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 single pool with many servers, 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 (abandonment distribution) for waiting that depends on their individual service requirement, or due to having their service-time distribution be a function of the time spent in queue. We refer to the former dependence mechanism as "exogenous dependence" and to that latter as "endogenous dependence." Since exact analysis of the stochastic system under either dependence mechanism is intractable, we propose a deterministic approximation for 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 are constant (and staffing levels are fixed), 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. However, the UFM may possess multiple equilibria, with each equilibrium point being either locally stable--so that any trajectory of the UFM passing through a neighborhood of that point will converge to it--or unstable, so that any trajectory is repelled away from that point (unless the UFM is initialized at that point). The implications for the stochastic system of the UFM having multiple equilibrium points are two-fold. First, the stochastic fluctuations in steady state may be an order of magnitude larger than the typical fluctuations in many-server queueing systems. Second, the system may experience congestion collapse, namely, the system is substantially more congested than it should be under the current staffing and arrival rate (e.g., an underloaded system may get "stuck" in a severe overload state). Simulation examples verify the accuracy of the UFM, and demonstrate the implications of our analyses to the stochastic system that the UFM approximates.