M ODELING OF E VACUATION P LANNING O F B UILDING USING D YNAMIC E XITS By: Prachi Garg Roll No : ______________________________________ under the guidance of Prof. N. L. Sarda 1

O UTLINE  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 2

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. 3

O UTLINE  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

M ODELING OF B UILDING Combinatorial Data Model ex co Geometric Network Model ex co co 2 Corridor room1 room2 room3 room4 Exit 3D Building 5 Geometric Network Model ex co co 2 In most of the approaches a network is taken as a directed graph

H EURISTIC 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. 6

H EURISTIC 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 7

C APACITY C ONSTRAINED R OUTE 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. 8

C APACITY C ONSTRAINED R OUTE PLANNER 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 9

C APACITY C ONSTRAINED R OUTE PLANNER Pre-process network: add super source node s 0 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 with time schedule using one generalized shortest path search from super source s 0 to all destinations, (where s ∊ S,d ∊ D,n 0 =s, n k =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),t i )> 0, ∀ i ∊ {0,1,...,k-1}, and Available Node Capacity(n i+1,t i + 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 10

C APACITY C ONSTRAINED R OUTE PLANNER flow=min( number of evacuees still at source node s, Available Edge Capacity(e(n i,n i+1 ),t i ), ∀ i{0,1,...,k-1}, Available Node Capacity(n i+1,t i + 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),t i ) reduced by f low; (5) Available Node Capacity(n i+1,t i + Travel time( e (ni,ni+1) )) reduced by flow; (6) // Make reservation of capacity on route R }(7) }(8) Output evacuation plan;(9) 11

C APACITY C ONSTRAINED R OUTE PLANNER 12

O PTIMALITY ISSUES WITH C APACITY C ONSTRAINED R OUTE P LANNER CCRP produces results which is near to optimal but not optimal. For example: Example N6 N2N3N4N1 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: 5 10 Source 13

O UTLINE  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 14

M OTIVATION 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. 15

O UTLINE  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 16

E VACUATION P LANNING U SING D YNAMIC E XITS 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. 17

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. M ODELING OF BUILDING USING D YNAMIC E XITS 18

P ROBLEM 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 H EURISTIC APPROACH FOR D YNAMIC E XITS BASED E VACUATION P LANNING (HDEEP) 20

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. 21

1. Run CCRP on G and label each source s ∈ S, with the evacuation time ts of last evacuee. 22 HDEEP1 A LGORITHM //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. 23 HDEEP1 A LGORITHM 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's o But not t's → ts → people_count For each lp ∈ LP: o ts + t's + people_count 24 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. 25

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. 26

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. 27 HDEEP2 A LGORITHM 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: o dis → density o density → dis For each lp ∈ LP: o density+dis 28

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. 29

HDEEP1 AND HDEEP2 E XAMPLE 30

HDEEP1 – H1 Ladder(N ode) tssourcet’speople_countTime(max=34) L4(42) L7(39) L3(28) L9(37) L8(38) L1(45) L5(41) L2(44) L6(40) L10(36) (ts →t’s →people_count )

HDEEP1 – H2 Ladder(N ode) tssourcet’speople_countTime(max=34) L1(45) L4(42) L5(41) L3(28) L2(44) L7(39) L6(40) L9(37) L8(38) L10(36) ( people_count → ts →t’s )

HDEEP1 – H3 Ladder (Node) tssourcet’sp_cp_c+ts+t’sTime(max= 34) L4(42) L7(39) L3(28) L1(45) L5(41) L9(37) L2(44) L8(38) L6(40) L10(36) ( people_count + ts +t’s )

HDEEP2 – H1 NodedensitydistanceTime(max=34) ( density (2nd-neighbor) → dis )

HDEEP2 – H2 NodedensitydistanceTime(max=34) ( density (distance=10) → dis )

HDEEP2 – H3 Nodedensitydistancedensity+ distance Time(max=34 ) ( density (distance=10) + dis )

HDEEP2 – H4 Nodehf2Time(max=34)

E XPERIMENTAL R ESULT NetworkNumber of nodes Number of exits Number of Dynamic Exits Detail of the network is as follows: 38

H OW 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 Evacuation-time(in Sec.) V/s Number of Dynamic Exits Run-time(in Min.) V/s Number of Dynamic Exits

H OW 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 Evacuation-time(in Sec.) V/s Number of Source nodes Run-time(in Min.) V/s Number of Source nodes

A RE 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 Evacuation-time(in Sec.) V/s Number of Nodes Run-time(in Min.) V/s Number of Nodes

H OW DOES THE NUMBER OF LADDERS AFFECT THE PERFORMANCE OF BOTH APPROACHES ? 42 Evacuation-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 L IMITATIONS 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. 43

O UTLINE  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 44

C ONCLUSION 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. 45

O UTLINE  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 46

F UTURE 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. 47

O UTLINE  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 48

R EFERENCES Alka Bhushan and N. L. Sarda. Building Evacuation Planning Using Dynamic Exits, Submitted to European Journal of Operational Research, June Jiyeong Lee. A Spatial Access-Oriented Implementation of a 3-D GIS Topological Data Model for Urban Entities. In GeoInformatica 8:3, pages Kluwer Academic Publishers, 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 , H.W. Hamacher and S.A. Tjandra. Mathematical Modeling of Evacuation Problems:A state of the art. In Pedestrian and Evacuation Dynamics, pages Sangho Kim, Betsy George, and Shashi Shekhar. Evacuation route planning: Scalable Heuristics. In GIS, page 20,

T HANK Y OU 50