Non-uniform structures and synchronization patterns in shared-channel communication networks

In this dissertation we study an important property of shared channel communication networks--the self-synchronization property. Our goal is to study systems which tend to naturally synchronize themselves. The advantage of this property is that the system will be efficient under both heavy and low loads without using artificial means. The contributions of this dissertation fall into two disciplines: one, the discipline of shared channel communication networks, in which we uncover and study synchronization properties of several systems; the other, queueing theory, in which we study several general-application systems, the studies of which are required for the analysis of the shared channel systems. As related to queueing theory, the main contributions of this dissertation are the following: (1) We develop a novel approach to study the delay in the queue with starter. This approach is shown to be very powerful in analyzing many variations of the queue with starter. (2) We introduce the random polling system as a queueing model for distributed control systems. We analyze this system and compare it with the "traditional" cyclic polling system. The main contributions to the discipline of shared channel communication networks are: (1) We analyze the expected delay in the exhaustive slotted ALOHA system. (2) We study the throughput of a slotted ALOHA directional tandem and observe the demonstration of its self-synchronization properties. It is shown that the "level of synchronization" observed in the system continuously increases with the transmission rate and, thus, the system throughput monotonically increases with the transmission rate. (3) We study the throughput in a very-fast bidirectional bus system. This system is analyzed under the basic assumption that the parameter a (packet transmission time divided by the propagation delay) is very big. Two important results are observed for this system: (a) Under perfect scheduling, a system capacity of practically 2 is obtained. (b) Under stochastic arrivals, the system synchronizes itself. For this reason, the system is very stable and efficient, in contradiction to the predictions of previous studies.