This paper considers the slotted ALOHA protocol in a communication channel shared by N users. It is assumed that the channel has the multiple-packet reception (MPR) capability that allows the correct reception of up to M ( @math ) time-overlapping packets. To evaluate the reliability in the scenario that a packet needs to be transmitted within a strict delivery deadline D ( @math ) (in unit of slot) since its arrival at the head of queue, we consider the successful delivery probability (SDP) of a packet as performance metric of interest. We derive the optimal transmission probability that maximizes the SDP for any @math and any @math , and show it can be computed by a fixed-point iteration. In particular, the case for D = 1 (i.e., throughput maximization) is first completely addressed in this paper. Based on these theoretical results, for real-life scenarios where N may be unknown and changing, we develop a distributed algorithm that enables each user to tune its transmission probability at runtime according to the estimate of N. Simulation results show that the proposed algorithm is effective in dynamic scenarios, with near-optimal performance.
The first attempt to study slotted ALOHA under MPR was made by @cite_27 @cite_10 , in which they proposed the symmetric MPR channel model and analyzed stability properties under an infinite-user assumption. @cite_24 extended the stability study to finite-user systems without posing any limitation on the MPR model, and in addition investigated the average delay in capture channels. @cite_20 further established the throughput and stability regions for finite population over a standard MPR channel in which simultaneous packet transmissions are not helpful for the reception of any particular group of packets.
@cite_24 @cite_27 @cite_10 @cite_20
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The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered. This channel is a generalization of the usual collision channel, in that it allows the correct reception of one or more packets involved in a collision. The number of successfully received packets in each slot is modeled as a random variable which depends exclusively on the number of simultaneously attempted transmissions. This general model includes as special cases channels with capture, noise, and code-division multiplexing. It is shown by drift analysis that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity. The properties of the backlog in the nonergodicity region are examined. > A decentralized control algorithm is sought that maximizes the stability region of the infinite-user slotted multipacket channel and is easily implementable. To this end, the perfect state information case in which the stations can use the instantaneous value of the backlog to compute the retransmission probability is studied first. The vest throughput possible for a decentralized control protocol is obtained, as well as an algorithm that achieves it. These results are then applied to derive a control scheme when the backlog is unknown, which is the case of practical relevance. This scheme, based on a binary feedback, is shown to be optimal, given some restrictions on the channel multipacket reception capability. > This paper studies finite-terminal random multiple access over the standard multipacket reception (MPR) channel. We characterize the relations among the throughput region of random multiple access, the capacity region of multiple access without code synchronization, and the stability region of ALOHA protocol. In the first part of the paper, we show that if the MPR channel is standard, the throughput region of random multiple access is coordinate convex. We then study the information capacity region of multiple access without code synchronization and feedback. Inner and outer bounds to the capacity region are derived. We show that both the inner and the outer bounds converge asymptotically to the throughput region. In the second part of the paper, we study the stability region of finite-terminal ALOHA multiple access. For a class of packet arrival distributions, we demonstrate that the stationary distribution of the queues possesses positive and strong positive correlation properties, which consequently yield an outer bound to the stability region. We also show the major challenge in obtaining the closure of the stability region is due to the lack of sensitivity analysis results with respect to the transmission probabilities. Particularly, if a conjectured "sensitivity monotonicity" property held for the stationary distribution of the queues, then equivalence between the closure of the stability region and the throughput region follows as a direct consequence, irrespective of the packet arrival distributions.