Modeling of Evacuation Planning Of Building using Dynamic Exits

1. Modeling of Evacuation Planning Of Building using Dynamic Exits By: Prachi Garg Roll No : 09305012 ______________________________________ under the guidance of Prof. N. L. Sarda

2. 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

3. 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.

4. 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

5. Modeling of Building ex 3 co1 1 ex ex Exit Corridor 4 co2 2 3 1 3 co1 1 room3 room1 co Geometric Network Model room4 room2 4 4 co2 2 2 3D Building Combinatorial Data Model Geometric Network Model In most of the approaches a network is taken as a directed graph

6. 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.

7. 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

8. 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.

9. Capacity Constrained Route 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

10. //Find nearest pair (Source S, Destination D), based on current available capacity of nodes and edges Capacity Constrained Route planner 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)

11. //Compute available flow on shortest route R(S,D) Capacity Constrained Route planner 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) 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)

12. Capacity Constrained Route planner

13. Optimality issues with Capacity Constrained Route Planner CCRP produces results which is near to optimal but not optimal. For example: Source N6 Edge: name(max_capacity/travel_time) 5 E4(5/4) Source N1 N2 N3 N4 E2(5/2) E3(5/2) E1(5/2) 5 E5(5/4) 5 Total evacuees at t=6: 10 N5 Example

14. 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

15. 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.

16. 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

17. 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.

18. Modeling of building using Dynamic Exits • 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.

19. 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

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

21. 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.

22. HDEEP1 Algorithm 1. Run CCRP on G and label each source s ∈ S, with the evacuation time ts of last evacuee. //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

23. HDEEP1 Algorithm 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. //finding the value of t’s and people_count 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". //calculate the value of heuristic function and remove the ladder from the place whose hf1 value is small.

24. HDEEP1 • Heuristics function can be calculated in two ways: • For each lp ∈ LP: • ts→t's→people_count • people_count→ ts→ t's • But nott's→ts→people_count • For each lp∈LP: • ts + t's + people_count

25. 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.

26. 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.

27. HDEEP2 Algorithm 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. //Calculating the shortest distance from destination to each dynamic exit 2. for each p∈P { Run BFS(p) } //finding the density through BFS algorithm 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’. //calculate the value of heuristic function and add the ladder from the place whose hf2 value is large.

28. HDEEP2 • Heuristics function can be calculated in three ways: • For each lp ∈ LP: • dis → density • density → dis • For each lp∈LP: • density+dis

29. HDEEP2 • For eachlp ∈ 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.

30. HDEEP1 and HDEEP2 Example

31. HDEEP1 – H1 (ts →t’s →people_count)

32. HDEEP1 – H2 (people_count→ ts →t’s)

33. HDEEP1 – H3 (people_count+ ts +t’s)

34. HDEEP2 – H1 (density(2nd-neighbor)→ dis)

35. HDEEP2 – H2 (density(distance=10)→ dis)

36. HDEEP2 – H3 (density(distance=10) + dis)

37. HDEEP2 – H4

38. Experimental Result Detail of the network is as follows:

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

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

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

42. How does the number of ladders affect the performance of both approaches? Network size : 500 nodes; Number of evacuees : 5000; Number of dynamic exits : 112; Number of ladders : from 0 to 120. Evacuation-time(in Sec.) V/s Number of Ladders

43. 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.

44. 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

45. 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.

46. 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

47. 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.

48. 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

49. 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.

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