Queueing and Stability Analysis of Buffered CSMA/CD Local Networks.

This dissertation develops a joint probability generating function for the message quene lengths in a slotted p-persistent CSMA/CD (Carrier-Sense Multiple-Access with Collision Detection) system with a finite population of buffered users. Each user is assumed to have an independent and identical process of packet generation and an infinite buffer for storing outstanding packets. A closed form formula is obtained for the generating function in case of a two user system. Analytic formulas for the stability condition of a p-persistent CSMA/CD system are derived using the generating function. The range of the transmission probability p that leads to stability is examined through numerical analysis over a wide variety of the user\u27s communication demand, the packet length distribution, the number of users on the network, and the time to detect and abort collided packets

Stability Region of a Slotted Aloha Network with K-Exponential Backoff

Stability region of random access wireless networks is known for only simple network scenarios. The main problem in this respect is due to interaction among queues. When transmission probabilities during successive transmissions change, e.g., when exponential backoff mechanism is exploited, the interactions in the network are stimulated. In this paper, we derive the stability region of a buffered slotted Aloha network with K-exponential backoff mechanism, approximately, when a finite number of nodes exist. To this end, we propose a new approach in modeling the interaction among wireless nodes. In this approach, we model the network with inter-related quasi-birth-death (QBD) processes such that at each QBD corresponding to each node, a finite number of phases consider the status of the other nodes. Then, by exploiting the available theorems on stability of QBDs, we find the stability region. We show that exponential backoff mechanism is able to increase the area of the stability region of a simple slotted Aloha network with two nodes, more than 40\%. We also show that a slotted Aloha network with exponential backoff may perform very near to ideal scheduling. The accuracy of our modeling approach is verified by simulation in different conditions.Comment: 30 pages, 6 figure