R

} (7)

} (8)

Output evacuation plan; (9)11


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OPTIMALITY ISSUES WITH CAPACITY CONSTRAINED ROUTE PLANNER

CCRP produces results which is near to optimal but not optimal. For example:

Example

N6

N2 N3 N4N1

N5

E1(5/2) E2(5/2) E3(5/2)

E5(5/4)

E4(5/4)

Edge: name(max_capacity/travel_time)

5

5

Total evacuees at t=6:510

Source

Source

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OUTLINE

Introduction Literature Survey• Modeling of a building




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MOTIVATION

Due to high degree of disaster or blockage of some exits, the evacuation plan obtained from existence models may not be acceptable due to large evacuation time.

ladders provide a simple and practical way of creating additional “dynamic exits” with the potential to significantly reducing the evacuation time.

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OUTLINE



Evacuation Planning(HDEEP) Conclusion Future Scope References 16

EVACUATION PLANNING USING DYNAMIC EXITS

Ladders can be utilized effectively when they are placed at appropriate places. Optimal placement of limited number of ladders is not possible without any systematic approach.

Two approaches are described here, HDEEP1 and HDEEP2 which places dynamic exits in the building graph at suitable places.

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Building is modeled as undirected graph. Capacity of ladder = 1 Dynamic exit points = non-destination nodes where

ladders can be place. A ladder is modeled as an edge, which connects a

dynamic exit point to a safe place. The travel time of a ladder = Function of height. Maximum Load represents the maximum number of

evacuees that can be present on the ladder at any point of time.

Load is different for ladder from for normal edges. CCRP is modified to consider difference between a normal

edge and a ladder edge.

MODELING OF BUILDING USING DYNAMIC EXITS

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PROBLEM DEFINITION Objective:

Minimize the total evacuation time Minimize the computational cost of producing the evacuation plan.

Input: Evacuation Network with non-negative integer capacity constraints

on nodes and edges, Travel time on edges, Initial capacities of the nodes.

Set of source nodes Set of destination nodes Set of dynamic exit points with load and travel time Number of ladders

Output: Evacuation plan consisting of routes, Suitable places for creating dynamic exits 19

Two approaches are described: HDEEP1 HDEEP2

Symbols : G(N,E): A graph G with a set of nodes n∊N and a set of

edges e∊E. S: Set of Sources , S⊆N D: Set of Destinations D⊆N P: Set of Dynamic exit points with load l and travel time t L: Number of ladders

HEURISTIC APPROACH FOR DYNAMIC EXITS BASED EVACUATION PLANNING(HDEEP)

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HDEEP1

This approach use the output of CCRP to find the suitable place.

Adds ladders at each dynamic exit point and run the modified CCRP algorithm.

Now iteratively removes the ladders which are used less.

Heuristic are used in order to remove the ladders.

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1. Run CCRP on G and label each source s ∈ S, with the evacuation time ts of last evacuee.

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HDEEP1 ALGORITHM

//ts is time of last evacuee with respect to source

2. Create |P| new nodes of label n + 1,..., n + |P|. Let LP be the array

of new nodes.

for i = 1 to |P|

u=P[i];

create edge(u,n+i) of capacity 1, load l travel time ti;

end loop

//Connect ladder to each dynamic exit point

3. Run modified CCRP on new graph G’ obtained from step 2. For each new destination node u ∈ LP, label u with

(a) t’s, which is the maximum evacuation time of last evacuee exiting from node u.

(b) the people_count i.e. number of person exiting from node u.

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HDEEP1 ALGORITHM

4. for i=1 to |LP|

calculate hf1(i).

5. Sort LP with respect to hf1.

6. Remove first |P|− L nodes (smallest) from LP.

7. Run modified CCRP with the new graph G".

//finding the value of t’s and people_count

//calculate the value of heuristic function and remove the ladder from the place whose hf1 value is small.

Heuristics function can be calculated in two ways:• For each lp ∈ LP:

o ts → t's → people_count o people_count → ts → t'so But not t's → ts → people_count

• For each lp∈LP:o ts + t's + people_count

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HDEEP1

HDEEP2

Ladders are added to those nodes which are farthest from its nearest destination.

Finds the shortest time and the density of the each dynamic exit node p ∈ P .

Adds a super destination node D_0 to each destination in order to reduce cost to find shortest time.

Heuristic are used in order to select dynamic exit point to add the ladders.

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HDEEP2

Density can be calculated as:• By adding initial capacities of node p and its

neighbours(1st-neighbour), 2nd -neighbour and so on.

• By adding initial capacities of neighbour up-to a certain distance.

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Pre-processing: Add one super destination node D_0 to each destination node d∈D, such that edge have travel_time=0 and node’s initial_Capacity(D_0)=0;

1. Run Shortest Path from D_0, until shortest distance of each dynamic exit point p∈P is computed.

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HDEEP2 ALGORITHM

2. for each p∈P { Run BFS(p) }

//Calculating the shortest distance from destination to each dynamic exit

3. calculate hf2 and Sort P with respect to hf2 in decreasing order.

4. Create new L nodes and connect them to first L node of |P| in

Graph G.

5. Now run modified CCRP with new graph G’.

//finding the density through BFS algorithm

//calculate the value of heuristic function and add the ladder from the place whose hf2 value is large.

HDEEP2

Heuristics function can be calculated in three ways:• For each lp ∈ LP:

odis → density odensity → dis

• For each lp∈LP:odensity+dis

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HDEEP2

• For each lp ∈ LP:hf2 = dis + ⌈density/maxCapacity⌉ + tl * ⌈density/ladderFlow⌉Where,

dis = shortest distance from the nearest destination,

maxCapacity = maximum capacity of the shortest path from the node to its nearest destination,

ladderFlow = number of evacuee which can go from the ladder in tl time,

tl = travel time of the ladder.

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HDEEP1 AND HDEEP2 EXAMPLE

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HDEEP1 – H1Ladder(Node)

ts source t’s people_count

Time(max=34)

L4(42) 24 33 29 8 29

L7(39) 25 23 31 10 30

L3(28) 27 22 33 9 30

L9(37) 27 22 33 12 30

L8(38) 28 21 33 12 30

L1(45) 29 31 34 7 31

L5(41) 29 31 34 8 32

L2(44) 29 31 34 9 32

L6(40) 29 31 34 11 33

L10(36) 29 31 34 13 34 31

(ts →t’s →people_count)


ts source t’s people_count

Time(max=34)

L1(45) 29 31 34 7 29

L4(42) 24 33 29 8 30

L5(41) 29 31 34 8 30

L3(28) 27 22 33 9 31

L2(44) 29 31 34 9 31

L7(39) 25 23 31 10 32

L6(40) 29 31 34 11 32

L9(37) 27 22 33 12 33

L8(38) 28 21 33 12 34

L10(36) 29 31 34 13 34 32

(people_count → ts →t’s)


ts source t’s p_c p_c+ts+t’s

Time(max=34)

L4(42) 24 33 29 8 61 29

L7(39) 25 23 31 10 66 30

L3(28) 27 22 33 9 69 30

L1(45) 29 31 34 7 70 30

L5(41) 29 31 34 8 71 31

L9(37) 27 22 33 12 72 32

L2(44) 29 31 34 9 72 32

L8(38) 28 21 33 12 73 32

L6(40) 29 31 34 11 74 33

L10(36) 29 31 34 13 76 34 33

(people_count + ts +t’s)

HDEEP2 – H1Node density distance Time(max=34)

38 34 23 33

43 33 14 33

44 33 12 32

42 32 16 32

45 31 10 32

37 29 26 31

41 27 17 31

39 22 21 30

40 13 19 30

36 9 28 2934

(density(2nd-neighbor)→ dis)

HDEEP2 – H2Node density distance Time(max=34)

39 194 21 33

43 181 14 33

40 178 19 32

42 178 16 32

41 177 17 31

38 167 23 31

44 142 12 31

37 141 26 30

36 129 28 30

45 97 10 2935

(density(distance=10)→ dis)

HDEEP2 – H3Node density distance density+

distanceTime(max=3

4)

39 194 21 215 33

40 178 19 197 33

43 181 14 195 32

41 177 17 194 32

42 178 16 194 31

38 167 23 190 31

37 141 26 167 31

36 129 28 157 30

44 142 12 154 30

45 97 10 107 29 36

(density(distance=10) + dis)

HDEEP2 – H4Node hf2 Time(max=34)

36 50 33

37 46 33

38 41 32

39 37 32

40 33 31

41 29 30

42 26 30

43 22 29

44 18 30

45 14 2937

EXPERIMENTAL RESULT

Network Number of nodes

Number of exits

Number of Dynamic

Exits

1 350 14 60

2 500 14 112

3 700 28 120

4 1000 28 224

Detail of the network is as follows:

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HOW DOES THE NUMBER OF DYNAMIC EXITS AFFECT THE PERFORMANCE OF BOTH APPROACHES?

Network size : 700 nodes; Number of ladders : 60;

Number of evacuees : 6000; Number of dynamic exits : from 30 to 120.

39Evacuation-time(in Sec.) V/s

Number of Dynamic ExitsRun-time(in Min.) V/s

Number of Dynamic Exits

HOW DOES THE NUMBER OF SOURCE NODE AFFECT THE PERFORMANCE OF BOTH APPROACHES?

Network size : 500 nodes; Number of ladders : 50;

Number of evacuees : 6000; Number of dynamic exits : 120;

Number of Source node : from 100 to 400.

40Evacuation-time(in Sec.) V/s

Number of Source nodesRun-time(in Min.) V/s

Number of Source nodes

ARE THE ALGORITHMS SCALABLE TO THE SIZE OF THE NETWORKS?

Number of Source nodes : 300 nodes; Number of ladders : 25;

Number of evacuees : 6000; Number of node : from 350 to 1000.

41Evacuation-time(in Sec.) V/sNumber of Nodes

Run-time(in Min.) V/sNumber of Nodes

HOW DOES THE NUMBER OF LADDERS AFFECT THE PERFORMANCE OF BOTH APPROACHES?

42Evacuation-time(in Sec.) V/s Number of Ladders

Network size : 500 nodes; Number of evacuees : 5000;

Number of dynamic exits : 112; Number of ladders : from 0 to 120.

HDEEP1 AND HDEEP2 LIMITATIONS

Assumes that one dynamic exit point can afford only one ladder but if window is wide then more ladders can be keep if available.

Can not reuse the ladder if not in use further. HDEEP1 is based on CCRP and it run the CCRP

almost thrice it takes more time for execution.

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CONCLUSION Due to high degree of disaster or blockage of some exits,

the evacuation plan obtained from existence models may not be acceptable due to large evacuation time.

Ladders provide a simple and practical way of creating additional “dynamic exits” with the potential to significantly reducing the evacuation time.

To find the places to create dynamic exits two approaches have been described: HDEEP1 and HDEEP2.

CCRP has been modified to consider the difference between a normal edge and ladder edge.

The experimental results on various building graphs show that the proposed heuristics reduce the evacuation time effectively with marginal increase in computational cost.

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FUTURE SCOPE

Approaches can be modified to add more ladders at wide windows

Can be modified to reuse the ladder if not in use further.

Results of these experiments are to be compared with optimal solution.

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OUTLINE



Evacuation Planning(HDEEP) Conclusion Future Scope References

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REFERENCES

Alka Bhushan and N. L. Sarda. Building Evacuation Planning Using Dynamic Exits, Submitted to European Journal of Operational Research, June 2011.

Jiyeong Lee. A Spatial Access-Oriented Implementation of a 3-D GIS Topological Data Model for Urban Entities. In GeoInformatica 8:3, pages 237-264. Kluwer Academic Publishers, 2004.

Jiyeong Lee. 3D Data Model for Representing Topological Relations of Urban Features. Delaware County Regional Planning Commission.

Qingsong Lu, Betsy George, and Shashi Shekhar. Capacity Constrained Routing Algorithms for Evacuation Planning:A Summary of Results. In SSTD, pages 291-307, 2005.

H.W. Hamacher and S.A. Tjandra. Mathematical Modeling of Evacuation Problems:A state of the art. In Pedestrian and Evacuation Dynamics, pages 227-266. 2002.

Sangho Kim, Betsy George, and Shashi Shekhar. Evacuation route planning: Scalable Heuristics. In GIS, page 20, 2007. 49

THANK YOU

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m odeling of e vacuation p lanning o f b uilding using d ynamic e xits by: prachi garg roll no :...

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