Recent advances in various wireless data networking technologies and their successful implementations have put the dream of ubiquitous high-quality multimedia communications within our reach. However, achieving reasonable service quality is still a main challenge. It is necessary to evaluate the performance of a new or functional network and to study its service quality factors, such as delay and throughput. This thesis proposes and evaluates a set of analytical techniques based on the modern min-plus system theory that collectively presents an effective methodology for modeling, performance evaluation and quality of service (QoS) provisioning in wireless networks. Min-plus system theory is a successful alternative and complement to queuing theory, whose application in deterministic QoS guarantees is known as Network Calculus (NC) or (σ, ρ)-calculus.

The contributions of this work can be grouped under three main categories:​ slope domain modeling, stochastic min-plus system theorems and their applications in wireless networking, and filter-bank-based wireless channel models. Slope domain modeling is a useful technique whose role in min-plus theory is similar in concept to that of the Fourier domain in traditional system theory. It facilitates analysis of communications networks, and for certain problems is the only viable solution. This method is used in numerous applications, such as system identification, optimal smoothing and priority scheduling.

This thesis proposes a stochastic min-plus system theory approach that is used as a practical and efficient methodology for QoS performance evaluations in wireless networks, when the service can be defined by its second-order statistics. The method is then used in optimal traffic shaping and resource allocation for transmission over wireless fading channels. Finally, the concept of load spectrum is introduced as the slope domain representation of this stochastic minplus theory.

As an alternative method, a wireless link model based on the filter banks of NC elements is introduced. The model employs modular concatenations of selected NC components to represent the effect of a wireless link on the statistical QoS performance at the link layer. This technique is used in optimal smoothing to successfully solve the problem of playback delay and buffer size calculations for multimedia streaming via a wireless network.