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
2105747968 2163569758 2964276712 1998010325
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. This paper considers random access protocols with multipacket reception (MPR), which include both slotted-Aloha and slotted τ-persistent CSMA protocols. For both protocols, each node makes a transmission attempt in a slot with a given probability. The goals of this paper are to derive the optimal transmission probability maximizing a system throughput for both protocols and to develop a simple random access protocol with MPR, which achieves a system throughput close to the maximum value. To this end, we first obtain the optimal transmission probability of a node in the slotted-Aloha protocol. The result provides a useful guideline to help us develop a simple distributed algorithm for estimating the number of active nodes. We then obtain the optimal transmission probability in the τ-persistent CSMA protocol. An in-depth study on the relation between the optimal transmission probabilities in both protocols shows that under certain conditions the optimal transmission probability in the slotted-Aloha protocol is a good approximation for the τ-persistent CSMA protocol. Based on this result, we propose a simple τ-persistent CSMA protocol with MPR which dynamically adjusts the transmission probability τ depending on the estimated number of active nodes, and thus can achieve a system throughput close to the maximum value. In this paper, we consider a two-user and a three-user slotted ALOHA network with multi-packet reception (MPR) capabilities and a queue-aware transmission control. In this setting, the nodes can adapt their transmission probabilities and their transmission parameters based on the status of the other nodes. Each user has external bursty arrivals that are stored in their infinite capacity queues. We focus on the fundamental problem of characterizing the stable throughput region, as well as of investigating the queueing delay. For the two- and the three-user cases, we obtain the exact stability region, whereas in the former case, we also provide the conditions under which the stability region is a convex set. We perform a detailed mathematical analysis to study the queueing delay in the two-user case by formulating two boundary value problems, the solution of which provides the generating function of the joint stationary probability distribution of the queue size at user nodes. Furthermore, for the two-user symmetric case with MPR, we obtain a lower and an upper bound for the average delay without the need of solving a boundary value problem. In addition, we provide a closed form expression for the gap between the lower and the upper bound. The bounds as it is seen in the numerical results appear to be tight. Explicit expressions for the average delay are obtained for the symmetrical model with capture effect. We also provide a closed form expression for the optimal transmission probability that minimizes the average delay in the symmetric capture case. Finally, we evaluate numerically the presented theoretical results. We derive the closed-form delay distributions of slotted ALOHA and nonpersistent carrier sense multiple access (CSMA) protocols under steady state. Three retransmission policies are analyzed. We find that under a binary exponential backoff retransmission policy, finite average delay and finite delay variance can be guaranteed for G<2S and G<4S 3, respectively, where G is the channel traffic and S is the channel throughput. As an example, in slotted ALOHA, S<(ln2) 2 and S<3(ln4-ln3) 4 are the operating ranges for finite first and second delay moments. In addition, the blocking probability and delay performance as a function of r sub max (maximum number of retransmissions allowed) is also derived.