Theoretical analysis of beaconless geocast protocols in 1D

TL;DR

This paper analyzes six beaconless geocast protocols in 1D to quantify network load via the maximum number of messages a node can receive (RecMess). It introduces a 1D message-grid model and analyzes both worst-case and fair-medium-access probabilistic activation orders, deriving tight bounds for each protocol under unbounded and bounded reach. The results show CD-P scales as Theta(k log n) in the unbounded case and Theta(k) in the bounded case, while CD exhibits stronger load when k grows with n, with CD-P avoiding that blow-up. Overall, the work confirms several simulation-based observations and provides a theoretical basis for protocol design and 2D extensions.

Abstract

Beaconless geocast protocols are routing protocols used to send messages in mobile ad-hoc wireless networks, in which the only information available to each node is its own location. Messages get routed in a distributed manner: each node uses local decision rules based on the message source and destination, and its own location. In this paper we analyze six different beaconless geocast protocols, focusing on two relevant 1D scenarios. The selection of protocols reflects the most relevant types of protocols proposed in the literature, including those evaluated in previous computer simulations. We present a formal and structured analysis of the maximum number of messages that a node can receive, for each protocol, in each of the two scenarios. This is a measure of the network load incurred by each protocol. Our analysis, that for some of the protocols requires an involved probabilistic analysis, confirms behaviors that had been observed only through simulations before.

Figures (7)

• Figure 1: A geocast example in 2D where a message should be sent from the sender (red node) to the geocast region marked as a blue rectangle.
• Figure 2: The 1D scenario serves as a first step towards the general question, and is already relevant in situations where the local geometry is essentially 1-dimensional, e.g., in narrow passages. In the figure, points represent nodes and green polygons obstacles.
• Figure 3: Illustration of the scenarios. Top: with unbounded reach, the $k$ messages arrive immediately to all nodes, but that does not prevent intermediate nodes from forwarding the messages. Bottom: with range $r=2$, the messages sent from node $1$ only reach up to node $3$, so forwards are necessary to reach the target, $n$.
• Figure 4: The different protocols run on an example data set with $k=4$ and $n=6$, for the unbounded reach scenario. The activation order used in the illustration for the top five protocols is $\langle 3,2,5,1,4,2 \rangle$.
• Figure 5: The different protocols run on an example data set with $k=4$ and $n=6$, for the bounded reach scenario. The activation order used in the illustration is $\langle 3,2,5,1,4,2 \rangle$.

Theorems & Definitions (41)

• Theorem 1
• proof
• Lemma 2
• proof
• Theorem 3
• Theorem 4
• Theorem 5
• Theorem 6
• Theorem 7
• proof