Stability and pricing of queueing models

A queueing system can be described as a population of customers which from time to time utilize the resources of a service provider in order to obtain service. Since it is a difficult task to analyze a stochastic model, often macroscopic models are utilized to gain insight on high level properties of the real model. The contributions of this thesis can be summarized in three parts. In the first and second parts of the thesis, we investigate the stability of the fluid models and the relationship between the fluid and the stochastic models. In the third part, we use queueing theory to tackle a revenue management problem of a monopolistic firm. First, we investigate a fundamental property of fluid solutions in multiclass fluid networks. In [14] it is shown that if a fluid network has the finite decomposition property and is not weakly stable, then any queueing network associated with the fluid network is not rate stable. In particular, we show that the finite decomposition property holds for certain classes of two-pass fluid networks. Next, we try to characterize the intersection of stability regions of the static buffer priority service disciplines for a certain type of three station networks. The results expand the known stability region by utilizing fluid trajectories and a new methodology is proposed to identify if a service rate vector is in the aforementioned stability region or not. Finally, we investigate the pricing problem of a firm which dominates the market. In our model, there is a single server with exponential service times and arrivals follow a compound Poisson process where the number of customers in a group is a random variable. We let the firm to adjust the price as the length of the queue changes. A major difference between this research and the previous literature is that we allow group arrivals and the firm may only accept or reject customer groups as a whole. We identify the optimal acceptance policy that maximizes the revenue and show that this policy is also socially optimal.