Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

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1 Estimating scalability issues while finding an optimal assignment for carpooling Luk Knapen Universiteit Hasselt IMOB July 17, 2013 Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

2 Basic Idea - Concepts Application Area : Evaluation of Carpooling Advisor Software 1 Commuting, periodic trip execution 2 Provide global matcher service 3 Matcher shall advise so that carpooling negotiation success is maximal 4 Feedback from negotiation is used to train the advisor Hypotheses 1 Sufficient business model so that people provide feedback 1 about negotiation result 2 mutual qualifications (reputation) 2 Single driver constraint : route for each passenger is embedded in the driver s route 3 No carpool parkings considered Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

3 Basic Idea - Concepts Agent based model used to support matcher software evaluation 1 critical mass of users required 2 performance and effectiveness 3 investigate transient effects at startup Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

4 Basic Idea - Concepts Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

5 Determining carpool negotiation probablity Negotiation success is determined using similarities Profile similarity (Person,Person) attribute Safety reputation Person attribute Path similarity (Trip,Trip) attribute Cohesion Pool attribute Time Interval similarity (Person,Person,Trip) attribute Timeliness reputation (Person,Trip) attribute Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

6 Determining carpool negotiation probablity Functions Used Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

7 Determining carpool negotiation probablity Profile similarity 1 Consists of factors relevant for homophily Socio-economic class discrete, ordered Age discrete, ordered Gender discrete, categorical 2 Motivation : limit number of inputs to logit estimator { 1 if v0 = v s cat (v 0,v 1 ) = 1 0 else s ord (v 0,v 1 ) = 1 v 0 v 1 range profsim = i (1) (2) s i w i (3) Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

8 Determining carpool negotiation probablity Path similarity 1 TAZ (Traffic Analysis Zone) based 2 Not symmetric 3 Compares carpooled and solo paths for driver pathsim = d(o A,D A ) d(o A,O B )+d(o B,D B )+d(d B,D A ) (4) Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

9 Determining carpool negotiation probablity Time Interval Compatibility Estimating scalability issues while finding an optimal assignmentjuly for 17, carpooling / 24

10 Determining carpool negotiation probablity Time Interval Similarity based on common periods to start/finish trip d(l) = dur(w(i,l) W(j,L)) (5) tis(t A,T B,L) = 1 e α d(l) (6) tis(t A,T B ) = min(tis(t A,T B,Orig(B),tis(T A,T B,Dest(B))) (7) Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

11 Determining carpool negotiation probablity Estimating negotiation success probability Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

12 Periodic Trip to Vehicle Assignment Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

13 Periodic Trip to Vehicle Assignment Linear problem statement for assignment i,j [0,N 1] : x i,j 1 (8) i [0,N 1] : x i,j = 1 (9) j [0,N 1] : i [0,N 1] j [0,N 1] x i,j cap(v j ) (10) i,j [0,N 1],i j : x i,j x i,i 0 (11) i identifies trip Eqn(1) x i,j are boolean j identifies vehicle Eqn(2) Each trip assigned to one vehicle N number of persons Eqn(3) Vehicle capacity is limited Eqn(4) Car owner shall drive Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

14 Periodic Trip to Vehicle Assignment Problem size can become a problem 1 Problem size is large (Flanders : 6e6 people, 2.5e6 commuters) 2 20% randomly (uniform) selected persons are assumed to show interest for carpooling 3 Dynamic 1 Links are deleted and added by (de)registration 2 Link weights evolve over time (by changing reputation and cohesion) 4 Matrix is sparse 5 Integer programming problem 6 Try to find solution starting from previous one Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

15 Periodic Trip to Vehicle Assignment The assignment problem is a star cover problem Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

16 Graph Characteristics nedges nvertices Probab. nvertices nedges completeness ncomps Threshold E E E E E E E E E E Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

17 Graph Characteristics Component size frequency...misleading : see next slide Number of components Prob=0.725 Prob=0.750 Prob=0.775 Prob=0.800 Prob=0.825 Prob=0.850 Prob=0.875 Prob=0.900 Prob=0.925 Prob=0.950 Prob= Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

18 Graph Characteristics Eight largest components in each graph Prob cs1 cs2 cs3 cs4 cs5 cs6 cs7 cs Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

19 Graph Characteristics : Trivial Stars Prob ncomp ntrivial Size Size Size Threshold stars Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

20 Graph Characteristics : Node Degrees Vertex InDegree Frequency Distribution Number of vertices Prob=0.760 Prob=0.770 Prob=0.780 Prob=0.790 Prob=0.800 Prob=0.810 Prob=0.820 Prob=0.830 Prob=0.840 Prob=0.850 Prob=0.860 Prob=0.870 Prob=0.880 Prob=0.890 Prob=0.900 Prob=0.910 Prob=0.920 Prob=0.930 Prob=0.940 Prob=0.950 Prob= Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

21 Graph Characteristics : Node Degrees Vertex OutDegree Frequency Distribution Number of vertices Prob=0.760 Prob=0.770 Prob=0.780 Prob=0.790 Prob=0.800 Prob=0.810 Prob=0.820 Prob=0.830 Prob=0.840 Prob=0.850 Prob=0.860 Prob=0.870 Prob=0.880 Prob=0.890 Prob=0.900 Prob=0.910 Prob=0.920 Prob=0.930 Prob=0.940 Prob=0.950 Prob= Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

22 Graph Characteristics : Connected Components Number of Components Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

23 Graph Characteristics : Connected Components Largest Component Size Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24

24 Conclusions 1 Problem size causes non-trivial issues 2 Partitioning is easy 3 From threshold 0.85 on, grid computing is useful 4 Allocate tasks to processors in decreasing size order (load balancing) Estimating scalability issues while finding an optimal assignment July for17, carpooling / 24