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Part III: Travel Demand Modeling

13 Last Step of Four Step Modeling (Trip Assignment Models)

Chapter Overview

Chapter 13 presents trip assignment, the last step of the Four-Step travel demand Model (FSM). This step determines which paths travelers choose for moving between each pair of zones. Additionally, this step can yield numerous results, such as traffic volumes in different transportation corridors, the patterns of vehicular movements, total vehicle miles traveled (VMT) and vehicle travel time (VTT) in the network, and zone-to-zone travel costs. Identification of the heavily congested links is crucial for transportation planning and engineering practitioners. This chapter begins with some fundamental concepts, such as the link cost functions. Next, it presents some common and useful trip assignment methods with relevant examples. The methods covered in this chapter include all-or-nothing (AON), user equilibrium (UE), system optimum (SO), feedback loop between distribution and assignment (LDA),  incremental increase assignment, capacity restrained assignment, and stochastic user equilibrium assignment.

Learning Objectives

Student Learning Outcomes

•  Describe the reasons for performing trip assignment models in FSM and relate these models’ foundation through the cost-function concept.
• Compare static and dynamic trip assignment models and infer the appropriateness of each model for different situations.
• Explain Wardrop principles and relate them to traffic assignment algorithms.
• Complete simple network traffic assignment models using static models such as the all-or-nothing and user equilibrium models.
• Solve modal split analyses manually for small samples using the discrete choice modeling framework and multinominal logit models

Introduction

In this chapter, we continue the discussion about FSM and elaborate on different methods of traffic assignment, the last step in the FSM model after trip generation, trip distribution, and modal split. The traffic assignment step, which is also called route assignment or route choice , simulates the choice of route selection from a set of alternatives between the origin and the destination zones (Levinson et al., 2014). The first three FSM steps determine the number of trips produced between each zone and the proportion completed by different transportation modes. The purpose of the final step is to determine the routes or links in the study area that are likely to be used. For example, when updating a Regional Transportation Plan (RTP), traffic assignment is helpful in determining how much shift or diversion in daily traffic happens with the introduction an additional transit line or extension a highway corridor (Levinson et al., 2014). The output from the last step can provide modelers with numerous valuable results. By analyzing the results, the planner can gain insight into the strengths and weaknesses of different transportation plans. The results of trip assignment analysis can be:

• The traffic flows in the transportation system and the pattern of vehicular movements.
• The volume of traffic on network links.
• Travel costs between trip origins and destinations (O-D).
• Aggregated network metrics such as total vehicle flow, vehicle miles traveled (VMT) , and vehicle travel time (VTT).
• Zone-to-zone travel costs (travel time) for a given level of demand.
• Modeled link flows highlighting congested corridors.
• Analysis of turning movements for future intersection design.
• Determining the Origin-Destination (O-D) pairs using a specific link or path.
• Simulation of the individual choice for each pair of origins and destinations (Mathew & Rao, 2006).

Link Performance Function

Building a link performance function is one of the most important and fundamental concepts of the traffic assignment process. This function is usually used for estimating travel time, travel cost, and speed on the network based on the relationship between speed and travel flow. While this function can take different forms, such as linear, polynomial , exponential , and hyperbolic , one of the most common functions is the link performance function which represents generalized travel costs (United States Bureau of Public Roads, 1964). This equation estimates travel time on a free-flow road (travel with speed limit) adding a function that exponentially increases travel time as the road gets more congested. The road volume-to-capacity ratio can represent congestion (Meyer, 2016).

While transportation planners now recognize that intersection delays contribute to link delays, the following sections will focus on the traditional function. Equation (1) is the most common and general formula for the link performance function.

• t and x are the travel time and vehicle flow;
• t 0 is the link free flow travel time;
• k is the link capacity;
• α and β are parameters for specific type of links and calibrated using the field data. In the absence of any field data, it is usually assumed = 0.15, and β= 4.0.

α and β are the coefficients for this formula and can take different values (model parameters). However, most studies and planning practices use the same value for them. These values can be locally calibrated for the most efficient results.

Figure 13.1 demonstrates capacity as the relationship between flow and travel time. In this plot, the travel time remains constant as vehicle volumes increase until the turning point , which indicates that the link’s volume is approaching its capacity.

The following example shows how the link performance function helps us to determine the travel time according to flow and capacity.

Performance Function Example

Assume the traffic volume on a path between zone i and j was 525. The travel time recorded on this path is 15 minutes. If the capacity of this path would be 550, then calculate the new travel time for future iteration of the model.

Based on the link performance function, we have:

Now we have to plug in the numbers into the formula to determine the new travel time:

Traffic Assignment Models

Typically, traffic assignment is calculated for private cars and transit systems independently. Recall that the impedance function differs for drivers and riders, and thus simulating utility maximization behavior should be approached differently. For public transit assignment, variables such as fare, stop or transfer, waiting time, and trip times define the utility (equilibrium) (Sheffi, 1985). For private car assignment, however, in some cases, the two networks are related when public buses share highways with cars, and congestion can also affect the performance.

Typically, private car traffic assignment models the path choice of trip makers using:

• algorithms like all-or-nothing
• user equilibrium
• system optimum assignment

Of the assignment models listed above, user equilibrium is widely adopted in the U.S. (Meyer, 2016). User equilibrium relies on the premise that travelers aim to minimize their travel costs. This algorithm achieves equilibrium when no user can decrease their travel time or cost by altering their travel path.

• incremental
• capacity-restrained
• iterative feedback loop
• Stochastic user equilibrium assignment
• Dynamic traffic assignment

All-or-nothing Model

Through the all-or-nothing (AON) assignment, it is assumed that the impedance of a road or path between each origin and destination is constant and equal to the free-flow level of service. This means that the traffic time is not affected by the traffic flow on the path. The only logic behind this model is that each traveler uses the shortest path from his or her origin to the destination, and no vehicle is assigned to other paths (Hui, 2014). This method is called the all-or-nothing assignment model and is the simplest one among all assignment models. This method is also called the 0-1 assignment model, and its advantage is its simple procedure and calculation. The assumptions of this method are:

• Congestion does not affect travel time or cost, meaning that no matter how much traffic is loaded on the route, congestion does not take place.
• Since the method assigns one route to any travel between each pair of OD, all travelers traveling from a particular zone to another particular zone choose the same route (Hui, 2014).

To run the AON model, the following process can be followed:

• Step 0: Initialization. Use free flow travel costs Ca=Ca(0) , for each link a on the empty network. Ɐ
• Step 1: Path finding. Find the shortest path P for each zonal pair.
• Step 2: Path flows assigning. Assign both passenger trips (hppod) and freight trips (hfpod) in PCEs from zonal o to d to path P.
• Step 3: Link flows computing. Sum the flows on all paths going through a link as total flows of this link.

Example 2 illustrates the above-mentioned process for the AON model

All-or-nothing Example

Table 13.1 shows a trip distribution matrix with 4 zones. Using the travel costs between each pair of them shown in Figure 13.2, assign the traffic to the network. Load the vehicle trips from the trip distribution table shown below using the AON technique. After assigning the traffic, illustrate the links and the traffic volume on each on them.

Table 13.1 Trip Distribution Results.

To solve this problem, we need to find the shortest path among all alternatives for each pair of zones. The result of this procedure would be 10 routes in total, each of which bears a specific amount of travels. For instance, the shortest path between zone 1 and 2 is the straight line with 5 min travel time. All other routes like 1 to 4 to 2 or 1 to 4 to 3 to 2 would be empty from travelers going from zone 1 to zone 2. The results are shown in Table 13.2.

As you can see, some of the routes remained unused. This is because in all-or-nothing if a route has longer travel time or higher costs, then it is assumed it would not be used at all.

User Equilibrium

The next method for traffic assignment is called User Equilibrium (UE). The rule or algorithm is adapted from the well-known Wardrop equilibrium (1952) conditions (Correa & Stier-Moses, 2011). In this algorithm, it is assumed that travelers will always choose the shortest path, and equilibrium conditions are realized when no traveler is able to decrease their travel impedance by changing paths (Levinson et al., 2014).

As we discussed, the UE method is based on the first principle of Wardrop : “for each origin- destination (OD) pair, with UE, the travel time on all used paths is equal and less than or equally to the travel time that would be experienced by a single vehicle on any unused path”( Jeihani Koohbanani, 2004, p. 10). The mathematical format of this principle is shown in equation (3):

For a given OD pair, the UE condition can be expressed in equation (3):

This model assumes that all paths have equal travel time. Additionally, the model includes the following general assumptions:

• The users possess all the knowledge needed about different paths.
• The users have perfect knowledge of the path cost.
• Travel time in a route is subject to change only by the cost flow function of that route.
• Travel times increases as we load travel into the network (Mathew & Rao, 2006).

Hence, the UE assignment comes to an optimization problem that can be formulated using equation (4):

k  is the path x a equilibrium flow in link a t a  travel time on link a f k rs  flow on path  connecting OD pairs q rs  trip rate between  and δ a, k rs is constraint function defined as 1 if link a belongs to path k and 0 otherwise

Example 3 shows how the UE method can be applied for the traffic assignment step. This example is a very simple network consisting of two zones with two possible paths between them.

UE Example 

In this example, t 1 and t 2 are travel times measured by min on each route, and x 1 and x 2 are traffic flows on each route measured by (Veh/Hour).

Using the UE method, assign 4,500 Veh/Hour to the network and calculate travel time on each route after assignment, traffic volume, and system total travel time.

According to the information provided, total flow (X 1 +X 2 ) is equal to 4,500 (4.5).

First, we need to check, with all traffic assigned to one route, whether that route is still the shortest path. Thus we have:

T 1 (4.5)=23min

T 2 (0)=3min

if all traffic is assigned to route 2:

T 1 (0)=3min

T 2 (4.5)=43.5 min

Step 2: Wardrope equilibrium rule: t 1 =t 2        5+4x 1 =3+ 2x 2 2         and we have x 1 =4.5-x 2

Now the equilibrium equation can be written as: 6 + 4(4.5 − x2)=4+ x222

x 1 = 4.5 − x 2 = 1.58

Now the updated average travel times are: t 1 =5+4(1.58)=11.3min and T 2 =3+2(2.92)2=20.05min

Now the total system travel time is:

Z(x)=X 1 T 1 (X 1 )+X 2 T 2 (X 2 )=2920 veh/hr(11.32)+1585 veh/hr(20.05)=33054+31779=64833 min

System Optimum Assignment

One traffic assignment model is similar to the previous one and is called system optimum (SO). The second principle of the Wardrop defines the model’s logic. Based on this principle, drivers’ rationale for choosing a path is to minimize total system costs with one another to minimize total system travel time (Mathew & Rao, 2006). Using the SO traffic assignment, one can solve various problems, such as optimizing the departure time for a single commuting route, minimizing the total travel time from multiple origins to a single destination, or minimizing travel time in stochastic time-dependent O-D flows from several origins to a single destination ( Jeihani & Koohbanani, 2004).

One other traffic assignment model similar to the previous one is called system optimum (SO) in which the second principle of the Wardrop defines the logic of the model. Based on this principle, drivers’ rationale for choosing a path is to minimize total system costs with one another in order to minimize total system travel time (Mathew & Rao, 2006). Using the SO traffic assignment, problems like optimizing departure time for a single commuting route, minimizing total travels from multiple origins to one destination, or minimizing travel time in stochastic time-dependent OD flows from several origins to a single destination can be solved (Jeihani Koohbanani, 2004).

The basic mathematical formula for this model that satisfies the principle of the model is shown in equation (5):

In example 4, we will use the same network we described in the UE example in order to compare the results for the two models.

In that simple two-zone network, we had:

T 1 =5+4X 1    T2=3+2X 2 2

Now, based on the principle of the model we have:

Z(x)=x 1 t 1 (x 1 )+x 2 t 2 (x 2 )

Z(x)=x 1 (5+4x 1 )+x 2 (3+2x 2 2 )

Z(x)=5x 1 +4x 1 2 +3x 2 +2x 2 3

From the flow conservation. we have: x 1 +x 2 =4.5     x 1 =4.5-x 2

Z(x)=5(4.5-x 2 )+4(4.5-x 2 )2+4x 2 +x 2 3

Z(x)=x 3 2 +4x 2 2 -27x 2 +103.5

In order to minimize the above equation, we have to take derivatives and equate it to zero. After doing the calculations, we have:

Based on our finding, the system travel time would be:

T 1 =5+4*1.94=12.76min     T 2 =3+ 2(2.56)2=10.52 min

And the total travel time of the system would be:

Z(x)=X 1 T 1 (X 1 )+X 2 T 2 (X 2 )=1940 veh/hr(12.76)+2560 veh/hr(10.52)=24754+26931=51685 min

Incremental Increase model

Incremental increase is based on the logic of the AON model and models a process designed with multiple steps. In each step or level, a fraction of the total traffic volume is assigned, and travel time is calculated based on the allocated traffic volume. Through this incremental addition of traffic, the travel time of each route in step (n) is the updated travel time from the previous step (n-1) (Rojo, 2020).

The steps for the incremental increase traffic assignment model are:

• Finding the shortest path between each pair of O-Ds (Origin Destination).
• Assigning a portion of the trips according to the matrix (usually 40, 30, 20 and 10 percent to the shortest path).
• Updating the travel time after each iteration (each incremental increase).
• Continuing until all trips are assigned.
• Summing the results.

The example below illustrates the implementation process of this method.

A hypothetical network accommodates two zones with three possible links between them. Perform an incremental increase traffic assignment model for assigning 200 trips between the two zones with increments of: 30%, 30%, 20%, 20%. (The capacity is 50 trips.)

Incremental Increase Example

Step 1 (first iteration): Using the method of AON, we now assign the flow to the network using the function below:

Since the first route has the shortest travel time, the first 30% of the trips will be assigned to route 1. The updated travel time for this path would be:

And the remaining route will be empty, and thus their travel times are unchanged.

Step 2 (second iteration): Now, we can see that the second route has the shortest travel time, with 30% of the trips being assigned to this route, and the new travel time would be:

Step 3 (third iteration): In the third step, the 20% of the remaining trips will be assigned to the shortest path, which in this case is the first route again. The updated travel time for this route is:

Step 4 (fourth iteration): In the last iteration, the remaining 10% would be assigned to first route, and the time is:

Finally, we can see that route 1 has a total of 140 trips with a 8.85 travel time, the second route has a total of 60 trips with a 9.17 travel time, and the third route was never used.

Capacity Restraint Assignment

So far, all the presented algorithms or rules have considered the model’s link capacity. The flow is assigned to a link based on travel time as the only factor. In this model, after each iteration, the total number of trips is compared with the capacity to observe how much increase in travel time was realized by the added volume. In this model, the iteration stops if the added volume in step (n) does not change the travel time updated in step (n-1). With the incorporation of such a constraint, the cost or performance function would be different from the cost functions discussed in previous algorithms (Mathew & Rao, 2006). Figure 13.6 visualizes the relationship between flow and travel time with a capacity constraint.

Based on this capacity constraint specific to each link, the α, β can be readjusted for different links such as highways, freeways, and other roads.

Feedback Loop Model (Combined Traffic Assignment and Trip Distribution)

The feedback loop model defines an interaction between the trip distribution route choice step with several iterations. The model allows travelers to change their destination if a route is congested. For example, the feedback loop models that the traveler has a choice of similar destinations, such as shopping malls, in the area. In other words, in a real-world situation, travelers usually simultaneously decide about their travel characteristics (Qasim, 2012).

The chart below shows how the combination of these two modes can take place:

Equation (6), shown below for this model, ensures convergence at the end of the model is:

where C a (t) is the same as previous

P a , is total personal trip flows on link a,

f a ; is total freight trip flows on link a,

T od is the total flow from node o to node d,

p od is personal trip from node o to node d,

F od is freight trip from node o to node d,

ζ is a parameter estimated from empirical data,

K is a parameter depending on the type of gravity model used to calculate T od , Evans (1976) proved that K’ equals to 1 for distribution using doubly constrained gravity model and it equals to 1 plus attractiveness for distribution using singly constrained model. Florian et al. (1975) ignored K for distribution using a doubly constrained gravity model because it is a constant.

Stochastic User Equilibrium Traffic Assignment

Stochastic user equilibrium traffic assignment is a sophisticated and more realistic model in which the level of uncertainty regarding which link should be used based on a measurement of utility function is introduced. This model performs a discrete choice analysis through a logistic model. Based on the first Wardrop principle, this model assumes that all drivers perceive the costs of traveling in each link identically and choose the route with minimum cost. In stochastic UE, however, the model allows different individuals to have different perceptions about the costs, and thus, they may choose non-minimum cost routes (Mathew & Rao, 2006). In this model, flow is assigned to all links from the beginning, unlike previous models, which is closer to reality. The probability of using each path is calculated with the following logit formula shown in equation (7):

P i is the probability of using path i

U i is the utility function for path i

In the following, an example of a simple network is presented.

Stochastic User Equilibrium Example

There is a flow of 200 trips between two points and their possible path, each of which has a travel time specified in Figure 13.7.

Using the mentioned logit formula for these paths, we have:

Based on the calculated probabilities, the distribution of the traffic flow would be:

Q 1 =175 trips

Q 2 =24 trips

Q 3 =1 trips

Dynamic Traffic Assignment

Recall the first Wardrop principle, in which travelers are believed to choose their routes with the minimum cost. Dynamic traffic assignment is based on the same rule, but the difference is that delays result from congestion. In this way, not only travelers’ route choice affects the network’s level of service, but also the network’s level of service affects travelers’ choice. However, it is not theoretically proven that an equilibrium would result under such conditions (Mathew & Rao, 2006).

Today, various algorithms are developed to solve traffic assignment problems. In any urban transportation system, travelers’ route choice and different links’ level of service have a dynamic feedback loop and affect each other simultaneously. However, a lot of these rules are not present in the models presented here. In real world cases, there can be more than thousands of nodes and links in the network, and therefore more sensitivity to dynamic changes is required for a realistic traffic assignment (Meyer, 2016). Also, the travel demand model applies a linear sequence of the four steps, which is unlike reality. Additionally, travelers may have only a limited knowledge of all possible paths, modes, and opportunities and may not make rational decisions.

In this last chapter of landuse/transportation modeling book, we reviewed the basic concepts and principles of traffic assignment models as the last step in travel demand modeling. Modeling the route choice and other components of travel behavior and demand for transportation proven to be very challenging and can incorporate multiple factors. For instance, going from AON to incremental increase assignment, we factor in the capacity and volume (and resulting delays) relationship in the assignment to make more realistic models.  Multiple-time-period assignments for multiple classes, separate specification of facilities like high-occupancy vehicle (HOV) and high-occupancy toll (HOT) lanes; and, independent transit assignment using congested highway travel times to estimate a bus ridership assignment, are some of the new extensions and variation of algorithms that take into account more realities within transportation network. A new prospect in traffic assignment models that adds several capabilities for such efforts is emergence of ITS such as data that can be collected from connected vehicles or autonomous vehicles. Using these data, perceived utility or impedances of different modes or infrastructure from individuals perspective can be modeled accurately, leading to more accurate assignment models, which are crucial planning studies such as growth and land use control efforts, environmental studies, transportation economies, etc.

Route choice is the process of choosing a certain path for a trip from a very large choice sets.

Regional Transportation Plan is long term planning document for a region’s transportation usually updated every five years.

Vehicles (VMT) is the aggregate number of miles deriven from in an area in particular time of day.

• Total vehicle travel time is the aggregate amount of time spent in transportation usually in minutes.

Link performance function is function used for estimating travel time, travel cost, and speed on the network based on the relationship between speed and travel flow.

Hyperbolic function is a function used for linear differential equations like calculating distances and angels in hyperbolic geometry.

Free-flow road is situation where vehicles can travel with the maximum allowed travel speed.

• Algorithms like all-or-nothing an assignment model where we assume that the impedance of a road or path between each origin and destination is constant and is equal to free-flow level of service, meaning that the traffic time is not affected by the traffic flow on the path.

Capacity-restrained is a model which takes into account the capacity of a road compared to volume and updates travel times.

User equilibrium is a traffic assignment model where we assume that travelers will always choose the shortest path and equilibrium condition would be realized when no traveler is able to decrease their travel impedance by changing paths.

System optimum assignment is an assignment model based on the principle that drivers’ rationale for choosing a path is to minimize total system costs with one another in order to minimize total system travel time.

• Static user-equilibrium assignment algorithm is an iterative traffic assignment process which assumes that travelers chooses the travel path with minimum travel time subject to constraints.
• Iterative feedback loop is a model that iterates between trip distribution and route choice step based on the rational that if a path gets too congested, the travel may alter travel destination.

First principle of Wardrop is the assumption that for each origin-destination (OD) pair, with UE, the travel time on all used paths is equal and less than or equally to the travel time that would be experienced by a single vehicle on any unused path.

System optimum (SO) is a condition in trip assignment model where total travel time for the whole area is at a minimum.

• Stochastic time-dependent OD is a modeling framework where generation and distribution of trips are randomly assigned to the area.

Incremental increase is AON-based model with multiple steps in each of which, a fraction of the total traffic volume is assigned, and travel time is calculated based on the allocated traffic volume.

Stochastic user equilibrium traffic assignment employs a probability distribution function that controls for uncertainties when drivers compare alternative routes and make decisions.

Dynamic traffic assignment is a model based on Wardrop first principle in which delays resulted from congestion is incorporated in the algorithm.

Key Takeaways

In this chapter, we covered:

• Traffic assignment is the last step of FSM, and the link cost function is a fundamental concept for traffic assignment.
• Different static and dynamic assignments and how to perform them using a simplistic transportation network.
• Incorporating stochastic decision-making about route choice and how to solve assignment problems with regard to this feature.

Prep/quiz/assessments

• Explain what the link performance function is in trip assignment models and how it is related to link capacity.
• Name a few static and dynamic traffic assignment models and discuss how different their rules or algorithms are.
• How does stochastic decision-making on route choice affect the transportation level of service, and how it is incorporated into traffic assignment problems?
• Name one extension of the all-or-nothing assignment model and explain how this extension improves the model results.

Correa, J.R., & Stier-Moses, N.E.(2010).Wardrope equilibria. In J.J. Cochran( Ed.), Wiley encyclopedia of operations research and management science (pp.1–12). Hoboken, NJ: John Wiley & Sons. http://dii.uchile.cl/~jcorrea/papers/Chapters/CS2010.pdf

Hui, C. (2014). Application study of all-or-nothing assignment method for determination of logistic transport route in urban planning. Computer Modelling & New Technologies , 18 , 932–937. http://www.cmnt.lv/upload-files/ns_25crt_170vr.pdf

Jeihani Koohbanani, M. (2004).  Enhancements to transportation analysis and simulation systems (Unpublished Doctoral dissertation, Virginia Tech). https://vtechworks.lib.vt.edu/bitstream/handle/10919/30092/dissertation-final.pdf?sequence=1&isAllowed=y

Levinson, D., Liu, H., Garrison, W., Hickman, M., Danczyk, A., Corbett, M., & Dixon, K. (2014). Fundamentals of transportation . Wikimedia. https://upload.wikimedia.org/wikipedia/commons/7/79/Fundamentals_of_Transportation.pdf

Mathew, T. V., & Rao, K. K. (2006). Introduction to transportation engineering. Civil engineering–Transportation engineering. IIT Bombay, NPTEL ONLINE, Http://Www. Cdeep. Iitb. Ac. in/Nptel/Civil% 20Engineering .

Meyer, M. D. (2016). Transportation planning handbook . John Wiley & Sons.

Qasim, G. (2015). Travel demand modeling: AL-Amarah city as a case study . [Unpublished Doctoral dissertation , the Engineering College University of Baghdad]

Rojo, M. (2020). Evaluation of traffic assignment models through simulation. Sustainability , 12 (14), 5536. https://doi.org/10.3390/su12145536

Sheffi, Y. (1985). Urban transportation networks: Equilibrium analysis with mathematical programming method . Prentice-Hall. http://web.mit.edu/sheffi/www/selectedMedia/sheffi_urban_trans_networks.pdf

US Bureau of Public Roads.  (1964). Traffic assignment manual for application with a large, high speed computer . U.S. Department of Commerce, Bureau of Public Roads, Office of Planning, Urban Planning Division.

https://books.google.com/books/about/Traffic_Assignment_Manual_for_Applicatio.html?id=gkNZAAAAMAAJ

Wang, X., & Hofe, R. (2008). Research methods in urban and regional planning . Springer Science & Business Media.

Polynomial is distribution that involves the non-negative integer powers of a variable.

Hyperbolic function is a function that the uses the variable values as the power to the constant of e.

A point on the curve where the derivation of the function becomes either maximum or minimum.

all-or-nothing is an assignment model where we assume that the impedance of a road or path between each origin and destination is constant and is equal to free-flow level

Incremental model is a model that the predictions or estimates or fed into the model for forecasting incrementally to account for changes that may occur during each increment.

Iterative feedback loop is a model that iterates between trip distribution and route choice step based on the rational that if a path gets too congested, the travel may alter travel destination

Wardrop equilibrium is a state in traffic assignment model where are drivers are reluctant to change their path because the average travel time is at a minimum.

second principle of the Wardrop is a principle that assumes drivers’ rationale for choosing a path is to minimize total system costs with one another in order to minimize total system travel time

Stochastic time-dependent OD is a modeling framework where generation and distribution of trips are randomly assigned to the area

feedback loop model is type of dynamic traffic assignment model where an iteration between route choice and traffic assignment step is peformed, based on the assumption that if a particular route gets heavily congested, the travel may change the destination (like another shopping center).

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Transportation modeling: Building future-proof mobility

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Transport models are the foundation of transportation and traffic planning. Transportation systems involve many components and stakeholders, each with their own perspective and interests. Further, transportation is closely linked to many other aspects of society.

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Using transportation modeling

Transport models are the foundation of mobility and traffic planning. Using transportation modeling enables mobility experts to:

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To make public transportation the preferred choice of more people, planners need to address multiple questions: How to expand the public transport network? Where does a new bus line make sense, where to add new stops? Which frequency serves the demand?

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Nevertheless, transportation modeling provides a detailed representation of all modes of public transport such as bus, taxi, as well as heavy and light rail. It allows planners to design reliable transit services which optimally serve passengers needs and allow efficient operations.

London’s new standard

Here’s an example on how London’s transportation authorities successfully use transportation modeling:

Transport for London ( TfL ) is responsible for the capital city’s transport system. Its Operational Network Evaluator (ONE) is a tactical highway traffic assignment model, used to assess the impact of schemes and to evaluate mitigation strategies.

Built in PTV Visum software, ONE provides a simplified representation of real-world road traffic conditions. It is one of the largest and most detailed junction-based highway models in the world: It covers 5,692 zones; 53,500 kilometers of links; and over 17,000 junctions modeled in detail, of which more than 5,500 are signalized.

The ONE model in PTV Visum has been intensively used by TfL for many years, with excellent results. It has helped to assess the impact of schemes including cycle routes and major road redesign schemes. It also helped the operational analysis of road and river crossing closures, and their impact on bus journey times.

Recently, TfL updated the model with the version PTV Visum 2022 , which includes a move from scripted to built-in assignment. As a result, the model sets a new standard for the industry for highway assignment runtimes on regular hardware. It converges within 2.5 hours, including a bespoke outer loop for taxi in bus lane adjustments. Without this outer loop, which is unique to TfL’s application, the runtime would be even shorter less than 1 hour!

These faster run times will significantly increase the computation resources available for the TfL team and speed up the assessment of transport schemes in London.

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• Reimagining the operating model for global talent mobility

10 predictions on the evolution of global mobility functions

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This article is based on predictions that professionals from KPMG firms’ Global Mobility Services (GMS) practices from around the world have made in relation to how global mobility function may evolve in the years to come. By their very nature as predictions, they are not intended to provide any guarantees to future outcomes.

As organizations move into the recovery stage of the pandemic, new demands on global talent mobility teams are ramping up. Employees want more flexible remote work options. Technology and virtual work are influencing new talent mobility options. Tax and regulatory risks from business travel are rising as governments and societies demand more data and accountability about a business’s activities and contributions. Companies are looking to reduce costs, go digital and refocus their teams on delivering value.

Amid the disruption and uncertainty of recent times, it may be difficult to know how these demands are influencing the corporate global mobility functions of tomorrow. The following are 10 predictions on how global mobility functions may evolve over the next few years.

After the initial shock of the pandemic-driven shift to working from home offices, many knowledge workers found that they prefer remote work and many businesses were surprised at its success in maintaining continuity and productivity. As the pandemic wore on, work-from-anywhere arrangements allowed many city-dwelling workers to move further way from their employers’ locations, both within their home countries and, for some, internationally. It’s widely predicted that many workers, especially those in professional services, will still favor working remotely at least part of the time as local restrictions ease and businesses are opening their doors again. According to the 2021 KPMG CEO Outlook survey, CEOs are focused on providing increased flexibility for their workforce. Global executives are looking to implement a hybrid working model for their staff with 51 percent of CEOS investing in shared workspaces and 37 percent looking to have most employees working remotely at least two or more days a week.

This trend may present significant challenges for global talent mobility and HR teams as they work to keep their talent satisfied and productive, while also managing global tax, social security, immigration, and other regulatory compliance issues that remote work brings. For example, when an employee works some or all the time in a different international jurisdiction than that of their employer, risks can arise for the employee due to tax residency rules for individuals, as well as income tax and payroll reporting requirements. Employers can face tax obligations stemming from corporate permanent establishment determinations, transfer pricing policies and corporate residency rules.

In the US, these risks can also arise at the state level. For example, state tax and payroll reporting obligations can arise if an employee works in a different state from their employer. While these risks are not new, they may multiply as more employees opt for remote working options and these arrangements become a point of negotiation with potential recruits. If a company decides to continue with some level of remote workforce, global talent mobility teams will need to establish clear policies with firm guardrails to determine employee eligibility, manage the risks arising from employee movements (often supported through technology), as well as implement mechanisms to document for authorities and other stakeholders that employees adhere to these policies in practice under compliant remote work arrangements.

In addition to the compliance considerations, companies with work-from-anywhere programs are solving other issues. Most people have experienced how important ‘watercooler’ interactions with co-workers are. These random meetings often serve as an informal exchange of ideas and exchange of information. How can these interactions happen in a virtual environment? And while it’s great to gain some extra time by not commuting, people are social creatures who depends on social and in-person interaction for their well-being. These and other topics will need to be looked at and resolved to make “working from anywhere” a successful tool for talent acquisition, employee engagement and productivity, and retention.

Kelly Stoltz Manager, Global Mobility Services KPMG in Germany [email protected]

Over the past several years, evolving business models and the war for talent have led to the development of an array of new talent mobility types. Pandemic-related complications have led to more innovation and more reliance on some of these options as organizations sought to accommodate diverse talent needs through various types of work opportunities abroad.

As borders reopen and lockdowns ease, we fully expect business travel to resume, albeit with less frequency and shorter trips. It would be difficult to match the level of intercultural and global business skills development, team building, networking and cross-pollination of ideas that comes with in-person interaction over time. For global organizations, curtailing mobility could hamper efforts to recruit talent, especially among younger generations who may be more mobile and aspire to obtain international work experience as part of their careers. Further, it could deny opportunities for organizations to improve the overall diversity and social consciousness of their workforces through the cultural immersion of employees living and working in foreign locales.

As employees get better at working virtually, staffing models will become less local and more projects will be completed with a mix of in-person and virtual collaboration. For example, rather than sending a subject matter expert from New York to London for a six-month project, that person could take part through a couple of shorter business trips and contribute remotely for the rest of the time.

As with work-from-anywhere arrangements, mobility teams will need to establish clear policies and processes for governing and administering all the various business travel alternatives. This enhanced structure is needed to manage the tax and other compliance risks that can arise from extended business trips. It is also important for ensuring that business travel programs are in line with the company’s corporate and HR talent strategies, and that different employee groups are treated consistently and equitably.

Where talent mobility is concerned, we expect many companies to broaden their programs to include more diverse arrangements like virtual/in-person hybrids, extended business trips (e.g. three months), short-term international assignments (e.g. less than one year), indefinite country-to-country transfers and cross-border commuting arrangements.

According to the 2021 KPMG Global Assignment Policies and Practices (GAPP) Survey report , 22 percent of respondents said they expect the use of their policy for long-term international assignments (i.e. one to five years) would decrease over the next five years, while 37 percent expect their policy on these assignments to remain unchanged. In contrast, 67 percent expect to see an increase in assignments under 12 months, and 42 percent expect an increase in commuter arrangements (both fly-in fly-out and cross-border).

Glen Collins Senior Manager, Global Mobility Services KPMG in the US [email protected]

As the risks of climate change have grown more apparent, the past few years have seen rising consensus globally over the situation’s urgency — across businesses, governments, and communities. While the COVID-19 pandemic took center stage temporarily, many governments are expected to encourage recovery and growth through measures to encourage a greener, more sustainable economy. This is promoting a movement toward greater ESG across global companies, and global talent mobility teams may be called on to contribute positively to improved company performance on ESG goals.

As has been seen, Diversity, Equity and Inclusion (DEI) is one dimension of ESG where global talent mobility teams can make a difference, for example, by opening global work opportunities to broader candidate pools and understanding the unique supports that diverse international assignee talent may need.

Contributing to good governance is also vital for global talent mobility teams. As business travel returns and varied talent mobility types evolve, companies need to have clear, well-communicated policies for managing their mounting tax, regulatory and financial risks, as well as systems and processes for monitoring and reporting on their ESG effectiveness to internal stakeholders and external authorities.

These mobility policies can also help guide better environmental performance, for example, by bringing attention to reducing or offsetting the carbon footprints of business travelers and international assignees. These policies could involve:

• Setting guidelines for determining when virtual meetings are preferred over in-person meetings that require travel.
• Enabling virtual secondments, where the work is done remotely from the employee’s home location.
• Supporting longer-term business travel, where an employee stays in a host location for a longer term instead of more frequent trips back and forth to get a project done.
• Calculating employee carbon footprints and including carbon offsets in global talent mobility policies and practices.

There is pent-up demand for international moves that have been paused due to COVID-19 and companies are now restarting international moves and business trips. However, they are more carefully considering the risks and consequences and taking steps to monitor and control employee mobility, as well as actively manage compliance obligations and ESG implications.

In a KPMG survey on ESG Considerations for Global Mobility and Reward Programs, nearly half of the respondents said their sustainability agenda would affect their return to business travel and about 40 percent of respondents expect to implement a new approach to sustainable travel after the pandemic. Some respondents also said ESG considerations may lead their companies to become more selective about international assignments, and some said they intend to source more talent locally.

As the focus on ESG performance intensifies, global talent mobility teams will need to bring a new mindset toward aligning their programs and operating models in ways that help make their companies more sustainable, socially responsible, and accountable.

Marc Burrows Head of Global Mobility Services KPMG International [email protected]

Just as lockdowns and stay-at-home orders spurred the move to remote work, these measures also interrupted many international assignments that were planned or in progress when the pandemic began.

As COVID-19 infection rates fluctuated from one country to another, some international assignees were given the option to return home or stay at their host country location or temporarily move to another country to continue their assignments remotely.

In concept, conducting cross-border assignments virtually has some obvious advantages in reducing the administration and disruption involved in a temporary international move, as well as eliminating the need for relocation support and ongoing housing and living allowances.

Employees have become used to utilizing technology to effectively work cross-team without the need for in-person meetings. In the future, if a comparable business objective can be achieved without sending an employee abroad, companies could lean toward a virtual assignment option rather than a traditional expat assignment, as it could be significantly cheaper to administer.

Virtual assignments still create some notable tax and compliance obligations, and while this area continues to evolve, there is a heightened risk of unforeseen tax liabilities and non-compliance. Immigration and labor laws, corporate tax risks, employee cost charging, and payroll reporting obligations also need to be addressed.

As certainty increases in travel and organizations become more experienced in leveraging virtual assignments, the creation and application of a clear and comprehensive policy to structure such arrangements and mitigate the related risks will be vital.

While virtual assignments are likely here to stay, there are experiential and intangible benefits of physical international assignments/transfers which a virtual assignment will never replicate. As a result, we expect virtual assignments will simply be an additional armament for organizations to leverage in the war for talent.

Craig Robinson Director, People Services KPMG Australia [email protected]

With increasingly mobile, virtually connected workforces creating risk in areas such as tax, social security, immigration, and employment laws, managing compliance will be even more challenging and the stakes will be higher for organizations to ensure global compliance.

During the pandemic, many tax authorities took a lenient approach to residency and other tax issues created by remote workers. As governments turn their attention to the recovery and restoring their treasuries, tax authorities may well enhance their approach to compliance, especially as temporary emergency remote work situations evolve into more formal arrangements. It’s also possible that tax authorities could introduce new tax reporting rules to deal directly with organizations and employees in remote work situations.

In addition to financial risks, non-compliance could bear more reputational risk. In the years before 2020, social attitudes toward tax responsibility were already changing, with rising calls for companies to be more transparent about their tax strategies. After the pandemic, we expect there will be even more scrutiny of how companies manage their tax obligations and the extent of their contributions to the communities they operate in.

During the recovery and beyond, it will be crucial for talent mobility teams to monitor the local laws and keep up with any changes in their interpretation by tax and other regulatory authorities. They can then help their companies understand the compliance risks and set clear policies for employee movements, supported with clear guidance on the dos and don’ts for avoiding exposures.

Bob Mischler National Principal-in-Charge, Global Mobility Services KPMG in the US [email protected]

As global talent mobility teams confront rising complexity and risk, they also face demands from their own management, finance departments, business units, tax authorities, and other regulators — all requesting more information with tighter turnaround times. This new reality requires a future-focused approach to managing both internal risks across the organization and external risks from local, domestic, and international regulators. To do so, more and more companies are looking to advancing technology to provide a comprehensive data management solution that acts as a 'single source of truth' that spans the whole spectrum of mobility.

As part of this focus on digital transformation, many global talent mobility teams are evaluating how to bring further innovations to their business models and how technology can augment their human workforce and expand mobility’s strategic abilities. According to the results of KPMG’s GAPP Survey report, participants are particularly interested in solutions for automating assignment initiations, producing assignment cost projections, and creating assignment documents.

Introducing artificial intelligence and robotics for repetitive tasks can bring in more efficiency and reduce operating costs. More importantly, it can also help shift mobility teams to higher value tasks, providing more rewarding challenges and helping with employee retention. Mobility teams can also use automation to speed up administrative and transactional processes and to deliver a better experience for assignees and employees who are training, onboarding, and collaborating with colleagues in other locations.

However, KPMG’s 2021 GAPP Survey report also shows that many mobility teams are not yet realizing the benefits of these advances. Sixty-three percent of respondents said their global talent mobility teams do not have a strategic vision for automation and robotics, while 65 percent are not using automation to streamline portions of the global mobility process.

Regardless, technology is leading the way. KPMG predicts that within five years, global talent mobility teams will focus more on supporting higher value talent mobility objectives, including development and retention objectives across employment lifecycles versus administrative processes and transactions that will benefit from increased automation and artificial intelligence.

Frederic Le Gall Global Mobility Services Partner, Head of Technology KPMG in Switzerland [email protected]

As companies invest in digital transformation, they can gain easier access to higher-quality data across the organization. In fact, global mobility sits at a unique crossroads within the organization, bridging HR, finance, and tax. Therefore, global mobility often has access to a more complete data than other parts of the business. For global mobility, this rich mine of current and historical data can enable powerful predictive workforce analytics to support program success and measure assignee experiences. This helps enable evidence-based decisions and ensure that global mobility, talent, and human capital are aligned with broader organizational goals.

Thirty-two percent of KPMG’s 2021 GAPP Survey respondents reported that they are using analytics to guide their global mobility policy and decision-making. Supporting the strategic partnership between global mobility and the business is the primary value that participants believe mobility analytics can bring to the organization, while also providing a foundation for policy and process decisions. Of the various mobility analytics metrics, assignment costs (91 percent), employee satisfaction (64 percent) and budget versus actual costs (62 percent) are the top three metrics (operational or assignment related) that respondents believe bring the most value to internal stakeholders currently.

As digital transformation continues and mobility teams grow more adept in their use of analytic techniques to predict wider patterns, trends, and irregularities, we believe they will be able to contribute significantly more value by delivering strategic insights into areas such as:

• Operational effectiveness across multiple business units
• Assignment spend, cost control and budgeting
• Root cause analysis of rising costs
• Employee attrition statistics and outliers (for both internal and assignee-based analytics)
• Post-repatriation retention and attrition
• Business traveler and equity compensation exposure analysis
• Career mobility and business unit success

These types of insights can promote higher-quality, strategic business decisions and help elevate the profile of global mobility teams across organizations as strategic business partners who create value.

Robert Smith Senior Manager, Global Mobility Services KPMG in the US [email protected]

Many global organizations are pursuing strategies to improve employee DEI. We expect global mobility teams will provide increasing support in this area given their shared objectives. DEI and mobility leaders are each looking to attract the best talent and critical new skills for the future; fill talent gaps temporarily or permanently; and provide innovative opportunities to engage, develop and retain their most valuable employees.

DEI provides equal opportunities for all employees and promotes acceptance, understanding and the value of enabling the best organization for everyone. A formal DEI initiative embedded in an organization’s values and culture can also create an innovative, productive environment that’s better positioned to meet organizational goals. Diverse workplaces produce diverse thinking, ideas, and skills – all of which are crucial in an environment of disruption, uncertainty, and opportunity.

Where global mobility is concerned, companies have much to gain by aligning mobility programs with their DEI agenda. With strategies that address both mobility and broader talent management needs, mobility teams can help turn challenges into talent and business development opportunities. Competitive advantages can be achieved, for example, by reviewing program demographics, designing strategies for broader talent pools, and creating broader educational and communication plans for audience expansion and penetration.

Diversifying global mobility policies and programs for wider applications can help keep key DEI objectives front and center. Seeking out and valuing diversity in all its forms can help ensure that all talents are utilized and aligned with the organization’s talent, culture, brand and business development goals, with the aim of creating an organization that embraces the full spectrum and power of diversity.

Some leading practices for embedding DEI into global mobility programs include:

• Linking the company’s general recruitment strategy to the selection of prospective global mobility candidates
• Using diverse candidate slates for international assignments
• Visibly targeting diverse groups for international assignment opportunities, including women, racial and ethnic minorities, and LGBTQ candidates
• Factoring in more lead times for diverse talent assignees, as they may require more time for pre-assignment activities

The clear overlap between DEI and global mobility creates strong synergies for formally aligning international assignment programs with the broader DEI agenda. Global mobility leaders can contribute significant insights, knowledge and experience in mobilizing and supporting the growth, development, and retention of a diverse pool of talent.

Nita Patel Partner, Global Mobility Services KPMG in the US [email protected]

Companies are taking a more purposeful approach to mobilizing talent globally by strengthening the connections between talent management and talent mobility. Even during 2021, 93 percent of 2021 KPMG GAPP Survey participants still ranked supporting overall business and talent development objectives as a top program goal for their international assignments.

In a world where employees can be hired from and work anywhere, attracting and retaining the right people will be more important than ever. Before the rise of remote work, it was a well-known fact that being able to retain people that build the organizational culture and focus on employee morale promoted retention and organizational growth. As virtual working practices are becoming more prominent, increased training on emotional intelligence (EQ) and building virtual teams will be top of mind for many organizations. Being able to identify and measure these skills in the performance management process and determining their value in compensation discussions will be important for business success.

In addition to EQ and team building, trust in the virtual work environment is going to be more important than ever. Managerial styles and approaches will need to be assessed and measured, with mechanisms for upward feedback becoming increasingly more important. Knowing you are hiring and retaining employees and leaders that you can trust with the professional development and emotional well-being of their teams will be a primary talent management objective.

As both talent management and global mobility become leaner, more strategic, and more aligned with broader organizational strategy, their talent planning and workforce building activities will become more integrated. Uniting the two teams within a comprehensive “talent mobility” function may be the logical next step. By joining forces, the new team can be better placed to view talent through a global lens and to collaborate on building the best possible experience for their employees while delivering value and maintaining global compliance.

Chris Cowell Partner, Global Mobility Services KPMG in the UK [email protected]

With fewer traditional relocations, more assignment flexibility and an emphasis on cost savings, many companies may look to outsource more of their global mobility and payroll programs. As business travel and international assignments return, this could be especially true for companies that were forced to downsize their internal teams for the pandemic’s duration.

KPMG predicts a greater focus on talent, not transactions. Fast-moving companies do not want to be bogged down in transactions and typically outsource high-volume complex transactions like tax, payroll, compensation, equity, and business traveler activity so they can focus on providing a superb employee experience, participate in talent planning and workforce shaping with HR, and demonstrate a return on investment for the company on mobility spend.

In fact, one of the key benefits of managed services is the ability to rely on the provider to adjust resources up and down in pace with mobility service demands.

Other key reasons why companies may opt for managed services models include:

• Opportunities to streamline global mobility activities and tasks to achieve system and process efficiencies, often via technology enhancements available through third-party service providers
• Lower head counts
• Less need to invest in developing and maintaining homegrown mobility software solutions
• Improved processes that eliminate redundant efforts and enhance the use of technology interfaces between vendor and company systems
• Access to the global resources, leading practices, and proven know-how of the vendor organizations.

From immigration and logistical relocation support to compensation/payroll to assignee tax reimbursements and compliance, companies can choose to outsource some or all the tactical functions of global mobility while retaining ownership and accountability for the program. In KPMG’s 2021 GAPP Survey, tax preparation services (90 percent), immigration services (92 percent), and relocation management services (84 percent) were the activities most commonly outsourced to support mobility logistics and global compliance.

Along with the potential for securing greater program cost efficiencies, and faster and more consistent service delivery, engaging third-party providers can help create a more satisfying environment for leaner and more strategically-focused mobility teams, with less routine and more work that delivers challenge, variety and intellectual reward. Rather than spending time on day-to-day administration, talent mobility teams will be freed to play a more strategic role in supporting core business initiatives.

Achim Mossmann Principal, Global Mobility Services KPMG in the US [email protected]

In summary, companies and businesses may want to reimagine how they view their mobility and talent functions as they merge into nimble talent mobility teams in a complex environment rife with risk, compliance, and regulatory challenges. At the same time, we anticipate they’ll apply new processes, technologies, and skills to support the business with more efficiency and use data-driven insights to deliver value. Based on the transformations already seen in progress, we believe the future will see talent mobility functions that are digitized, leaner, more focused on talent, more inclusive, and more integrated as true strategic partners with the business.

Throughout this [document/film/release/website], “we”, “KPMG”, “us” and “our” refers to the global organization or to one or more of the member firms of KPMG International Limited (“KPMG International”), each of which is a separate legal entity.

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The Morning

Baruch college, an upward-mobility machine.

The New York school is praised as a model college in a new report on diversity in higher education.

By David Leonhardt

City College of New York often serves as a nostalgic symbol of American higher education’s past. The college did not charge tuition for decades, and its students, many of them poor, went on to become Nobel laureates, chief executives, civil rights leaders and more. By contrast, higher education today can seem both less accessible and less rigorous.

But it turns out that the school that occupies City College’s original 19th-century campus, on the East Side of Manhattan, has done a fine job of living up to its predecessor’s legacy.

That school is Baruch College, and it is an upward-mobility machine.

More than 60 percent of Baruch students receive Pell grants, which means they typically come from the bottom half of the income distribution. About 75 percent of undergraduates are people of color. The average annual cost of attending Baruch for low-income students is less than $2,000. And Baruch’s six-year graduation rate is 74 percent, well above the national average.

When I asked S. David Wu, an engineering scholar who is Baruch’s president, about City College’s original vision of educating the masses, he told me, “In many ways, Baruch is realizing that vision, but in a 21st-century way.”

In today’s newsletter, I’ll tell you about a new report that tracks how other colleges are doing.

A worrisome decline

After Michael Bloomberg finished being mayor of New York City in 2013, he turned his attention to philanthropy and decided that increasing economic diversity in higher education was a priority. “America needs to have as big a pool of talented, hard-working, well-educated people as it can possibly get,” Bloomberg told me.

His main program is known as the American Talent Initiative, and its goal is to persuade colleges with high graduation rates to diversify. This morning, the group released its latest report , and it praises Baruch as a model college.

“There are very few colleges in the country like Baruch,” said Josh Wyner of the Aspen Institute, which helps run the American Talent Initiative. Indeed, among all U.S. colleges with a graduation rate above 70 percent, Baruch may be the most economically diverse. It both holds down tuition costs and creates clear pathways for students to earn degrees, Wyner said.

Other parts of the new report, however, are worrisome.

Bloomberg’s group set a goal almost a decade ago: Lift the annual enrollment of low- and moderate-income students at colleges with high graduation rates by 50,000 — or roughly 10 percent. The group planned to do so partly by building a membership organization where colleges could share strategies.

Initially, the progress was impressive. Enrollment jumped by more than 20,000 in the initiative’s first three years, putting it comfortably on pace to achieve the goal within a decade.

But momentum stalled in 2019-20. The reasons weren’t completely clear, but I’ve noticed that economic diversity often declines when college administrators aren’t paying close attention. Other priorities — sports teams, fund-raising, U.S. News’s rankings — take over. Covid made the situation worse, by exacerbating K-12 inequality and preventing some lower-income students from making it to college.

By fall 2021, all the early progress had been erased. Enrollment of lower-income students at colleges with high graduation rates was slightly below its 2015 level.

In response, the initiative got tougher. To remain members, college now must commit to specific lower-income enrollment levels, rather than vaguely promising to make progress. A small number of colleges have since dropped out. Among them, according to public records, were Penn State and Virginia Tech, as well as several private schools, including Wake Forest, which is among the country’s least economically diverse colleges, and Denison, in Ohio.

( This Times feature lets you look up economic diversity at nearly 300 colleges.)

But 125 colleges remained, including the entire Ivy League and the flagship state universities in California, Michigan, Texas and Wisconsin. About 15 schools more have recently joined. Baruch is among them, as are Colorado College, Illinois State and Towson.

At these member schools, lower-income enrollment has fully recovered from its recent decline. Updated data isn’t available for the roughly 200 other colleges with a graduation rate of at least 70 percent, but their trend is unlikely to be so positive:

Successful strategies

The new report cities several promising strategies for lifting diversity, such as:

Reduce so-called merit aid , which tends to go to affluent students, and direct scholarships to students who demonstrate both academic excellence and financial need. Boston University has recently done so.

Recruit more transfers from community colleges , where top students from modest backgrounds often start . Central Florida, Dayton, George Mason and the University of California all emphasize community-college transfers, and Princeton recently started a program.

Help students navigate higher education . Its bureaucracy can be so maddening that it keeps students from graduating. In response, Baruch has created an office called BOSS — Baruch One Stop Shop — where students can get help enrolling in classes or filling out aid forms. The college has also created cohorts of first-year students who take classes together and can help one another.

Baruch’s mission, Wu told me, is to educate a student body that resembles society at large — and increase upward mobility as a result. “Our diversity,” he said, “very much reflects the diversity of New York.”

Some colleges will soon charge $100,000 a year. My colleague Ron Lieber explains how it happened.

President Biden will announce student debt relief for millions of borrowers in a Wisconsin speech.

THE LATEST NEWS

Israel-hamas war.

The Israeli military has reduced the number of troops in Gaza. Only a fraction of the soldiers that it deployed to the enclave earlier in the war remain.

Despite the drawdown of troops, the military has promised a future mission in Rafah , southern Gaza.

The war reached the six-month mark with the conflict at an impasse.

Nicaragua, a supporter of Palestine, is bringing a case against Germany at the International Court of Justice for supplying arms to Israel.

War in Ukraine

Some Ukrainians, unable or unwilling to leave home, remain in villages on the front lines. See photos .

Donald Trump has a secret, long-shot plan to end the war by pressuring Ukraine to give up some territory, The Washington Post reports.

“I am still learning how to forgive”: Rwandans marked 30 years since a genocide there killed around 800,000 people.

A British endurance athlete known as the Hardest Geezer ran the length of Africa in just under a year , The Guardian reports.

Trump has made many populist promises, but many corporate executives believe that his second-term agenda couldn’t really happen . They might be in denial.

Trump said at a fund-raiser that he wants immigrants in the U.S. from “nice” countries “like Denmark.”

An examination of Trump’s public statements revealed how he distorts his opponents’ record and exaggerates.

Many of today’s seniors have voted Democratic at every stage of their lives. Nate Cohn explains why .

A bipartisan group of former national security officials have asked lawmakers to impose limits on a president’s power to deploy troops on domestic soil .

Other Big Stories

The U.S. will experience its second total solar eclipse in seven years today. Read how to watch and see the cloud forecast where you are .

In coastal cities, commuters — spurred by new routes and faster boats — are using ferries to get around .

A Southwest Boeing 737-800 made an emergency landing after an engine cover fell off during takeoff.

Maryland passed two privacy bills that limit how tech platforms can harvest and use personal data of consumers and young people.

Economists sent similar résumés to job postings at about 100 of the largest U.S. companies — but changed the applicants’ names to suggest an ethnicity. Some companies discriminated against Black applicants much more than others.

America was once the country begging richer allies for help. It can pay it back by supporting Ukraine , Stacy Schiff writes.

If Gmail is making you miserable, stop using it , as Ezra Klein has.

Gail Collins and Bret Stephens discuss the election and tech regulation .

Here are columns by David French on the parallels between Gaza and Iraq and Maureen Dowd on Trump’s “blood bath” comments .

MORNING READS

Away games: Meet a group of New Yorkers who pooled money to buy a Danish minor league soccer team .

Health tech: Patients can pay to have artificial intelligence read their mammograms. Experts are both excited and concerned .

Metropolitan Diary: Best taxi ride in 50 years .

Lives Lived: Albert Heath was a virtuoso jazz drummer who collaborated with John Coltrane and Nina Simone. He died at 88 .

Women’s college basketball: South Carolina beat Iowa , 87-75, to win their second national title in three years. Iowa’s defeat comes days before Caitlin Clark is expected to be the No. 1 pick in the W.N.B.A. Draft.

A G.O.A.T.: Dawn Staley, South Carolina’s coach, thanked Clark for making women’s basketball more popular. “ She carried a heavy load ,” Staley said. Read about Clark’s collegiate career .

Men’s college basketball: John Calipari is nearing a deal to coach at Arkansas .

UConn: The Huskies face Zach Edey and Purdue with a chance to become the first repeat men’s college basketball national champions since Florida in 2006 and 2007.

ARTS AND IDEAS

“University Challenge”: The New Yorker Brandon Blackwell knew that if he wanted to have a career in competitive quizzing, he had to move to its epicenter: London.

Despite already having a degree, he applied to Imperial College London to get a visa. Then, he competed for the college on the Britain’s premier quiz show, “University Challenge.” Blackwell’s appearance on the show in 2020 turned him into a national figure and Imperial — which had not won the competition since 2001 — into a “University Challenge” powerhouse .

More on culture

The “3 Body Problem,” a Netflix show, has outraged people in China despite it being from the country. That highlights how censorship has shaped public opinion , Li Yuan writes.

For nearly two decades, a gang stole items from small U.S. museums , including Yogi Berra’s championship rings.

In the finale of “Curb Your Enthusiasm,” Larry David essentially restaged the contentious “Seinfeld” ending, The Washington Post reports.

THE MORNING RECOMMENDS …

Finish any blend of cheese in your fridge with this quick stovetop mac and cheese .

Trick your brain to love running with these three tips .

Buy a gift for under $25 .

Keep your dog warm and dry on rainy days with a raincoat .

Take our news quiz .

Here is today’s Spelling Bee . Yesterday’s pangrams were curtain and taciturn .

And here are today’s Mini Crossword , Wordle , Sudoku , Connections and Strands .

Thanks for spending part of your morning with The Times. See you tomorrow. — David

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David Leonhardt runs The Morning , The Times’s flagship daily newsletter. Since joining The Times in 1999, he has been an economics columnist, opinion columnist, head of the Washington bureau and founding editor of the Upshot section, among other roles. More about David Leonhardt