Research

Airlines tend to design their flights schedules with the primary concern of the minimization of operational costs. However, the recently emerging idea of resilient scheduling defined as staying operational in case of unexpected disruptions and adaptability should be of great importance for airlines as well due to the high opportunity costs caused by the flight cancellations and passenger inconvenience caused by delays in the schedule. In this study, we integrate resilient airline schedule design, aircraft routing and fleet assignment problems with uncertain non-cruise times and controllable cruise times. We follow a data-driven method to estimate flight delay probabilities to calculate the airport congestion coefficients required for the probability distributions of non-cruise time random variables. We formulate the problem as a bi-criteria nonlinear mixed integer mathematical model with chance constraints. The nonlinearity caused by the fuel consumption and CO2 emission function associated with the controllable cruise times in our first objective is handled by second order conic inequalities. We minimize the total absolute deviation of the aircraft path variability’s from the average in our second objective to generate balanced schedules in terms of resilience. We compare the recovery performances of our proposed schedules to the minimum cost schedules by a scenario-based posterior analysis.

We consider queueing systems with a large agent pool, assuming the service time of each customer depends on the delay of that customer in queue. Such dependence can be due to the customers having patience for waiting that depends on their individual service requirement, or due to having their service-time distribution being a function of the time spent in queue. We refer to the former dependence mechanism as exogenous and to that latter as endogenous. Since exact analysis of the stochastic system under either dependence mechanism is intractable, we propose a deterministic approximation of the (mean) queueing dynamics, and refer to that approximation as a Unified Fluid Model (UFM) since it captures both dependence mechanisms simultaneously. When the arrival rates and staffing levels are constant, we characterize conditions for the existence of a unique stationary point for the UFM, and prove that those conditions always hold when the dependence is exogenous. In the endogenous-dependence case, the UFM may possess multiple equilibria, with each equilibrium point being either locally stable, so that any trajectory of the UFM passing in a neighborhood of that point will converge to it, or unstable, so that any trajectory is “repelled” from that point (unless initialized at that point). The implications for the stochastic system of the UFM having multiple equilibria are twofold: First, the stochastic fluctuations may be an order of magnitude larger than the typical fluctuations in many-server systems. Second, the system may experience congestion collapse, namely, become substantially more congested than it should be under the current staffing level and arrival rate.

Service systems often exhibit complex dynamics when customer service times depend on the delay experienced in queue, a phenomenon observed across various settings such as healthcare and hospitality. This delay-dependent service time introduces non-Markovian dynamics that render exact analysis of large service systems intractable. Deterministic fluid models approximating the system dynamics uncover some operational challenges arising from delay-dependence. These systems can exhibit multi-stability, where the queue fluctuates between multiple equilibria. In large systems, these transitions become infrequent, potentially leading to prolonged periods of severe congestion referred as congestion collapse. Conversely, in smaller systems, the system frequently shifts between equilibria, causing high variability. To mitigate these issues, we propose two tailored strategies: For large systems, we introduce the “slingshot policy”, a dynamic control that alternates between first-come-first-served (FCFS) and last-come-first-served (LCFS) scheduling to stabilize the system at the more desirable equilibrium. For smaller systems, we propose a “depooling mechanism”, where the service pool is strategically divided into smaller, uni-stable subsystems, effectively eliminating multi-stability at the design stage. Our framework provides actionable solutions for system design and control. The proposed approaches are supported by both theoretical analysis and simulation studies, offering practical insights to improve the stability, reliability, and efficiency of service systems affected by delay-dependent dynamics.