Passengers Matter: Why Transit Assignment is the Key to TfL’s Route Changes

The recent announcement by Transport for London (TfL) regarding cuts to key bus routes like the 19, 38, 259, and 349 is more than a simple operational adjustment; it is a textbook example of a complex network design problem that requires rigorous mathematical modeling to solve effectively.

The Challenge: More Than Just Matching Supply to Demand

TfL justifies these changes by citing reduced passenger numbers and the need to "better match levels of service with passenger demand." On the surface, this sounds reasonable. The 279 bus carries 9.7 million passengers annually, yet TfL plans to shorten it from Manor House to Stamford Hill, removing the direct link to the Piccadilly line. The 349, despite serving 4.2 million passengers, is slated for complete withdrawal due to "significant overlap" with other routes.

But here's the critical oversight: passenger demand is not a fixed input—it is an output of the network design itself.

The Bi-Level Programming Framework

In my research, I formalize this type of decision-making as a Bi-level Programming problem. As demonstrated in my study, Transit route and frequency design: Bi-level modeling and hybrid ABC approach, the formulation involves two distinct but interacting levels:

1. The Upper Level (Operator/TfL): This level seeks to minimize total operating costs and fleet size—exactly what TfL is attempting by removing "duplication" and reducing frequencies on routes like the 38 (from every 6 minutes to every 12 minutes on evenings and Sundays).

2. The Lower Level (Passengers): Passengers react to these changes by adjusting their behavior to maximize their own utility (minimizing travel time, transfers, and cost).

The danger lies in treating the Lower Level as static. When a direct link like the 349 between Ponders End and Stamford Hill is axed, passengers don't simply vanish—they re-optimize their paths. This redistribution of flow can lead to unexpected congestion elsewhere in the network, a phenomenon I explored in Transit assignment: Approach-based formulation, extragradient method, and paradox, which is closely related to the Braess Paradox.

Beyond Simple Route Choice

The "9.7 million passengers" or "4.2 million passengers" cited in the news are not immutable facts. They are the result of complex behavioral choices involving multiple dimensions:

Route Choice

If the 19 is shortened to terminate at Victoria rather than Battersea Bridge, passengers heading to King's Road or Sloane Square must find alternative paths, potentially overloading substitute routes. TfL acknowledges this, stating that 356 passengers per day on the 19 would need to change buses—but this is a static estimate that ignores induced demand shifts.

Departure Time Choice

Reduced frequency forces passengers to alter when they travel. The 38 dropping from every 7-8 minutes to every 12 minutes on Sundays doesn't just mean longer waits but could be a further reduction in the patronage.

Mode Choice and Bounded Rationality

In Incorporating personalization and bounded rationality into stochastic transit assignment model, I highlighted that passengers have bounded rationality. A "theoretical" alternative route that requires two transfers might be rejected if it exceeds a passenger's complexity threshold, pushing them toward private cars or ride-hailing—effectively defeating the public transport purpose and increasing road congestion.

The Reliability Imperative

TfL's justification often relies on "average" demand. However, my research consistently emphasizes the importance of Reliability-Based Transit Assignment. As shown in Reliability-Based Transit Assignment for Congested Stochastic Transit Networks, robust network design must account for the variability of travel times and demand.

A frequency cut on the 38 or 279 might look acceptable on paper for average demand, but it strips the system of the resilience needed to handle day-to-day fluctuations. The news specifically mentions that the 424 is "often unreliable due to congestion"—cutting frequency on similar routes will only exacerbate this issue during peak demand periods.

The Case of the 19: An Icon at Risk

The 19 bus is not just another route—it was immortalized in the Dire Straits song "Wild West End" and has been operating for 120 years. Beyond its cultural significance, it serves critical destinations including Great Ormond Street children's hospital. TfL estimates 1,007 passengers per day on the 38 would need to change buses—a number that seems to ignore the cumulative network effects and the real-world reluctance of passengers (especially those with children or health concerns) to make additional transfers.

How Our Expertise Can Contribute

Restructuring the London bus network is necessary for efficiency, but it must be approached with quantitative rigor, not just spreadsheet arithmetic. Decision-makers should:

1. Employ Bi-level Optimization Models that simulate the complex, adaptive behavior of passengers in response to network changes.

2. Account for Induced Demand Shifts rather than treating current passenger counts as fixed constraints.

3. Prioritize Reliability Over Average Cost by stress-testing proposed cuts against demand variability and peak-period scenarios.

4. Consider Behavioral Complexity including transfer aversion, bounded rationality, and mode choice elasticity.

Without this, cost-saving measures risk degrading overall network performance—saving money at the operational level while costing passengers significantly in time, reliability, and ultimately, driving them away from public transport altogether.

References

• Jiang, Y., Szeto, W.Y., 2014. Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach. Transportation Research Part B: Methodological 67, 111-131.
• Jiang, Y., Szeto, W.Y., 2014. Transit assignment: Approach-based formulation, extragradient method, and paradox. Transportation Research Part B: Methodological 68, 1-23.
• Jiang, Y., Szeto, W.Y., Long, J., Han, K., 2020. Modeling and optimizing a fare incentive strategy to manage queuing and crowding in mass transit systems. Transportation Research Part B: Methodological 138, 247-271.
• Jiang, Y., Tirachini, A., Cottrill, C.D., 2021. Incorporating personalization and bounded rationality into stochastic transit assignment model. Transportation Research Part C: Emerging Technologies 127, 103127.