The throughput and access delay of slotted-aloha with exponential backoff

The behavior of exponential backoff (EB) has challenged researchers ever since its introduction, but only approximate and partial results have been produced up to this date. This paper presents accurate results about the effect of protocol parameters on throughput and delay, assuming queues in saturation. Among the manifold results, we first introduce a simple model that provides close-form results for the approximated model known as 'decoupling assumption.' Since the latter fails to provide well approximated results in many cases, we also introduce a Markovian model able to trade the precision of the results with complexity even with an infinite number of users, enabling us to get definite throughput results, such as 0.3706 with binary EB, and 0.4303 with an optimized base. Analytical considerations allow to derive the tail of the access-delay distribution, found to be slowly decreasing and with no variance as the number of users goes to infinity. Taking into account the overall performance, preliminary results seem to indicate that the exponential base b=1.35 is more appealing than the standard value b=2.