Zephyr Code Library for Transportation Analysis

forward shortest path

A shortest path computation that starts at the origin node. This is used when there is a preferred departure time.

Related Terms

acyclic subgraph

An acyclic subgraph is a network without cycles (a cycle is a complete circuit). When following the network from node to node, a node is never visited twice.

backward shortest path

A the shortest path computation that starts at the destination node. This is used when there is a preferred arrival time.

downstream node

A node that is reachable from a node (forward shortest-path) or a node that can reach the current node (backward shortest path)

dynamic passenger assignment model

A model that simulates the performance (reliability) and dynamics (capacity constraints, interactions) of a system of passenger demand and scheduled or on-demand transportation services (transit, TNCs, taxis) that run on a physical transportation network.

dynamic transit passenger assignment model

A dynamic passenger assignment model that is designed for scheduled transit service.

emanating link

Links coming into or going out of a node.

hyperlink

A hyperlink consists of a set of transit links from a single origin to multiple possible destination nodes [ for forward-shortest-path finding ] or a set of links from a single destination to multiple possible origin nodes [ for backward-shortest-path finding ]. There may be multiple transit departures within a hyperlink.

hyperpath

An acyclic subnetwork with at least one link connecting the origin to the destination, and where at each node, there are probabilities for choosing the alternative links. In most hyperpath-based frameworks, this can be equivalent to the path choice set.

kirchoff model

An alternative formulation to the path-size logit model which considers the relative size of the total utilities of the path. For example, deltas of short paths are perceived differently than deltas on long paths. For paths that are generally the same size, the results will be similar to a logit model formulation.

departure time window

The ordered queue that contains stops with stop states that need to have their costs updated in order to find the shortest path. Stops are processed in order of cost, with least cost stops processed first.

overlap scale parameter

The parameter in the path-size logit model that scales the impact of the path size term.

passenger path set generation

The process of initializing the label stop queue, updating, and then finalizing the stop states. The origin or destination state now has a label that has a cost that encapsulates the costs of all the trip links and transfers, but with inaccuracies regarding the timing of the non-transit links, which must be updated using path enumeration.

passenger simulation

Probabilistic assignment of passengers to paths in their pathset based on costs. Update of pathset feasibility.

path choice model

A mathematical model for selecting a path from a set of feasible choices. Examples include the recursive logit model, path-size logit model, Kirchhoff model.

path cost

Path cost or generalized cost is a measure of impedance on a network object. It is typically composed of different variables, each with a fixed weight. Terms may include cost, in-vehicle time, number of transfers, wait time etc.

path labeling

path overlap variable

An additive measure of similarity between paths. In road-based path-choice models, this is often the distance of the shared links. In passenger-based path-choice models, this could include considerations for shared-routes, similar-routes, on/off stations, traversed stations, traverse distance and more. If the overlap variable is an indicator variable (𝛿), then it can be 1 or 0; if it distance or cost, then it is a continuous variable.

path overlap

In a set of possible paths through a transportation network, some portion of each of the paths may share a facility meaning that each choice in a choice set is not mutually exclusive. This is important in the context of choice modeling, since it violates the “Independence” in the IIA property of a Multinomial Logit. Formulations that compensate for this violation by discounting the “independence” of each path based on a measurement of commonality (the path overlap variable) include the path-size logit model.

path size logit model

A modified logit choice model where the utility equation for a path adds a path size variable to the utility of a path alternative in order to account for overlap between different path options.

stop label

In the context of a shortest path algorithm, stops are labeled with the overall generalized cost of travelling from that stop to the destination (in a forward shortest-path) or from that stop to the origin (in a backwards shortest-path). Stops can be iteratively updated throughout the algorithm.

stop state finalization

When all stops are removed from the label stop queue, the final costs for the destination (in forward-shortest-path) or origin (in backward-shortest-path) is finalized based on the cost labels of the emanating egress or access links.

stop state initialization

The first step of a shortest-path algorithm. Stop labels should be initialized to be greater-than or equal to their final cost and should allow for the greatest number of emanating links (i.e. for a walk access link in a forward-shortest-path, assume it is as early as possible). All stops are added to the label stop queue.