Burke’s theorem is a well-known fundamental result in queueing theory, stating that a stationary M/M/1 queue has a departure process that is identical in law to the arrival process and, moreover, for each time t , the following three random objects are independent: the queue length at time t , the arrival process after t and the departure process before t . Burke’s theorem also holds for a stat...

As the air traffic increases at a hub airport, some flights cannot land or depart at their preferred target time. This event happens because the airport runways become occupied to near their capacity. It results in extra costs for both passengers and airlines because of the loss of connecting flights or more waiting, more fuel consumption, rescheduling crew members, etc. Hence, devising an appr...

In terminal airspace, integrating arrivals and departures with shared waypoints provides the potential of improving operational efficiency by allowing direct routes when possible. Incorporating stochastic evaluation as a post-analysis process of deterministic optimization, and imposing a safety buffer in deterministic optimization, are two ways to learn and alleviate the impact of uncertainty a...

We consider a discrete population of users with homogeneous service demand who need to decide when to arrive to a system in which the service rate deteriorates linearly with the number of users in the system. The users have heterogeneous desired departure times from the system, and their goal is to minimize a weighted sum of the travel time and square deviation from the desired departure times....

The question of when in the course of a visit to a feeding place foraging honeybees (Apis mellifera) learn about its location was studied in Experiment 1 by moving the animals a short distance after they arrived and began to feed. A preference for the arrival place developed, although less rapidly than in control animals for which the arrival and departure places were the same. In Experiments 2...