Robust Management of Airport Security Queues Considering Passenger Non-compliance with Chance-Constrained Optimization

TL;DR

The paper addresses airport security queueing under uncertain passenger compliance to recommended arrival slots by formulating a second-order cone program with chance constraints that accounts for compliance variability via $\alpha_{it} \sim \mathcal{N}(\mu_{it}, \sigma_{it})$ and employs a lead-time distribution $p_i(t)$. The method yields two models: a deterministic baseline and a robust chance-constrained model, both evaluated against a BCN case study; the chance-constrained approach attains up to $85\%$ reduction in total waiting time, about $30\%$ more than the deterministic compliant model, and distributes arrivals more evenly during peak periods. The key contributions include a rigorous SOC reformulation of queue-capacity constraints under uncertainty and the integration of lead-time uncertainty into arrival-slot planning, providing a practical framework for robust airport queue management. This work offers significant operational implications for reducing security delays and informs future enhancements to incorporate flight-level compliance variability and staffing decisions, with potential field validation.

Abstract

The long waiting time at airport security has become an emergent issue as demand for air travel continues to grow. Not only does queuing at security cause passengers to miss their flights, but also reduce the amount of time passengers spend at the airport post-security, potentially leading to less revenue for the airport operator. One of the key issues to address to reduce waiting time is the management of arrival priority. As passengers on later flights can arrive before passengers on earlier flights, the security system does not always process passengers in the order of the degree of urgency. In this paper, we propose a chance-constrained optimization model that decides in which time slot passengers should be recommended to arrive. We use chance constraints to obtain solutions that take the uncertainty in passenger non-compliance into account. The experimental results, based on a sample day of flight schedules at the Barcelona airport, show a reduction of 85% in the total waiting time. Compared to the deterministic case, in which passengers are assumed to fully comply with the recommendations, we see a 30% increase in the reduction of the total waiting time. This highlights the importance of considering variation in passenger compliance in the management of airport security queues.

Figures (4)

• Figure 1: Distribution of lead time for passengers on flight $i$. Lead time is defined as the difference in time between when a passenger arrives at security and when the flight departs. The above distribution is defined with a mean $\mu=64$, standard deviation $\sigma=30$, and a skewness parameter $\alpha=3$. The notation $\beta_{it}$ is the probability mass of passengers arriving in the $t^{\text{th}}$ slot prior to flight departure.
• Figure 2: Solution to the two optimization problems. A) Solution to the deterministic optimization problem. B) Solution to the chance-constrained optimization problem assuming a average compliance rate, $\alpha_{it}$ of 0.7 with a standard deviation of 0.2. The reliability factor, $\gamma$, is set to 0.01.
• Figure 3: Queuing diagram of security checkpoint. We assume a capacity of 800 passengers per time slot
• Figure 4: Sensitivity analysis. We vary one parameter while keeping the rest fixed for comparison. (A)-(C) shows the solutions when varying $\gamma$. (D)-(F) shows the solutions when varying $\mu$. (G)-(I) shows the solutions when varying $\sigma$