A Distributed and Deterministic TDMA Algorithm for Write-All-With-Collision Model

arXiv:0808.0920v1 [cs.OS] 6 Aug 2008 A Distributed and Deterministic TDMA Algorithm for Write-All-With-Collision Model∗ Mahesh Arumugam Cisco Systems, Inc., San Jose, CA 95134 Email: maarumug@cisco.com Abstract Several self-stabilizing time division multiple access (TDMA) algorithms are proposed for sensor networks. In addition to providing a collision-free communication service, such algorithms enable the transformation of programs written in abstract models considered in distributed computing literature into a model consistent with sensor networks, i.e., write all with collision (WAC) model. Existing TDMA slot assignment algorithms have one or more of the following properties: (i) compute slots using a randomized algorithm, (ii) assume that the topology is known upfront, and/or (iii) assign slots sequentially. If these algorithms are used to transform abstract programs into programs in WAC model then the transformed programs are probabilis- tically correct, do not allow the addition of new nodes, and/or converge in a sequential fashion. In this paper, we propose a self-stabilizing deterministic TDMA algorithm where a sensor is aware of only its neighbors. We show that the slots are assigned to the sensors in a concur- rent fashion and starting from arbitrary initial states, the algorithm converges to states where collision-free communication among the sensors is restored. Moreover, this algorithm facilitates the transformation of abstract programs into programs in WAC model that are deterministically correct. Keywords: time division multiple access (TDMA), distance 2 coloring, self- stabilization, program transformation, write all with collision (WAC) model, sensor networks ∗Contact Information: Address: 170 W. Tasman Dr, San Jose, CA 95134 Phone: +1-408-853-3547 Fax: +1-408-527-9537 URL: http://aumahesh.googlepages.com/ 1 1 Introduction One of the important concerns in programming distributed computing platforms is the model of computation used to specify programs. Programs written for distributed computing platforms such as sensor networks and embedded systems often have to deal with several low level challenges of the platform. In sensor networks, especially, one has to write programs that deal with issues such as communication, message collision and race conditions among different processes. Therefore, to simplify the programming, it is important to abstract such low level issues. In other words, the ability to specify programs in an abstract model and later transform them into a concrete model that is appropriate to the platform is crucial. The problem of transformation of programs in an abstract model to programs in other models of computation has been studied extensively (e.g., [1–6]). These transformations cannot be applied to obtain concrete programs for sensor networks as the model of computation in sensor networks is write all with collision (WAC) model. In WAC model, communication is local broadcast in nature. As a result, whenever a sensor executes an action, it writes the state of all its neighbors in one atomic step. However, if two neighbors j and k of a sensor (say i) try to execute their write actions at the same time then, due to collision, state of i will remain unchanged. The actions of j and k may update the state of their other neighbors successfully. Existing transformations for WAC model. Recently, several approaches have been proposed to transform programs written in abstract models considered in distributed computing literature into programs in WAC model [7–10]. Such transformation algorithms can be classified into two categories: (a) randomized [7,8] and (b) deterministic [9,10]. In [7], the authors propose a cached sensornet transform (CST) that allows one to correctly simulate an abstract program in sensor networks. This transformation uses carrier sensor multiple access (CSMA) based MAC protocol to broadcast the state of a sensor and, hence, the transformed program is randomized. And, the algorithm in [9] uses time division multiple access (TDMA) to ensure that collisions do not occur during write actions. Specifically, in WAC model, each sensor executes the enabled actions in the TDMA slots assigned to that sensor. And, the sensor writes the state of all its neighbors in its TDMA slots. If the TDMA algorithm in [11], a self- stabilizing and deterministic algorithm designed for grid-based topologies, is used with [9] then the transformed program in WAC model is self-stabilizing and deterministically correct for grid-based topologies. And, if randomized TDMA algorithms proposed in [8, 12] are used with [9] then the transformed program is probabilistically correct. Finally, the algorithm in [10], a self-stabilizing and deterministic TDMA algorithm for arbitrary topologies, allows one to transform abstract programs into programs in WAC model that are deterministically correct for arbitrary topologies. In this paper, we are interested in stabilization preserving deterministic tra

…(Full text truncated)…

This content is AI-processed based on ArXiv data.