Non-Colliding First Messages in Slotted ALOHA: Further Insights Toward a Practical Solution

Abstract

Consider n nodes competing for access on a channel using slotted ALOHA. Our aim is to maximize the probability Φ that the first message within s slots does not collide. We derive an expression for the transmit probabilities in each slot, maximizing Φ. As opposed to previous work, the expression is non-recursive, thus easier to calculate and more convenient for practical implementations. Furthermore, we address the problem that, in practical applications, the number of competing nodes n is likely to be unknown and has to be estimated by each node. We study the sensitivity of channel access scheme with respect to deviations from the actual n via simulations. It is shown that overestimation of n is a better strategy than underestimation.

Contention-Based Estimation of Neighbor Cardinality

“…Moreover, the requirements on the accuracy of neighbor cardinality estimation depend on the application field. While inventorying and stockkeeping systems typically request low estimation errors (as low as one percent), neighbor estimation in mobile computing has sometimes less constraints, since also rough estimations may improve system performance (see, e.g., [20]). …”

Contention-based node selection with applications to relay communications and load balancing

“…Parts of this article, including some equations and results, were previously published in [10] and [11]. Those papers presented some first ideas and results of Section 2.…”

Reducing collision probability on a shared medium using a variational method

“…But we want to relax this assumption on the slotted synchronization between the nodes.This may be difficult to implement in some situations and a method is needed to deal with un-slotted situations. In [6] and [7], the same problem in the same slotted context is addressed, but the authors noticed that the collision probability can be reduced if the probability that the nodes answer is less than 1. An optimal value is given.…”

“…An optimal value is given. Moreover, the solution is explicit in [7] while it is only recursive in [6]. In [5], the authors address the same question without assuming any synchronization, but they do not derive analytically an exact solution.…”

“…In [5], the authors address the same question without assuming any synchronization, but they do not derive analytically an exact solution. Moreover, there is a mistake in the formula (7) of [5] where it is implicitely assumed a uniform distribution for the loss rate, we give the correct formula below: formula (7).…”