Where to Put Traffic Sensors When Demand Is Linked and Sensors Fail

Cities and transportation agencies want to know where trips start and where they end. They learn this from traffic sensors. Sensors are costly, so no agency can cover every road. The question is where to put a limited number of them. A paper in Transportation Research Part C: Emerging Technologies offers an answer. It holds up under two real-world conditions: linked demand and failing hardware.

Emily Zhu, Associate Professor of Information Systems and Analytics at McCoy College of Business, is a co-author. She publishes under the name Emily Zhu Fainman. Her co-authors are Weiwei Sun and Junlin Li of Fuyang Normal University, Hu Shao of China University of Mining and Technology, and Ting Wu of Nanjing University. All four are in China.

The problem

Planners describe travel as origin-destination demand, or OD demand. It is the number of trips between each pair of starting points and endpoints in a network. Sensors do not measure it directly. They measure flows on particular roads, and analysts work backward to estimate OD demand.

Two things make that harder than it looks. First, demand is correlated in space and time. A busy corridor in the morning tells you something about a connected corridor later in the day. Second, sensors break. Their failure rate changes as they age, and it differs by sensor type. Most placement models ignore one or both of these facts.

The study

The researchers build optimization models that choose sites for two kinds of sensors. Count sensors tally vehicles passing a point. Automatic vehicle identification (AVI) sensors recognize individual vehicles, which helps trace routes.

To handle correlation, the models estimate both the average OD demand and its covariance. Covariance measures how demand between different pairs and periods rises and falls together. The models then set an upper bound on estimation error. That means they do not need to know true demand in advance, which no planner has.

To handle failure, the authors use the Weibull distribution. It is a standard statistical tool for failure rates that follow a bathtub shape. Failures are high early, low in mid-life, and rise again with age. They fit its parameters to data with nonlinear least squares, a common curve-fitting method.

The models cover two settings. One is a network with no sensors yet. The other adds sensors to a network that already has some. Each model has two goals at once: reduce error in the demand average and reduce error in the covariance. Because two goals rarely agree, the authors use a non-dominated sorting genetic algorithm. It is a search method that produces a set of trade-off solutions rather than a single answer.

What the researchers found

In numerical examples, the best placement shifted with four factors. They were the strength of demand correlation, the sensor failure rate over time, the sensor types available, and the budget. According to the abstract, the proposed models produced more precise estimates and reached solutions faster than the alternatives tested.

What it means for managers

The direct audience is transportation agencies and the firms that design monitoring networks for them. The lesson is that correlation and equipment failure are not background noise. They change the right answer about where to spend.

The same logic applies to any operation that monitors flows with a limited number of sensors. Logistics networks, warehouse systems, and utilities all face the choice of where to measure. A plan that accounts for connected demand and aging equipment will need fewer surprises and fewer emergency replacements.

This summary is based on the paper’s abstract. The full article reports the data, methods, and detailed results.

What it means for managers

• Sensor placement should reflect how demand is connected. Flows between different origin-destination pairs and across time periods are related, and a placement plan that uses that structure needs fewer blind spots.
• Plan for sensors to fail. Failure rates change with age and differ by sensor type. Building that into the placement decision changes where the sensors go.
• Budget and sensor mix matter together. The models let an agency weigh counters against vehicle identification readers, and add to an existing network rather than start over.

Sun, W., Shao, H., Li, J., Wu, T., & Fainman, E. Z. (2025). Multi-type traffic sensor location problem for origin-destination estimation considering spatiotemporal correlation and sensor failure. Transportation Research Part C: Emerging Technologies, 179, 105288. 10.1016/j.trc.2025.105288