Michael Florian and Shuguang He (with the collaboration of Maximo Bosch, Christian Lopez and Manuel Diaz)

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Michael Florian and Shuguang He(with the
collaboration of Maximo Bosch, Christian Lopez
and Manuel Diaz)

• A Multi-Class Multi-Mode Variable Demand Network
  Equilibrium Model
• with
• Explicit Capacity Constraints in Transit Services

18-20 March 200216th International EMME/2
UGMAlbuquerque, New Mexico, USA
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Base Network
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STGO 2 Strategic Planning Model - developed by
Fernandez and DeCea (ESTRAUS) - ported to run an
EMME/2 with different equilibrium algorithm (STGO)

• Base network
• 409 centroids including 49 parking locations
• 1808 nodes, 11,331 directional links
• 1116 transit lines and 52468 line segments
• 11 modes, including 4 combined modes
• (bus-metro, txc-metro, auto-metro and auto
  passenger-metro)
• The demand
• subdivided into 13 socio-economic classes
• 3 trip purposes ( work, study, other )
• driving license holders can access to 11 modes
• no license holders can access to 9 modes

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STGO 2 Strategic Planning Model - developed by
Fernandez and DeCea (ESTRAUS) - ported to run an
EMME/2 with different equilibrium algorithm (STGO)

• The modes
• walk (wk)
• auto driver (ad)
• auto passenger (ap)
• taxi (tx)
• taxi collectivo (tc)
• bus (bs)
• metro (mt)

• auto driver-metro (dm)
• auto passenger-metro (pm)
• bus-metro (bm)
• taxi collectivo-metro (tm)

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Mode Choice Model
Mode choice function is a simple multinomial
logit
Where, m is mode p is trip purpose n is class
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Trip Ends and Conservation of Flow Constraints (1)
Total productions
Total productions
Where, Oipn,1 is the production of trips for
driving licence owners Oipn,2 is the production
of trips for the non licence owners p is trip
purpose n is class
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Trip Ends and Conservation of Flow Constraints (2)
Trip end constraints
Where, Tijpnm,1 is the trips for driver licence
owners Tijpnm,2 is the trips for the rest Djp
is the total trips on destination p is trip
purpose, n is class ?ipn,1, ?ipn,2, ?jp are the
dual variables
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Trip Distribution Model
The total demand for each p, n may be obtained as
the solution of the following multi-proportional
matrix balancing problem.
Subject to
Where
are the well known log-sum expressions which
are the impedance for each (i,j), p and n implied
by the logit mode choice function. The problem
may be easily shown to be equivalent to the
entropy maximization function, subject the above
constraints
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Conservation of Flow Constraints
Where, hrpnm,1, hrpnm,2 are path flows,
uijpnm,1, uijpnm,2, rrpnm,1, rrpnm,2, r are dual
variables
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Variational Inequality Formulation
Find (h,T) ? ? which satisfy,
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Capacity Constraints in Transit Services

• The mode choice proportions in the morning peak
  are roughly as follows (total of 1.34 106
  trips)
• walk 11.6
• car driver 22.6
• car passenger 15.6
• taxi 0.4
• taxi collectivo 1.6
• bus 42.0
• metro 3.2
• combined modes 2.8
• (auto driver-metro, auto pass.-metro, bus-metro,
  txc-metro )

38.2
47.2
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Capacity Constraints in Transit Services

• The metro is an attractive mode and in many
  scenarios considered that transit trips assigned
  to metro exceed the capacity of the metro lines
• There was a need to model the limited capacity
  of the metro lines. The mechanism used to model
  the increased waiting times is that of effective
  frequency
• As the transit segments become congested, the
  comfort level decrease and the waiting times
  increase. These phenomena are modeled with
  increasing convex cost functions to model
  discomfort and with increased headway to model
  increased waiting times.

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Effective Frequency of a Transit Line (segment)

• The effective frequency of a line is defined
  as the frequency of a line with infinite capacity
  and Poisson arrivals (exponentially distributed
  inter-arrival times) which yields the waiting
  time obtained by the adjusted headway
• The waiting time at a stop are best modeled by
  using steady state queuing formulae, which take
  into account the residual capacity, the
  alightings and the boardings. A simplified steady
  state equilibrium is used inspired from

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Explicit Capacity Constraints - Metro

• After each iteration, which includes a transit
  assignment, that headway are adjusted according
  to the formula

• In order to model the crowding effect in the
  metro vehicles, the segment travel times are
  updated for segments which are over capacity

• is the successive average of
  the metro line segment volumes and serve to
  compute new transit time components at each
  iteration

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Explicit Capacity Constraints - Metro
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Determining the demand for combined modes
(auto-metro and bus/txc-metro)

• In order to compute the demand for the metro for
  the combined modes which use the metro, the
  following steps are taken

(i) find the transfer station k with the least
generalized cost, if bus is the first mode
(ii) find the transfer station k with the least
generalized cost, if metro is the first mode
(iii) the least generalized cost of the combined
mode cm
(iv) the demand is split into bus demand and
metro demand
(v)
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Solution Algorithm
Start and Initialize
Trip Distribution and Mode Choice
Auto Assignment
Multiple Transit Assignments
Transit Auto equivalent flow
Standard Transit Assignment for buses
Transit Assignment with adjusted headway for
metro
MSA Auto Volume
Congested time
Auto Skims
Metro MSA Impedance
Bus Impedance
Auto Impedance
Convergence?
Park-and-Ride Model for auto-metro and bus-metro
end
All Impedances
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Convergence of equilibration
Auto demand
Auto link volume
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Waiting times Changes
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Assigned vs. Equilibrium Metro Segment Volume
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Metro Line Segment Volume convergence
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Metro Volume (non-congested vs. congested version)
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Metro Volume Changes
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Metro Volume - metro 5A, non-congested version
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Metro Volum2 - metro 5A, congested version
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Auto-metro volume (non-congested vs. congested
version)
Congested
Non-congested
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Mode Split Demand Changes
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Metro usage of combined modes
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Metro Boarding and Alighting
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Conclusions

• It is possible to consider explicit capacity
  constraints on transit line segments in an
  equilibration scheme
• Even though the MSA algorithm is a heuristic
  method its application is satisfactory for the
  equilibration of complex models
• The flexibility of EMME/2 and the power of the
  macro language make it possible to implement such
  a complex model
• It is VERY NICE to show the results with Enif!

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EMME/2 System Architecture
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Bus-metro and Txc-metro volume (non-congested
vs. congested version)
Congested
Non-congested
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