Self-stabilizing TDMA Algorithms for Wireless Ad-hoc Networks without External Reference

Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, $\xi$, and then combine them into frames of uniform size, $\tau$. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, $\delta$, and no access to external references for collision detection, time or position, we consider the problem of collision-free self-stabilizing TDMA algorithms that use constant frame size. We demonstrate that this problem has no solution when the frame size is $\tau < \max\{2\delta,\chi_2\}$, where $\chi_2$ is the chromatic number for distance-$2$ vertex coloring. As a complement to this lower bound, we focus on proving the existence of collision-free self-stabilizing TDMA algorithms that use constant frame size of $\tau$. We consider basic settings (no hardware support for collision detection and no prior clock synchronization), and the collision of concurrent transmissions from transmitters that are at most two hops apart. In the context of self-stabilizing systems that have no external reference, we are the first to study this problem (to the best of our knowledge), and use simulations to show convergence even with computation time uncertainties

Topics in Distributed Algorithms: On Wireless Networks, Distributed Storage and Streaming

Distributed algorithms are executed on a set of computational instances. Werefer to these instances as nodes. Nodes are runningconcurrently and are independent from each other. Furthermore, they have their own instructions and information. In this context, the challenges are to show thatthe algorithm is correct, regardless of computational, or communication delaysand to show bounds on the usage of communication.We are especially interested the behaviour after transient faults and underthe existence of Byzantine nodes.This thesis discusses fundamental communication models for distributed algorithms. These models are implementing abstract communication methods. First, we address medium access control for a wireless medium with guaranteeson the communication delay. We discuss time division multiple access(TDMA) protocols for ad-hoc networks and we introduce an algorithm that creates aTDMA schedule without using external references for localisation, or time. We justify our algorithm by experimental results.The second topic is the emulation of shared memory on message passingnetworks. Both, shared memory and message passing are basic interprocessorcommunication models for distributed algorithms. We are providing a way ofemulating shared memory on top of an existing message passing network underthe presence of data corruption and stop-failed nodes. Additionally, we ensurethe privacy of the data that is stored in the shared memory. The third topic looks into streaming algorithms and optimisation. We study the problem of sorting a stream ofvehicles on a highway with severallanes so that each vehicle reaches its target lane. We look into optimality interms of minimising the number of move operations, as well as, minimising the length of the output stream. We present an exact algorithm for the case oftwo lanes and show that NP-Hardness for a increasing number of lanes

Relocation Analysis of Stabilizing MAC Algorithms for Large-Scale Mobile Ad Hoc Networks

Throughput is a basic measure for communication efficiency. It is defined as the average fraction of time that the channel is employed for useful data propagation. This work considers the problem of analytically estimating the throughput of protocols for media access control (MAC) in mobile ad hoc networks (MANETs). The dynamic and difficult to predict nature of MANETs complicates the analysis of MAC algorithms. We use simple extensions to the interleaving model and evolving graphs, for defining the settings that model the location of mobile nodes.This work improves the understanding on impossibility results, the possible trade-offs and the analysis of fault-tolerant algorithms in MANETs. As the first result in the paper and as motivation for the ones that follow, we show that there is no efficient deterministic MAC algorithm for MANETs. Moreover, we prove a lower bound of the throughput M the radical settings of complete random relocation between every two steps of the algorithm. The lower bound matches the throughput of a strategy that is oblivious to the history of wireless broadcasts.Subsequently, we focus on the analysis of non-oblivious strategies and assume a bound on the rate by which mobile nodes relocate, i.e., randomly changing their neighborhoods. Our analysis is the first to demonstrate a novel throughput-related trade-off between oblivious and non-oblivious strategies of MAC algorithms that depends on the relocation rate of mobile nodes. We present a non-oblivious strategy that yields a randomized, fault-tolerant algorithm that can balance between the trade-offs. The studied algorithm is the first of is kind because it is a "stateful" one that quickly converges to a guaranteed throughput

Relocation analysis of stabilizing MAC algorithms for large-scale mobile ad hoc networks

11 This work improves the understanding on impossibility results, the possible trade-offs and the analysis 12 of fault-tolerant algorithms in MANETs. As the first result in the paper and as motivation for the ones 13 that follow, we show that there is no efficient deterministic MAC algorithm for MANETs. Moreover, we 14 prove a lower bound of the throughput in the radical settings of complete random relocation between 15 every two steps of the algorithm. The lower bound matches the throughput of a strategy that is oblivious 16 to the history of broadcasts. 17 Subsequently, we focus on the analysis of non-oblivious strategies and assume a bound on the rate 18 by which mobile nodes relocate, i.e., randomly changing their neighborhoods. Our analysis is the first to 19 demonstrate a novel throughput-related trade-off between oblivious and non-oblivious strategies of MAC 20 algorithms that depends on the relocation rate of mobile nodes. We present a non-oblivious strategy 21 that yields a randomized, fault-tolerant algorithm that can balance between the trade-offs. The studied 22 algorithm is the first of is kind because it is a &quot;stateful&quot; one that quickly converges to a guaranteed 23 throughput

Relocation Analysis of Stabilizing MAC Algorithms for Large-Scale Mobile Ad Hoc Networks

Throughput is a basic measure for communication efficiency. It is defined as the average fraction of time that the channel is employed for useful data propagation. This work considers the problem of analytically estimating the throughput of protocols for media access control (MAC) in mobile ad hoc networks (MANETs). The dynamic and difficult to predict nature of MANETs complicates the analysis of MAC algorithms. We use simple extensions to the interleaving model and evolving graphs, for defining the settings that model the location of mobile nodes.This work improves the understanding on impossibility results, the possible trade-offs and the analysis of fault-tolerant algorithms in MANETs. As the first result in the paper and as motivation for the ones that follow, we show that there is no efficient deterministic MAC algorithm for MANETs. Moreover, we prove a lower bound of the throughput M the radical settings of complete random relocation between every two steps of the algorithm. The lower bound matches the throughput of a strategy that is oblivious to the history of wireless broadcasts.Subsequently, we focus on the analysis of non-oblivious strategies and assume a bound on the rate by which mobile nodes relocate, i.e., randomly changing their neighborhoods. Our analysis is the first to demonstrate a novel throughput-related trade-off between oblivious and non-oblivious strategies of MAC algorithms that depends on the relocation rate of mobile nodes. We present a non-oblivious strategy that yields a randomized, fault-tolerant algorithm that can balance between the trade-offs. The studied algorithm is the first of is kind because it is a "stateful" one that quickly converges to a guaranteed throughput