# SCS

## Seminar

### Stochastic geometry and wireless ad-hoc networks - from the coverage probability to the asymptotic end-to-end delay on long routes

Seminar Room 1, Newton Institute

#### Abstract

The aim of this talks is to show how stochastic geometry can be used to analyze some key phenomena that arise in the context of medium access (MAC) and routing in wireless ad-hoc networks.We limit ourselves to simple (yet not simplistic) model of Poisson mobile ad-hoc network (MANET) with slotted Aloha and concentrate on the so-called outage scenario, where a successful transmission requires a signal-to-Interference-and-Noise (SINR) larger than some threshold. We also assume Rayleigh fading. Starting from a simple explicit expression for the successful transmission probability we will show first how various network performance metrics related to the throughput can be evaluated in the scenario where all the receivers are located within some fixed distance to the receiver. Then we make a first step towards a joint analysis of MAC and routing considering a few more complex scenarios for receiver location, all motivated by the fact that real routing mechanisms typically select receivers in the vicinity of the respective emitters.

The analysis of these more adequate models reveals interesting phenomena related to the local delay in MANETS, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers.

We will show that in most cases, each node has a 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. In some cases it exhibits a phase transition, where the spatial average is finite when certain model parameters are below a threshold and infinite above.

Finally, we consider a fully cross-layer MAC/routing model, where there is no predefined route and where the routing scheme tries to take advantage of the variability of MAC and fading to decide on the next relay for each packet at each time slot.

An important negative consequence of the previous observation on local delays is that the mean end-to-end delay of a packet delivery in Poisson MANET scales superlinearly with the distance between source and destination, or, in other words, the asymptotic velocity of a typical packet is null, even if this packet is considered as a priority packet and experiences no queuing in the nodes.

The main positive result, formulated and proved using the framework of the first passage percolation on a SINR space-time graph, states that when adding a periodic node infrastructure of arbitrarily small intensity to the Poisson MANET makes the end-to-end delay scale linearly with the delivery distance.

The talk is based several papers written jointly with F. Baccelli, P. Muhlethaler and O. Mirsadeghi. A more detailed exposition of this subject can be found in the book "Stochastic Geometry and Wireless Networks, Volume II- Applications" by F. Baccelli and B.B., Foundations and Trends in Networking, NoW.

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