A Random Graph Model for Optical Networks of Sensors Josep Dı ´az, Jordi Petit, and Maria Serna Abstract—The main contribution of this paper is presenting a new model for Smart Dust networks communicating through optical links and showing its applicability when the goal of the network is monitoring an area under the surveillance of a base station. We analyze the basic parameters of these networks as a new model of random graphs and propose simple distributed protocols for basic communication. These protocols are designed to minimize the energy consumption. Index Terms—Optical networks of sensors, random scaled sector graphs, localization algorithm, random model of network. æ 1 INTRODUCTION T HE Smart Dust project at UC Berkeley is a promising approach to building wireless networks of very small sensors [12], [13], [18]. As opposed to most other networks of sensors, these smart dust systems use optical communica- tion rather than radio frequency. The current advances in hardware technology, digital circuitry, wireless communica- tion, and microelectromechanical systems allow the devel- opment of such networks. However, as reported in [13]: The missing ingredient is the networking and application layers needed to harness this revolutionary capability into a complete system. In this paper, we propose a random model to analyze the performance of smart dust networks communicating through optical devices. We also consider and analyze some basic algorithms for communication and localization in the proposed model. Such algorithms represent a current research challenge, mainly because of the optical nature of these networks, the presence of faulty connections among sensors, and the limited power supply. One of the settings of smart dust systems is to have a base station (BS) at a relative elevation (or in a small plane) monitoring periodically the information of a large amount of sensors (motes) that have been scattered on a terrain. Smart dust systems are supposed to be deployed in hazardous or hostile environments in order to permit monitoring of remote objects, detecting anomalous situa- tions such as fires, floods, seismic movement, vehicle tracking, etc. [1], [4], [11], [12], [19]. Motes are designed to be small, a few cubic millimeters, light and cheap. Besides sensing devices, motes are equipped with a tiny battery, a solar cell, a simple processor, a clock, a small memory, and communication devices. In order to minimize size and energy, the lastest generation of motes use free-space optical transmission rather than radio frequency. In this case, motes include a small laser cannon and a set of optical devices able to reflect and modulate the light they receive [13]. Free-space optical links have the limitation of an uninterrupted line-of-sight path for communication; on the other hand, optical links avoid radio interference. Current technology makes it possible to store in a mote a total amount of energy on the order of 1 Joule, which implies that the power consumption of sensors is limited to microwatts level. As a consequence, power management becomes a main ingredient in the design of algorithms. In this paper, the communications protocols are designed so as to minimize the number of times that a mote must orient and activate its laser cannon, which is the maximal source of energy consumption. In general, the communication will be initiated from the BS: The BS scans an area with its laser and each mote passively modulates and reflects the beam. This is the preferred way to communicate, as the mote spends little power. The BS can successfully decode simultaneous transmissions of dust motes; provided that the motes do not block one to another’s line-of-sight to the BS, which, in view of the motes’ small size and the relative elevation of the BS, can be considered to be unlikely. However, as the motes are scattered massively at random from a vehicle, some of them may fall in such a way that they cannot communicate with the BS. If a mote is shadowed from the BS, this mote must relay its information to the BS through other motes. Any mote can detect a failure of communica- tion with the BS by noticing that sufficient time has elapsed without communication. Communication between motes is done in an active way using their laser beams; this kind of transmission uses more power. To send information, motes use their orientable low power laser beam, which current technology allows to move sideward and upward about 40 degrees [16]. To receive information, motes have an optical device able to detect and interpret laser signals, as well as to evaluate the direction of the incoming beam. The detection and interpretation of messages does not consume a significant amount of energy. In this paper, we consider two main stages before an optical network of sensors can become operative. The first 186 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 2, NO. 3, JULY-SEPTEMBER 2003 . The authors are with the Departament de Llenguatges i Sistemes Informa`tics, Universitat Polite`cnica de Catalunya, Campus Nord C6, 08034 Barcelona. E-mail: {diaz, jpetit, mjserna}@lsi.upc.es. Manuscript received 22 Nov. 2002; revised 1 Apr. 2003; accepted 21 May 2003. For information on obtaining reprints of this article, please send e-mail to: tmc@computer.org, and reference IEEECS Log Number 10-112002. 1536-1233/03/$17.00 ß 2003 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS