In this work we consider a two-user and a three-user slotted ALOHA network with multi-packet reception (MPR) capabilities. 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. For the two- and the three-user cases we obtain the stability region of the system. For the two-user case we provide the conditions where the stability region is a convex set. We perform a detailed mathematical analysis in order to study the queueing delay by formulating two boundary value problems (a Dirichlet and a Riemann-Hilbert boundary value problem), 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 explicitly computing the generating function for the stationary joint queue length distribution. 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 which is a subclass of MPR models. We also provide the optimal transmission probability in closed form expression that minimizes the average delay in the symmetric capture case. Finally, we evaluate numerically the presented theoretical results.
 This paper considers cross-layer medium access control (MAC) protocol design in wireless networks. Taking a mutually interactive MAC-PHY perspective, we aim to design an MAC protocol that is in favor of the physical (PHY) layer information transmission, and the improved PHY, in turn, can improve the MAC performance. More specifically, we propose a novel MAC protocol, named hybrid ALOHA, which makes it possible for collision-free channel estimation and simultaneous multiuser transmission. The underlying argument is as follows: As long as good channel estimation can be achieved, advanced signal processing does allow effective signal separation given that the multiuser interference is limited to a certain degree. Comparing with traditional ALOHA, there are more than one pilot subslots in each hybrid ALOHA slot. Each user randomly selects a pilot subslot for training sequence transmission. Therefore, it is possible for different users to transmit their training sequences over nonoverlapping pilot subslots and achieving collision-free channel estimation. Relying mainly on the general multipacket reception (MPR) model, in this paper, quantitative analysis is conducted for the proposed hybrid ALOHA protocol in terms of throughput, stability, as well as delay behavior. It is observed that significant performance improvement can be achieved in comparison with the traditional ALOHA protocol based either on the collision model or the MPR model.  This paper proposes a martingale extension of effective-capacity, a concept which has been instrumental in teletraffic theory to model the link-layer wireless channel and analyze QoS metrics. Together with a recently developed concept of an arrival-martingale, the proposed service-martingale concept enables the queueing analysis of a bursty source sharing a MAC channel. In particular, the paper derives the first rigorous and accurate stochastic delay bounds for a Markovian source sharing either an Aloha or CSMA CA channel, and further considers two extended scenarios accounting for 1) in-source scheduling and 2) spatial multiplexing MIMO. By leveraging the powerful martingale methodology, the obtained bounds are remarkably tight and improve state-of-the-art bounds by several orders of magnitude. Moreover, the obtained bounds indicate that MIMO spatial multiplexing is subject to the fundamental power-of-two phenomena. In ad hoc networks, performance objectives are often in contention with each other. Indeed, due to the transmission errors incurred over wireless channels, it is difficult to achieve a high rate of transmission in conjunction with reliable delivery of data and low latency. In order to obtain favorable throughput and delay performances, the system may choose to compromise on its reliability and have nodes forcibly dropping a small fraction of packets. The focus of this paper is on the characterization of tradeoffs between the achievable throughput, end-to-end delay and reliability in wireless networks with random access. We consider a multihop ad hoc network comprising several source-destination pairs communicating wirelessly via the slotted ALOHA channel access scheme. Employing ideas from statistical mechanics, we present an analytical framework for evaluating the throughput, end-to-end delay and reliability performances of the system. The main findings of this paper are (a) when the system is noise-limited, dropping a small fraction of packets in the network leads to a smaller end-to-end delay though the throughput suffers as well, and (b) when the system is interference-limited, however, there exist regimes where dropping a few packets in the network may actually reduce the end-to-end delay as well as increase the system throughput. We also present some empirical results which corroborate the results obtained analytically. We consider a cognitive radio network where multiple secondary users (SUs) contend for spectrum usage, using random access, over available primary user (PU) channels. Our focus is on SUs' queueing delay performance, for which a systematic understanding is lacking. We take a fluid queue approximation approach to study the steady-state delay performance of SUs, for cases with a single PU channel and multiple PU channels. Using stochastic fluid models, we represent the queue dynamics as Poisson driven stochastic differential equations, and characterize the moments of the SUs' queue lengths accordingly. Since in practical systems, a secondary user would have no knowledge of other users' activities, its contention probability has to be set based on local information. With this observation, we develop adaptive algorithms to find the optimal contention probability that minimizes the mean queue lengths. Moreover, we study the impact of multiple channels and multiple interfaces, on SUs' delay performance. As expected, the use of multiple channels and or multiple interfaces leads to significant delay reduction.   Characterizing the performance of ad hoc networks is one of the most intricate open challenges; conventional ideas based on information-theoretic techniques and inequalities have not yet been able to successfully tackle this problem in its generality. Motivated thus, we promote the totally asymmetric simple exclusion process (TASEP), a particle flow model in statistical mechanics, as a useful analytical tool to study ad hoc networks with random access. Employing the TASEP framework, we first investigate the average end-to-end delay and throughput performance of a linear multihop flow of packets. Additionally, we analytically derive the distribution of delays incurred by packets at each node, as well as the joint distributions of the delays across adjacent hops along the flow. We then consider more complex wireless network models comprising intersecting flows, and propose the partial mean-field approximation (PMFA), a method that helps tightly approximate the throughput performance of the system. We finally demonstrate via a simple example that the PMFA procedure is quite general in that it may be used to accurately evaluate the performance of ad hoc networks with arbitrary topologies.  We consider a Poisson network of sources, each with a destination at a given distance and a buffer of infinite capacity. Assuming independent Bernoulli arrivals, we characterize the stability region when one or two classes of users are present in the network. We then derive a fixed-point equation that determines the success probability of the typical source-destination link and evaluate the mean delay at each buffer.