MEZZO: OPEN SOURCE MESOSCOPIC. Centre for Traffic Research Royal Institute of Technology, Stockholm, Sweden

Transcription

1 MEZZO: OPEN SOURCE MESOSCOPIC SIMULATION Centre for Traffic Research Royal Institute of Technology, Stockholm, Sweden 1

2 Introduction Mesoscopic models fill the gap between static assignment and microscopic simulation: Medium-large networks (typically links, zones) Dynamic, vehicle based, absolute capacities, stochastic route choice Can be used hybrid with micro models Commercial models: Dynameq Contram (no longer developed) Aimsun Transmodeler Vista Open source: Dynasty OpenTraffic Mezzo 2

3 Mezzo open source mesoscopic simulation 3

4 MEZZO: Event-Based Mesoscopic Model Vehicle-based, event-based Link model: Speed = f(density) Node model: Queue-servers for each turning Stochastic or deterministic Correct queue formation and dissipation Stochastic route choice, pre-trip and en- route diversions 4

5 Mezzo features Can be used as hybrid with micro models (VISSIM,MITSIMLab) Full support for transit modeling, passengers, route choice, interaction with car traffic (DYMOBUS) Fast: Greater Stockholm 150x realtime (6000+ links, 500 zones) Contram ca 1x, Dynameq ca 40x Reads CONTRAM networks & matrices Free & Open source Co-operation with PTV for commercially supported version with VISUM Download: 5

6 MEZZO development Has been developed at CTR for 10 years with support from: VINNOVA Stockholms Stads Trafikkontor Vägverket Cooperation with Technion university (DymoBus) Open source version: Will continue to be developed Can be used by academic and commercial users Test-platform for new models and components such as route choice, demand estimation & calibration, transit models. 6

7 Commercial Mezzo / PTV VISUM + Mezzo module: Prototype 2nd half of 2010 Full integration (linked in LGPL lib) by mid 2011 PTV provides support VISSIM + Mezzo hybrid: After VISUM+MEZZO integration, mid-end 2011 Linked in Mezzo lib avoids COM interface, expected speed-up of x for parts modeled in Mezzo 7

8 Current Projects DymoBus II (VINNOVA, Stockholms Stad): Dynamic modeling of bus public transit (Oded Cats) Hybrid simulation CitySpårvägen (Johan Wahlstedt, Stockholms Stad) Efficient i methods for dynamic OD estimation (Tatsiana Aneichyk) Integration with MODENA emissions calculation platform (Xiaoliang Ma) Modeling heavy traffic (OD estimation, route choice and emission i impacts) (Trafikverket) k Calibration of DTA models (with CTS) 8

9 Current Model Development Stochastic Dynamic Assignment OD estimation 9

10 Stochastic Assignment Stochastic Dynamic User Equilibrium (SDUE) Where, ˆt l t l ˆt t l L l rel gap t ˆ t l L l are the input link travel times are the output link travel times, for all time periods t and links l Relat tive gap 0,9 0,8 0,7 0,6 0,5 04 0,4 0,3 0,2 0,1 0 t l Free-flow link times Iteration Converged link times rel gap <

11 SDUE details Dynamic version of SUE equilibrium condition (Sheffi 1985): f q P ( ) t t t t k i k k Path flows Demand Path proportions For all time periods t, od pairs i, paths k Equivalent relative gap t t t t t fk qipk( k) t i I k Ki relgaprouteflows t f t k t i t i I k K k Experienced Path travel times is the experienced travel time on path k for time t interval t. Whereas f k is based on the perceived travel times ˆt, constructed from link travel times ˆ t l k So an equivalent relative gap can be defined for link travel times: t t ˆ t l L l rel gap t ˆ t l L l l 11

12 Route choice Pre-trip: Path-Size Logit (Ben Akiva & Bierlaire 1999) Corrects for overlaps between routes En-route diversion: Mixed Logit (Han et al 2001) Accounts for taste variation between drivers Estimated on Stockholm SP data (2000) Choice Set Generation: Pre-trip Iterative search for time-dependent shortest paths Each time a new shortest path is found it is added to the set of known paths Each iteration OD flows are assigned to paths using pre-trip ti choice model 12

13 Choice set generation Loop 1 : new routes Routes Travel Times Shortest Path algorithm New Routes Network Demand Mezzo New Travel Simulation times Loop 2 : SDUE 13

14 OD estimation Gradient-based (based on Spiess 1990): Quick convergence Can only use flows Modification (Kolechkina 2010): Uses functional approximation of assignment matrix to avoid problems when network is congested SPSA (based on Ramachandran 2005, 2007): Slower convergence, more sensitive to parameter settings Can use any measurements: flows, speeds, travel times. Currently we use modified Gradient, but Gradient + SPSA is a good candidate: Quick convergence to solution that matches flows Then use SPSA to match other measurements 14

15 Modified Gradient approach Usual formulation: Estimated OD rates Minimize deviation from historical matrix Minimize deviation from measured flows Where Assignment matrix Assignment matrix is usually assumed constant near x We assume Assignment matrix is itself a function of x: A=A(x) and therefore: Which gives: 15

16 Modified Gradient approach (ctd.) We assume a linear approximation of A(x): Start from two initial points x 0 and x 1 and sequentially approximate α and β for iterations i>1 using x i and x i-1 x i-k (optimal k=3, Kolechkina 2010), using least squares. 16

17 OD estimation test case The resulting algorithm applied to Södermalm network for test case : 1100 links, 250 count locations Generate seed (historical) matrix from true matrix: scaled up by 50% and add 25% random noise. Check not only objective function (match flows, minimize distance to seed) but also how well the true matrix is re-created 17

18 Estimation results: Objective Function Objective Function Iteration Method converges fast to solution and is very robust 18

19 Estimation results : Fit of flows Flows Seed True Flows Estimated True y = 1,4913x R² = 0, y = 1,0098x R² = 0,9962 Seed flows (veh h/h) stimated flows (v veh/h) E True flows (veh/h) True flows (veh/h) 19

20 Estimation results: OD matrix Seed OD flows (veh/h) OD pairs Seed True y = 1,4709x R² = 0,9662 d OD flows (veh/ /h) Estimate OD pairs Estimated True y = 1,0383x R² = 0, True OD flows (veh/h) True OD flows (veh/h) Even the true matrix is approximated by the estimation 20

21 Estimation results: Speeds Speeds Seed True y = 0,9954x R² = 0, Speeds Estimated True y = 1,0008x R² = 0,9822 speeds (km/h) Seed Estimate ed speeds (km/h) True speeds (km/h) Speeds are not approximated better with estimated OD matrix True speeds (km/h) Gradient method cannot incorporate speeds SPSA can incorporate speeds, and travel times etc, but converges much slower. Next step is to try using Gradient+SPSA: Gradient to match flows, then SPSA to match the remaining data (while matching the flows) 21

22 Gui developments Network Editor Output view 22

23 Network Editor 23

24 Network Editor (2) Download background maps from Yahoo maps using either Latitude & Longitude or location name 24

25 Editor (3) 25

26 Output Analysis: Flow & Speed Outflow and speed show the general throughput of the network, for each time slice 26

27 Output Analysis: Density & Speed Bottlenecks with high density and low speeds can be identified and analysed with this view 27

28 Model details 28

29 MEZZO: Link Model Running part Queue Part Running part contains all moving vehicles Vehicle speed= f(density in running Part) expected exit time t expected = t current + (link length / speed) At any time t: All vehicles with t expected < t current are on the running part All vehicles with t expected >= t current are on the queue part Only vehicles on the queue part can exit 29

30 Standard Speed = f(density) Where: Vfree, if k kmin a b k k min V( k) Vmin Vfree Vmin 1 if k [ kmin, kmax ] kmax k min Vmin if k kmax V(k) = speed assigned to the vehicle k = the current density on the running part of the link V min = minimum i speed V free = free flow speed k min = minimum density k max = maximum density a, b = model parameters 30

31 MEZZO: Node model Queue part contains all vehicles that should have left the link Stochastic queue-server for each turning movement Turning movements can block each other (look-back k limit) it) blocked Running part Queue Part 31

32 MEZZO: Shockwaves Many meso models generally do not model start-up shockwaves Essential to correctly model congestion Solution: Update the exit times according to shockwave theory (LWR) Follow the queue front at start-up Calculate the new exit time for each vehicle 32

33 Choice set generation: en-route diversion (incidents) Pre-trip paths connect OD pairs, for vehicles avoiding an incident en-route additional paths are needed For each (link i, destination)pair: Re-use pre-trip paths from all origins to same destination d that pass current link, If none of the (sub)paths avoid incident do a new shortest path search with large penalty for incident link. Saves computational time by avoiding all link to all destination searches 33

34 Pre-trip: Path Size Logit specification Ui () t e Pt i() la 1 U () ()) j t U i() t 1ln( Ti t 3Di 3PSi i PSi e L j S a i i aj j S Where P i (t) = Probability of path i being chosen, given departure time t. U i (t) = Utility of path i, given departure time t. S = Set of all eligible paths between given origin and destination. T i (t) = Travel time for path i, given departure time t PS i = Path Size of of path i β 1, β 2 = Parameters Г i = Set of links in path i l a = Length of link a L i = Length of path i δ ai = Dummy variable, 1 if link a is on path j, 0 otherwise ε = Gumbel distributed error term ε i Ben-Akiva, M., Bierlaire, M., Discrete choice methods and their applications to short-term travel decisions. In: Hall, R. (Ed.),Handbook of Transportation Science. Kluwer, pp

35 P En-route: Mixed Logit Specification Uni () t e () t () nj e U () t ' x ni U t j S ni n ni ni Where P ni (t) U ni (t) S n x ni ε ni ' = Probability of path i being chosen, given departure time t, for individual n = Utility of path i, given departure time t, for individual n = Set of all eligible paths between given origin and destination, = Parameter vector for individuals randomly drawn ~ N(μ,σ) = Variable vector for individual n and path i = Gumbel distributed error term B. Han, S. Algers, L. Engelson (2001), Accomodating drivers taste variation and repeated choices correlation in route choices modeling by using the mixed LOGIT model, Proc. of Transportation Research Board Annual Meeting 35

36 Mixed Logit Parameter values Variable Parameter estimate t value Delay Habitual route (mean) 0, ,66 Delay Habitual route (std dev.) 0, ,37 Delay Alternative (mean) 0,0734 7,48 Delay Alternative (std dev.) 0,0604 5,16 Don't know delay Habitual route (mean) 3,7178 2,83 Don t know delay Habitual route (std dev.) 6,5835 2,25 Constant Habitual route (mean) 2,8523 8,44 Constant Habitual route (std dev.) 2,0368 5,27 B. Han, S. Algers, L. Engelson (2001), Accomodating drivers taste variation and repeated choices correlation in route choices modeling by using the mixed LOGIT model, Proc. of Transportation Research Board Annual Meeting. 36

37 Hybrid Meso-MicroMicro Large network in Meso with small Micro islands Integration may improve overall performance: Origin-Destination flows for larger area Computational resources Input data Calibration Requirements Consistency in: Travel behavior, e.g route choice Network representation Boundary transitions micro <-> meso Traffic performance meso and micro Efficient data exchange between sub-models 37

38 Hybrid Framework Common Module Travel behavior Pre-trip En-Route Path generation Database Network graph Travel times Paths OD flows Route choices Travel times Route choices Travel times Meso Model Vehicles, Traffic conditions Micro Model 38

39 Simplified Framework Meso Nt Network graph Virtual links Link travel times Paths OD flows Route choice Pre-trip En-route Vehicles, Traffic conditions Travel Times Micro Sb Subnetwork Virtual links Link travel times Subpaths Route choice En-route For integration of existing models 39

40 Network Virtual Links Meso virtual links Micro virtual links Meso Meso Meso Micro Micro Virtual links Micro Meso Meso Meso Virtual links 40