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P Systems for Passenger Flow Simulation
P Systems for Passenger Flow Simulation
Zbynek Janoska
Department of Geoinformatics, Palacky University in Olomouc
October 30, 2012
P Systems for Passenger Flow Simulation
Introduction
P systems – Introduction
◮ Computational model from the family of natural computing
◮ Inspired by the living cell
◮ its structure
◮ its functionality
◮ Gheorghe Paun (1998) - Computing with membranes
◮ Research concerned with computational power, not biological
modelling
◮ No application to spatial phenomena (so far)
P Systems for Passenger Flow Simulation
Introduction
P systems – Introduction
Main components of P systems◮ membrane structure
◮ objects
◮ rules
Basic features
◮ maximal paralelism
◮ non-determinism
P Systems for Passenger Flow Simulation
Introduction
P 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
Introduction
P 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
Introduction
P 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
Introduction
P 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
Introduction
P 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
Introduction
P 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
Introduction
P systems – Introduction
Final configuration
[dd]1 [eeee]ENV
Calculation succesfull – no other rule
can be applied
P Systems for Passenger Flow Simulation
Transportation modelling
Transportation 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 model
Informal 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 model
Formal description
Rules describing passengers getting on and off the tram
◮ [tram empty ]−tram people → [tram people ]−tram
◮ [tram people ]−tramp1≤1−−−→ [tram empty ]−tram peopleOUT
◮ [tram people ]−tramp2≤1−−−→ [tram people ]−tram
P Systems for Passenger Flow Simulation
Proposed model
Formal description
Rules describing movement of the trams
◮ [i [tram ]+tram@j ]it≥1−−→ [j [tram ]−tram ]j
◮ [i [tram ]−tram ]i → [i [tram ]+tram ]i
P Systems for Passenger Flow Simulation
Proposed model
Formal description
Rules describing passenger arrival and departure from tram stops
◮ [i ]i → [i people ∗ N ]i
◮ [i peopleOUT ]i → [i ]i
P Systems for Passenger Flow Simulation
Proposed model
Parameters 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 1
Experimental 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 1
Experimental results – probability 0.50
0 200 400 600 800 1000
050
100
150
200
250
passengers waiting at the stop
time units
pass
enge
rs
P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.50
0 200 400 600 800 1000
010
2030
4050
empty spaces in tram
time units
empt
y sp
aces
P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.55
0 200 400 600 800 1000
020
4060
80
passengers waiting at the stop
time units
pass
enge
rs
P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.55
0 200 400 600 800 1000
010
2030
4050
empty spaces in tram
time units
empt
y sp
aces
P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.60
0 200 400 600 800 1000
010
2030
4050
passengers waiting at the stop
time units
pass
enge
rs
P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.60
0 200 400 600 800 1000
010
2030
4050
empty spaces in tram
time units
empt
y sp
aces
P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental 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
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P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental results – stop 1
0 200 400 600 800 1000
020
040
060
080
010
0012
00
passengers waiting at the stop
time units
pass
enge
rs
P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental results – stop 2
0 200 400 600 800 1000
020
4060
80
passengers waiting at the stop
time units
pass
enge
rs
P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental results – stop 3
0 200 400 600 800 1000
010
2030
4050
6070
passengers waiting at the stop
time units
pass
enge
rs
P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental results – empty spaces
0 200 400 600 800 1000
010
2030
4050
empty spaces in tram
time units
empt
y sp
aces
P Systems for Passenger Flow Simulation
Future work
Future and related work
Future work◮ P systems for vehicular
flow simulation
◮ Dvorsky et al, 2012 –
first ideas, XML
specification, software
◮ real data aquisition -
Breclav city
(population 25 000, 5
traffic lights)
◮ Background model for
traffic optimisation
Related work
◮ Population dynamics
modelling using P systems
◮ superior for small
populations
◮ previous research
available
◮ experimental results
proven usefull
P Systems for Passenger Flow Simulation
Conclusion
Conclusion
◮ 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
Conclusion
Conclusion
Advantages of proposed model
◮ discrete representation of
vehicles, passengers
◮ expressive
◮ easy to extend
Drawbacks of proposed model
◮ objects are not inteligent
◮ can not incorporate
representation of world by
the means of physical laws
◮ detail of the model is
limited
P Systems for Passenger Flow Simulation
Bibliography
[Dvorsky et al, 2012] J. Dvorsky, Z. Janoska & L. Vojacek.
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.
[Paun, 1998] Gh. Paun.
Computing with membranes,
TUCS Report 208, Turku Center for Computer Science, 2000.
[Paun, 2004] Gh. Paun.
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/
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