Evacuation Planning with Path Coordination at Junction

By: Virendra Kumar

Outline

• Introduction• Issues in CCRP• Requirement in CCRP (Modified CCRP)• Approach• Implementation• Comparison between CCRP and Modified

CCRP• Conclusions

Introduction

• What is Intersecting Path?? Lets take an example of 4-way junction

N1, N2: source nodes

N3, N4: Destination nodes

V: Junction Node

Let P1= N1-V-N3, P2= N2-V-N4, P3= N1-V-N3 and P4= N2-V- N3, Here P1 and P2 are intersecting path while P3 and P4 are not intersecting path.

V

N2

N3

N4

N1

• If at Junction all the signal is green at same time then collision can happen.

• We are using CCRP algorithm for Evacuation Planning.

• Can CCRP algorithm give intersecting path??• Answer is yes. Means collision can be possible

in CCRP.

Issues in CCRP

• Intersecting Path can arise• Frequently Signal changing occurs at junction• Evacuees are considered as of same natures• Initial Edge traffic is assumed zero• Traffic from source to destination only

Why Intersecting Path can arise??

• Because CCRP doesn’t say about Geometry of edges.

Requirement in CCRP(Modified CCRP)

• Intersecting path should not occur.• Minimization of signal changing• Outside to inside traffic should also allow (for

Ambulance, Fire Extinguisher etc.)• Two type of evacuees: Medical (Injured) and

General should be considered.• Initial edge traffic should be taken into

account.

Approach

• Take Geometry of edges into account.• New input data is required: Latitude and

Longitude value of each Junction node.• Ambulance and Fire Extinguisher information is also

needed in form of:-– n = No. of ambulance/Fire extinguisher.

– Ne = No. of evacuees equivalent to per Ambulance.

Approach

– K = .– Ni = Destination node from which ambulance will

start to go for source node.– t = time when ambulance will start from

destination node.– td = time taken to take injured people in

ambulance.

Approach

• More priority to injured people means more priority to ambulance.

• For Ambulance give maximum priority to sources which has more injured people and priority should be dynamically changing.

Implementation

• Clockwise Listing of arcs at every Junction• How to use above geometry??• To use this we have to store parent(previous)

node as an array of a node.• If from more than one parent node, cost is

same and minimum for a node then store all the parent nodes for that node.

• Changes required in Dijkstra Algorithm also.

N1 N4

N3N2

Nn

v

e2 e3

e1 e4

en

Let us take an example of N-way junction:-

• Each edge is bidirectional.• Junction node v is defined by a list of edges e1,

e2 ….. en where ei‘s are listed in clockwise direction.

• For each arc ei : (n-1) paths are possible-

Like ei to ei+1, ei to ei+2,….., ei to ei-1 (in case of i=1, i-1 will be n).

• Associate one signal light with each possible path for each edge Like for path ei to ej signal light is Lij.

n1 L12

L1n

L11

e1

en

e2

In this figure it is shown how signal light is associated with edge e1

• Make a L–Matrix (Compatible direction matrix) which will keep information as which Lij is green, idle and red.

Like, Lij = 0, no traffic; = 1, go from ei to ej;

= -1, not permitted to go from ei to ej.

• And L-Matrix can be represented as-

L11 L12 . . . . . . . . . . . . . . L1n

L21 L22 . . . . . . . . . . . . . . L2n

L =

Ln1 Ln2 . . . . . . . . . . . . . . Lnn

where ,

Lij–indicates from edge ei to edge ej

Let us take an example of consistent L-Matrix let n=4,

-1 1 0 1 L = -1 -1 -1 -1

-1 0 -1 0-1 -1 -1 -1

Compatibility Issue

• Any edge should not be used in both direction at same time.

Dijkstra Algorithm take care of this. • At any same time instance two paths should

not intersect.

When and How intersecting Path arises ??

• when any edge ei does not select its next clockwise edge or its last clockwise edge (next anticlockwise edge) then intersecting path might arise.

• If possible then select nearest clockwise or, anti clockwise edge in the path at junction.

• Does it guarantee that on taking nearest cw or acw will never arise intersecting path??

• Answer is NO.• How it arises and can be avoided??

Whenever any edge ei selects ej (where j ≠ i+1 or, j ≠ i-1) then if any edge ek (for k= i+1 to j-1), selects edge em (for m=j+1 to i-1) to go from junction at same time, then intersecting path arises.

• It can be expressed in terms of compatibility – ei .Lij ≠ ek .Lkm for k= i+1 to j-1 and m=j+1 to i-1;

----(1) ei .Lij ≠ em .Lmk for k= i+1 to j-1 and m=j+1 to i-1;

----(2)• To avoid intersecting path, update L-Matrix

according to equation (1) and (2) with time instance.

Comparison between CCRP and Modified CCRP

• Both Earlier CCRP and Modified CCRP Algorithm are suboptimal.

• They can differ in Egress Time and Average Evacuation time or can not, that depend on given scenarios of road network.

• Let us take some examples and compare the outputs given by CCRP and Modified CCRP.

Results

• Modified algorithm of CCRP never give intersecting paths.

• Average Evacuation time and egress time can remain same, increase or decrease depend on given scenarios of road network.

• Frequently signal changing decrease in Modified CCRP.

Conclusions

• When we use CCRP while taking Geometry into account then intersecting path can be avoided and frequently signal changing can be reduced.

Bibliography

• Shekhar, Q. L. (2005). Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results. Proc. of 9th International Symposium on Spatial and Temporal Databases (SSTD’05), (pp. 22-24).

Thank You.----------------------------