A New Phase Transition for Local Delays in MANETs

We consider Mobile Ad-hoc Network (MANET) with transmitters located according to a Poisson point in the Euclidean plane, slotted Aloha Medium Access (MAC) protocol and the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise (SINR) larger than some threshold. We analyze the local delays in such a network, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers. The analysis depends very much on the receiver scenario and on the variability of the fading. In most cases, each node has finite-mean geometric random delay and thus a positive next hop throughput. However, the spatial (or large population) averaging of these individual finite mean-delays leads to infinite values in several practical cases, including the Rayleigh fading and positive thermal noise case. In some cases it exhibits an interesting phase transition phenomenon where the spatial average is finite when certain model parameters are below a threshold and infinite above. We call this phenomenon, contention phase transition. We argue that the spatial average of the mean local delays is infinite primarily because of the outage logic, where one transmits full packets at time slots when the receiver is covered at the required SINR and where one wastes all the other time slots. This results in the "RESTART" mechanism, which in turn explains why we have infinite spatial average. Adaptive coding offers a nice way of breaking the outage/RESTART logic. We show examples where the average delays are finite in the adaptive coding case, whereas they are infinite in the outage case.Comment: accepted for IEEE Infocom 201

Coverage probability in wireless networks with determinantal scheduling

We propose a new class of algorithms for randomly scheduling network transmissions. The idea is to use (discrete) determinantal point processes (subsets) to randomly assign medium access to various {\em repulsive} subsets of potential transmitters. This approach can be seen as a natural extension of (spatial) Aloha, which schedules transmissions independently. Under a general path loss model and Rayleigh fading, we show that, similarly to Aloha, they are also subject to elegant analysis of the coverage probabilities and transmission attempts (also known as local delay). This is mainly due to the explicit, determinantal form of the conditional (Palm) distribution and closed-form expressions for the Laplace functional of determinantal processes. Interestingly, the derived performance characteristics of the network are amenable to various optimizations of the scheduling parameters, which are determinantal kernels, allowing the use of techniques developed for statistical learning with determinantal processes. Well-established sampling algorithms for determinantal processes can be used to cope with implementation issues, which is is beyond the scope of this paper, but it creates paths for further research.Comment: 8 pages. 2 figure

How wireless queues benefit from motion: an analysis of the continuum between zero and infinite mobility

This paper considers the time evolution of a queue that is embedded in a Poisson point process of moving wireless interferers. The queue is driven by an external arrival process and is subject to a time-varying service process that is a function of the SINR that it sees. Static configurations of interferers result in an infinite queue workload with positive probability. In contrast, a generic stability condition is established for the queue in the case where interferers possess any non-zero mobility that results in displacements that are both independent across interferers and oblivious to interferer positions. The proof leverages the mixing property of the Poisson point process. The effect of an increase in mobility on queueing metrics is also studied. Convex ordering tools are used to establish that faster moving interferers result in a queue workload that is smaller for the increasing-convex stochastic order. As a corollary, mean workload and mean delay decrease as network mobility increases. This stochastic ordering as a function of mobility is explained by establishing positive correlations between SINR level-crossing events at different time points, and by determining the autocorrelation function for interference and observing that it decreases with increasing mobility. System behaviour is empirically analyzed using discrete-event simulation and the performance of various mobility models is evaluated using heavy-traffic approximations.Comment: Preliminary version appeared in WiOPT 2020. New version with revision

HetNets with Random DTX Scheme: Local Delay and Energy Efficiency

Heterogeneous cellular networks (HetNets) are to be deployed for future wireless communication to meet the ever-increasing mobile traffic demand. However, the dense and random deployment of small cells and their uncoordinated operation raise important concerns about energy efficiency. On the other hand, discontinuous transmission (DTX) mode at the base station (BS) serves as an effective technology to improve energy efficiency of overall system. In this paper, we investigate the energy efficiency under finite local delay constraint in the downlink HetNets with the random DTX scheme. Using a stochastic geometry based model, we derive the local delay and energy efficiency in a general case and obtain closed-form expressions in some special cases. These results give insights into the effect of key system parameters, such as path loss exponents, BS densities, SIR threshold and mute probability on the system performance. We also provide the low-rate and high-rate asymptotic behavior of the maximum energy efficiency. It is analytically shown that it is less energy-efficient to apply random DTX scheme in the low-rate regime. In the high-rate regime, however, random DTX scheme is essential to achieve the finite local delay and higher energy efficiency. Finally, we extend the analysis to the loadaware DTX scheme where the mute probability depends on the user activity level