Input

Route structure is modeled as a set of locations. Ordered lists of stops by direction, typically available in transit agency databases and also published for the convenience of the general public, can be used to define location objects. Each location’s controller determines if the location is a terminal or a bus stop, and the next location in the sequence. When modeling a bus route at the segment level, locations are created for terminals and stops at segment ends, but not for stops within a segment.

Initialization

Data Collection for each replication

Simulation

Route Specification Distributions

Vehicles Demand Representation

Location Controllers

Performance Measures

Figure 3-2: Simulation model activity diagram showing inputs, outputs, and high-level tasks

Running Time Distributions

Distributions associated with each location are used to model running time to the next loca-tion. Different distributions may be used for different times of the day and for the different locations a vehicle may visit next. Distributions may be theoretical or empirical, univariate or multivariate. It is now common for transit agencies to have databases with large amounts of AVL data at the stop or segment level. This makes it possible not only to obtain good empirical distributions of segment running times, but also to capture correlations between them.

Distributions associated with a terminal and a stop within it model extra time at the end of the route. In many practical situations, arrival at the last bus stop of a route is equivalent to arrival at the terminal, and no extra time is needed. In such cases, the distributions may be defined as a constant zero so that vehicles jump instantaneously between terminals and the bus stops within them. On the other hand, if the route being modeled requires extra time at route ends (for instance, reflecting travel time from the last stop to a parking space designated for layover), a fitted theoretical or empirical univariate distribution may be used.

Vehicles

Vehicles in the simulation are dynamic objects with identity, so a set of vehicles must be specified as input to the model. At the very least, an insertion time and location must be used to initialize the event heap, but additional properties may also be specified if needed.

For example, if the removal of vehicles from service depends on a target time and location, these can be specified. In a similar manner, vehicle seating and standing capacities can be specified to capture capacity constraints and measure passenger comfort. In simulations

that model dwell times explicitly and have different types of vehicles, dwell time controllers can be added to the framework in order to determine dwell times for different vehicle types.

This is useful for simulations of rail transit, where different trains may have a different number of cars, and therefore different capacities and dwell time functions.

Demand Representation

Passengers are also modeled as dynamic objects with identity, so a set of passengers must be specified as input. Each passenger has an origin stop with an arrival time and a des-tination stop. Passengers are typically picked up by the first vehicle to visit their origin stop and subsequently dropped off at their destination stop. (They do not board and alight themselves, since boardings and alightings are handled by vehicles.) This process gives the passenger a boarding time, an alighting time, and possibly some measure of in-vehicle comfort.

Although demand representation is set a-priori, it is not restricted to be constant. A dif-ferent set of passengers can be given for each replication in order to introduce demand variability. The process that generates sets of passengers may be based on empirical data from an AFC database, especially if it has been processed to infer destinations and ex-panded to capture ridership not registered in the AFC database. (See Gordon, 2012 for details.) In this case, inferred historical boarding and alighting events of different days can be the demand input for different replications. Alternatively, the demand representation can be based on a random arrival process with assumed rates λ_o,d(t) for passengers going from o to d at time of day t. The simulation model can also be used without demand representation.

Passenger origins and destinations must be defined locations in the route specification.

Therefore, if the route specification is based on segments, each covering multiple stops, it may be necessary to pool the demand for all stops within each segment. This complicates the interpretation of vehicle load capacity and in-vehicle comfort, especially if there is significant turnover of passengers within the segment. In light of this, an all-stop route specification allows greater accuracy of load-based performance measures.

Location Controllers

Location controllers govern the behavior of vehicles at each location. At terminals, they are responsible for removing vehicles from service and for setting layover times. Vehicle removals can be based on target removal times for each vehicle. For example, there may be a rule to remove vehicle 235 from service when it completes a trip scheduled to end at 18:00. Alternatively, they can be based on a vehicle profile, in which case the controller removes vehicles when the active fleet size at a particular time exceeds that specified by a vehicle profile. An example is a rule to remove the first vehicle that arrives at the terminal if there are more than 12 active vehicles at 18:00. Controllers also determine layover time for each vehicle upon arrival at the terminal. Layover times can be based on a schedule or on headway, as discussed in Section 3.2.3.

At bus stops, location controllers govern dwell times, the next location the vehicle will visit, and the time it will take the vehicle to arrive at that location. In the simplest case, dwell

times are included in the running time distributions, so they are not explicitly modeled.

If running times do not include dwell times, then a dwell time model can be used, with the benefit of correlating boardings, alightings, and load with dwell time. Controllers can extend dwell times (beyond what is required for boardings and alightings) to model holding.

Typically, the next stop a vehicle visits is the next downstream in the direction of travel, but controllers may send the vehicle to other locations, which allows modeling of expressing, off-service dead-heading, and short-turning. In any case, the time of arrival at the next location is based on the distributions associated with the stop.