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    Janoska in dog Janoska in dog Presentation Transcript

    • P Systems for Passenger Flow Simulation P Systems for Passenger Flow Simulation Zbynˇk Janoˇka e s Department of Geoinformatics, Palack´ University in Olomouc y October 30, 2012
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction ◮ Computational model from the family of natural computing ◮ Inspired by the living cell ◮ its structure ◮ its functionality ◮ Gheorghe P˘un (1998) - Computing with membranes a ◮ Research concerned with computational power, not biological modelling ◮ No application to spatial phenomena (so far)
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Main components of P systems ◮ membrane structure ◮ objects ◮ rules Basic features ◮ maximal paralelism ◮ non-determinism
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Step 1 ◮ environment – # ◮ membrane 1 – # ◮ membrane 2 – # ◮ membrane 3 – ac ◮ a → ab ◮ a → bδ ◮ c → cc ac → abcc
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Step 2 ◮ environment – # ◮ membrane 1 – # ◮ membrane 2 – # ◮ membrane 3 – abcc ◮ a → ab ◮ a → bδ ◮ c → cc abcc → bbccccδ
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Step 3 ◮ environment – # ◮ membrane 1 – # ◮ membrane 2 – bbcccc ◮ b→d ◮ d → de ◮ (cc → c) > (c → δ) bbcccc → ddcc ◮ membrane 3 – dissolved
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Step 4 ◮ environment – # ◮ membrane 1 – # ◮ membrane 2 – ddcc ◮ b→d ◮ d → de ◮ (cc → c) > (c → δ) ddcc → ddcee ◮ membrane 3 – dissolved
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Step 5 ◮ environment – # ◮ membrane 1 – # ◮ membrane 2 – ddcee ◮ b→d ◮ d → de ◮ (cc → c)4 > (c → δ) ddcee → ddeeeeδ ◮ membrane 3 – dissolved
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Step 6 ◮ environment – # ◮ membrane 1 – ddeeee ◮ e → eOUT [ddeeee]1 → [dd]1 [eeee]ENV ◮ membrane 2 – dissolved ◮ membrane 3 – dissolved
    • P Systems for Passenger Flow Simulation IntroductionP systems – Introduction Final configuration [dd]1 [eeee]ENV Calculation succesfull – no other rule can be applied
    • P Systems for Passenger Flow Simulation Transportation modellingTransportation modelling Three levels of traffic flow models (Hoogendoorn & Bovy, 2001) ◮ microsimulation ◮ mesosimulation ◮ macrosimulation Public transportation models – meso-models – detailed passenger flow simulation, vehicle modelling omitted (Peeta & Ziliaskopoulos, 2001)
    • P Systems for Passenger Flow Simulation Proposed modelInformal description ◮ tram stops – membranes ◮ road network – graph topology ◮ trams – membranes ◮ passengers – objects ◮ behaviour – rules ◮ passengers getting on and off the tram ◮ tram moving between stops ◮ passenger decisions
    • P Systems for Passenger Flow Simulation Proposed modelFormal description Rules describing passengers getting on and off the tram ◮ [tram empty ]− people → [tram people ]tram tram − p1 ≤1 ◮ [tram people ]− − → [tram empty ]− people OUT tram − − tram p2 ≤1 ◮ [tram people ]− − → [tram people ]− tram − − tram
    • P Systems for Passenger Flow Simulation Proposed modelFormal description Rules describing movement of the trams t≥1 ◮ [i [tram ]+ @j ]i − → [j [tram ]− ]j tram − tram ◮ [i [tram ]− ]i → [i [tram ]+ ]i tram tram
    • P Systems for Passenger Flow Simulation Proposed modelFormal description Rules describing passenger arrival and departure from tram stops ◮ [i ]i → [i people ∗ N ]i ◮ [i people OUT ]i → [i ]i
    • P Systems for Passenger Flow Simulation Proposed modelParameters of the model ◮ topology of the network ◮ number of vehicles, their schedule ◮ capacity of vehicles ◮ number of passengers using the system ◮ probabilities of passengers getting off the tram
    • P Systems for Passenger Flow Simulation Experimental results Model 1Experimental results - model 1 ◮ topology of the network – circular ◮ number of vehicles, their schedule – 3 trams, 5 mins between stops ◮ capacity of vehicles - 55 passengers ◮ number of passengers using the system – Poisson dist. with λ = 3 ◮ probabilities of passengers getting off the tram – 0.50, 0.55, 0.60
    • P Systems for Passenger Flow Simulation Experimental results Model 1Experimental results – probability 0.50 passengers waiting at the stop 250 200 passengers 150 100 50 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 1Experimental results – probability 0.50 empty spaces in tram 50 40 30 empty spaces 20 10 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 1Experimental results – probability 0.55 passengers waiting at the stop 80 60 passengers 40 20 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 1Experimental results – probability 0.55 empty spaces in tram 50 40 empty spaces 30 20 10 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 1Experimental results – probability 0.60 passengers waiting at the stop 50 40 30 passengers 20 10 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 1Experimental results – probability 0.60 empty spaces in tram 50 40 30 empty spaces 20 10 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 2Experimental results - model 2 ◮ topology of the network – line ◮ number of vehicles, their schedule – 2 trams, 5 mins between stops ◮ capacity of vehicles - 55 passengers ◮ number of passengers using the system – Poisson dist. with λ = 3 ◮ probability of passengers getting off the tram – 0.95
    • P Systems for Passenger Flow Simulation Experimental results Model 2Experimental results – stop 1 passengers waiting at the stop 1200 1000 800 passengers 600 400 200 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 2Experimental results – stop 2 passengers waiting at the stop 80 60 passengers 40 20 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 2Experimental results – stop 3 passengers waiting at the stop 70 60 50 40 passengers 30 20 10 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Experimental results Model 2Experimental results – empty spaces empty spaces in tram 50 40 30 empty spaces 20 10 0 0 200 400 600 800 1000 time units
    • P Systems for Passenger Flow Simulation Future workFuture and related work Future work ◮ P systems for vehicular Related work flow simulation ◮ Population dynamics ◮ Dvorsk´ et al, 2012 – y modelling using P systems first ideas, XML specification, software ◮ superior for small ◮ real data aquisition - populations Bˇeclav city r ◮ previous research (population 25 000, 5 available traffic lights) ◮ experimental results ◮ Background model for proven usefull traffic optimisation
    • P Systems for Passenger Flow Simulation ConclusionConclusion ◮ P systems are computational models inspired by the living cell ◮ Enable hierarchical representation of modelled system, behavior is ruled by ’chemical equations’ ◮ Expressive and efficient ◮ Simple to extend existing models
    • P Systems for Passenger Flow Simulation ConclusionConclusion Drawbacks of proposed model Advantages of proposed model ◮ objects are not inteligent ◮ discrete representation of ◮ can not incorporate vehicles, passengers representation of world by ◮ expressive the means of physical laws ◮ easy to extend ◮ detail of the model is limited
    • P Systems for Passenger Flow Simulation Bibliography [Dvorsk´ et al, 2012] J. Dvorsk´, Z. Janoˇka & L. Voj´ˇek. y y s ac P systems for traffic flow simulation, Lecture Notes in Computer Science Volume 7564,, 2012. [Hoogendoorn & Bovy, 2001] S.P. Hoogendoorn & P.H.L. Bovy. State-of-the-art of vehicular traffic flow modelling, Delft University of Technology, Delft,, 2001. [P˘un, 1998] Gh. P˘un. a a Computing with membranes, TUCS Report 208, Turku Center for Computer Science, 2000. [P˘un, 2004] Gh. P˘un. a a Introduction to membrane computing,
    • P Systems for Passenger Flow Simulation Bibliography First brainstorming Workshop on Uncertainty in Membrane Computing, 2004. [Peeta & Ziliaskopoulos, 2001] S. Peeta & A. Ziliaskopoulos Foundations of dynamic traffic assignment: The past, the present and the future, Networks and Spatial Economics, 2001. [P systems web page] http://ppage.psystems.eu/