  This paper studies the buffered Aloha with K-exponential backoff collision
resolution algorithms. The buffered Aloha network is modeled as a multi-queue
single-server system. We adopt a widely used approach in packet switching
systems to decompose the multi-queue system into independent first-in-first-out
(FIFO) queues, which are hinged together by the probability of success of
head-of-line (HOL) packets. A unified method is devised to tackle the stability
and throughput problems of K-exponential backoff with any cutoff phase K. For
networks with a finite number of nodes, we show that the K-exponential backoff
is stable if the retransmission factor is properly chosen from the stable
region. The maximum stable throughput is derived and demonstrated via examples
of geometric retransmission (K=1) and exponential backoff (K=infinity). For
networks with an infinite number of nodes, we show that geometric
retransmission is unstable, and the stable network throughput of exponential
backoff can only be achieved at the cost of potential unbounded delay in each
input queue. Furthermore, we address the stability issue of the systems at the
undesired stable point. All analytical results presented in this paper are
verified and confirmed by simulations.
