1. 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

2. 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 P˘un (1998) - Computing with membranes
a
◮ Research concerned with computational power, not biological
modelling
◮ No application to spatial phenomena (so far)

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. P Systems for Passenger Flow Simulation
Introduction
P systems – Introduction
Final configuration
[dd]1 [eeee]ENV
Calculation succesfull – no other rule
can be applied

11. 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)

12. 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

13. P Systems for Passenger Flow Simulation
Proposed model
Formal 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

14. P Systems for Passenger Flow Simulation
Proposed model
Formal 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

15. 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 people OUT ]i → [i ]i

16. 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

17. 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

18. P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.50
passengers waiting at the stop
250
200
passengers
150
100
50
0
0 200 400 600 800 1000
time units

19. P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.50
empty spaces in tram
50
40
30
empty spaces
20
10
0
0 200 400 600 800 1000
time units

20. P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.55
passengers waiting at the stop
80
60
passengers
40
20
0
0 200 400 600 800 1000
time units

21. P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.55
empty spaces in tram
50
40
empty spaces
30
20
10
0
0 200 400 600 800 1000
time units

22. P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.60
passengers waiting at the stop
50
40
30
passengers
20
10
0
0 200 400 600 800 1000
time units

23. P Systems for Passenger Flow Simulation
Experimental results
Model 1
Experimental results – probability 0.60
empty spaces in tram
50
40
30
empty spaces
20
10
0
0 200 400 600 800 1000
time units

24. 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

25. P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental results – stop 1
passengers waiting at the stop
1200
1000
800
passengers
600
400
200
0
0 200 400 600 800 1000
time units

26. P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental results – stop 2
passengers waiting at the stop
80
60
passengers
40
20
0
0 200 400 600 800 1000
time units

27. P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental 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

28. P Systems for Passenger Flow Simulation
Experimental results
Model 2
Experimental results – empty spaces
empty spaces in tram
50
40
30
empty spaces
20
10
0
0 200 400 600 800 1000
time units

29. P Systems for Passenger Flow Simulation
Future work
Future 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

30. 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

31. P Systems for Passenger Flow Simulation
Conclusion
Conclusion
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

32. 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,

33. 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/