EQUILIBRIUM ANALYSIS AND CONTROL FOR DESIGN OF PACKET RESERVATION MULTIPLE ACCESS PROTOCOLS
Abed, Eyad H
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The Packet Reservation Multiple Access (PRMA) protocol and its variants have been considered as possible access schemes for communication media for indoor communications, terrestrial communications and satellite communications. Most recently, PRMA (and its variants) has been considered for applications such as beyond third generation and/or fourth generation communication systems, cooperative communication, and multimedia communication in dynamic environments. In this dissertation, equilibrium behavior of general voice and/or data systems employing PRMA are studied along with means for control of this behavior. The main objective is to determine conditions guaranteeing a unique equilibrium for these systems, as multistability can result in an unacceptable user experience. Systems considered include voice systems, voice and data systems, and voice systems with high propagation delay (these are studied both for an error-free channel and a random error channel). Also, various control schemes are introduced and their effect on these system is analyzed at equilibrium. Control schemes considered include a price based control, state estimation-based control, and control using multiple transmission power and capture. For each type of control, the effect of the control on the equilibrium structure of the system is studied, in the spirit of the methodology of bifurcation control. In bifurcation control, the number and nature of steady state solutions of a system are managed by appropriate design of system control laws. Several sufficient conditions for uniqueness of operating points of the PRMA systems under the studied control schemes is determined. Numerical analysis of the equilibrium equations of the systems is provided to support the analytical studies. The equilibrium behavior of voice systems and voice-data systems employing frame-based PRMA is also studied. Effects of price based control on these systems is analyzed. Further, the price based control studied in conjunction with the PRMA systems is extended to a finite buffer finite user slotted ALOHA system, and the equilibrium behavior of the system is studied using a tagged user approach. Among the contributions of the dissertation are analytical sufficient conditions guaranteeing a unique equilibrium point for the various classes of systems studied, control law designs that result in improved system capacity, and extensive numerical studies including comparisons with two previously proposed approaches. Analysis is also given proving the Markovian nature of the system's stochastic dynamics (under some basic assumptions) and the existence of a unique stationary probability law.