On the Stability of Finite Queue Slotted Aloha Protocol

We revisit the stability analysis of the well-known slotted Aloha protocol with a finite number of queues. Under standard modeling assumptions, we derive a sufficient condition for the stability by applying a positive recurrence criterion due to Rosberg (JAP, vol. 17, no. 3, 1980). Our sufficiency condition for stability is linear in arrival rates and does not require knowledge of the stationary joint statistics of queue lengths as has been the case in previous results. We also derive some sufficient conditions for instability of the protocol. We believe that the technique reported here could be useful in analyzing other stability problems in countable space Markovian settings.