Routes and Trip Segments
========================

In MetroSim, when an agent is traveling from an origin to a destination (optionally, with intermediate stops), he / she chooses between multiple routes to perform his / her trip.
A route describes the modes of transportation taken to travel from an origin to a destination.
Hence, in MetroSim, route choice is similar to mode choice.

More formally, a route is a combination of multiple trip segments, where each trip segment represents only one mode of transportation, allowing for inter-modal trips.
Routes can range from very simple (e.g., travel by car from O to D) to very complex (e.g., travel by car from O to I\ :sub:`1`, then take metro line 1 from I\ :sub:`1` to I\ :sub:`2`, then walk from I\ :sub:`2` to I\ :sub:`3`, then take bus line 5 from I\ :sub:`3` to D).
The figure below represents an example of route, with 2 segments.
The second segment is a public-transit segment containing 3 legs.

.. math::

   \overbrace{
      \mathbf{O} 
      \overbrace{\longrightarrow \text{Car} \longrightarrow}^{\text{segment 1}}
      \mathbf{I_1}
      \overbrace{
         \underbrace{\longrightarrow \text{Metro (line 1)} \longrightarrow}_{\text{leg 1}}
         \mathbf{I_2}
         \underbrace{\longrightarrow \text{Walk} \longrightarrow}_{\text{leg 2}}
         \mathbf{I_3}
         \underbrace{\longrightarrow \text{Bus (line 5)} \longrightarrow}_{\text{leg 3}}
      }^{\text{segment 2}}
      \mathbf{D}
   }^{\text{route}}


Trip Segments
-------------

MetroSim has three different types of trip segments.

Car segment
   It represents a trip by car from a source node to a target node.
   A car segment is only defined by its source and its target, i.e., there is no intermediate stop and the exact path taken is not determined a priori.

Public-transit segment
   It represents a public-transit trip from an access stop to an egress stop.
   A public-transit segment is defined by its access stop and its egress stop but also by the sequence of legs taken between the two stops, i.e., there can exist multiple public-transit segments between any two stops.
   A public-transit segment can include walking legs to transfer from one line to another but it always starts and ends with a public-transit leg.
   An example of public-transit segment is: take bus line 1 from stop A to stop B, then walk from stop B to stop C, then take metro line 3 from stop C to stop D.

Walking segment
   It represents a walking trip from a source node to a target node.


Trip segments can be classified in three categories, according to the characteristics of the travel utility they imply.

"Constant" trip segment
   Travel utility is time-invariant (e.g., walking segment).

"Continuous" trip segment
   Travel utility is continuously time-dependent (e.g., car segment).

"Discrete" trip segment
   Travel utility is discontinuously time-dependent (e.g., public-transit segment).


Route Type
----------

The route type depends on the type of its segments, according to the following rules:

- If at least one segment is discrete, then the route is *discrete*.
- If at least one segment is continuous but no segment is discrete, then the route is *continuous*.
- If all segments are constant, then the route is *constant*.

The route type is relevant when computing the expected utility of a route.
For discrete routes, the utility of all possible departure times is computed (at least partially).
For continuous routes, the utility is computed for a finite set of departure times.
For constant routes, the utility is computed only once.
See :doc:`/architecture/simulator/pre-day_model` for additional details.