Abstract
We present two projects in this thesis, both concerned with congestion, albeit in completely di?erent circumstances. The ?rst project studies congestion in bu?ered queues. We consider queueing processes with heavy-tailed service times and study approximations of severe congestion times. Large deviations for random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such random walks in the large deviation scale which we call hidden large deviations. We apply this idea to queueing processes to illustrate the need for these more re?ned approximations and provide a simulation study to examine the ?nite-sample accuracy of our approximations. Congestion due to motor tra?c is the second subject. There are large quantities of excess seat capacity spread throughout privately owned vehicles given traditional usage patterns. Often a car is used only a short fraction of time per day, and typically only one out of ?ve seats is ?lled when the car is traveling. New platform based businesses are creating a market for this excess capacity. There are promising studies regarding the algorithmic and engineering challenges of making ride sharing among strangers feasible, in particular highlighting the potential reduction in tra?c volume if cars are used more e?ciently. We introduce a model in which individuals may share rides for a certain fee, paid by the rider(s) to the driver through a ride sharing platform. Collective decision making is modeled as an anonymous non-atomic game with a ?nite set of strategies and payo? functions a?ne in the individuals’ types. Types are de?ned as the pair of an individual’s utility for using private transportation and the individual’s rate of income. Among others, we examine how ride sharing is organized and how congestion and ownership are a?ected if a platform which chooses the seat rental price to maximize either revenue or welfare is introduced to a population.