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.