Recently, tree algorithms have been combined with successive interference cancellation to achieve a substantially higher maximum stable throughput (MST). All previous work assumed either a single or an unbounded number of signal memory locations, with MSTs of 0.662 and 0.693, respectively. In this paper, we address the gap between these two algorithms by designing and analyzing two novel general k-signal memory location algorithms.

A new class of multiple access algorithms for systems without feedback is introduced and analyzed. A finite population of users is assumed, where each user transmits a packetRtimes within the nextNtime slots (and all packets have an equal length of one slot). To improve the performance achieved by randomly selecting theseRslots, user codes are invoked such that any two users will only transmit simultaneously in at most one slot, i.e., 2-(N,R, 1) designs. We argue that in most cases, the set of user codes can be generated easily using cyclic designs and provide a method to selectTuser codes from the set of user codesSN,Rin case the user population consists ofT<|SN,R|users. We further demonstrate how larger populations, withT>|SN,R|, can still benefit from these user codes in two different manners. Closed formulas that express the success probability of a packet are provided for all population setups. Finally, a comparison with the random selection strategy demonstrates the performance gain realized by the new multiple access algorithms and some engineering rules to optimize the performance are provided.

A simple numerical procedure is presented to determine the maximum stable throughput (MST) of various tree algorithms with free access by defining an associated multitype branching process such that the criticality of the branching process corresponds to the stability of the tree algorithm. More precisely, a bisection algorithm is proposed that only requires the computation of the dominant eigenvalue of the expectation matrix of the branching process, the size of which is typically below 20, at each step. Using this novel approach, many existing results on free-access tree algorithms are reproduced without much effort (e.g., channels with/without noise, variable length packets, interference cancellation, etc.). Furthermore, in an almost plug-and-play manner, the MST of the free access equivalent of many existing results on tree algorithms with blocked access is established (e.g., channels with capture, control signals, multireception capabilities, etc.). The method can be applied to the class of independent and identically distributed (i.i.d.) arrival processes, which includes the Poisson process as a special case. Apart from determining the MST, the probability that a sizeicollision is resolved in a finite amount of time when the arrival rate exceeds the MST can also be computed. Some limitations of the proposed methodology are discussed as well.

In this paper we present a new theoretical model to assess the performance of a class of batch scheduling orders in a forward DVB-S2 satellite link. The scheduling order in a DVB-S2 link will determine the order in which IP packets are transmitted to the receivers and thus determines the amount of required padding and sub-optimal transmissions. The validity of the model is investigated by various simulation runs which show a very close agreement with the theoretical model. Using this model we also identify the optimal scheduling order within this class of orders, given that some mild and realistic conditions on the modulation and coding schemes apply.