Stability of routing strategies for the maximum lifetime problem in ad-hoc wireless networks

TL;DR

This paper investigates the stability of optimal routing strategies in a one-dimensional ad-hoc wireless network with superadditive energy costs, analyzing how changes in data generation and node placement affect maximum network lifetime solutions.

Contribution

It provides a mathematical analysis of the stability regions for maximum lifetime solutions under parameter modifications in a specific network model with superadditive energy costs.

Findings

Derived estimates for the stability region around initial parameters.

Showed stability of solutions under small node position shifts.

Analyzed the impact of data generation variations on network lifetime.

Abstract

We solve the maximum lifetime problem for a one-dimensional, regular ad-hoc wireless network with one data collector $L_N$ for any data transmission cost energy matrix which elements $E_{i,j}$ are superadditive functions, i.e., satisfy the inequality $\forall_{i\leq j\leq k}\;E_{i,j}+E_{j,k}\leq E_{i,k}$. We analyze stability of the solution under modification of two sets of parameters, the amount of data $Q_i$, $i\in [1,N]$ generated by each node and location of the nodes $x_i$ in the network. We assume, that the data transmission cost energy matrix $E_{i,j}$ is a function of a distance between network nodes and thus the change of the node location causes change of $E_{i,j}$. We say, that a solution $q(t_0)$ of the maximum network lifetime problem is stable under modification of a given parameter $t_0$ in the stability region $U(t_0)$, if the data flow matrix $q(t)$ is a solution of the problem for any $t\in U(t_0)$. In the paper we estimate the size of the stability region $U(Q^0,d^0)$ for the solution of the maximum network lifetime problem for the $L_N$ network in the neighborhoods of the points $Q^0_i=1$, $d^0_i=0$, where $d_i\in (-1,1)$ describes the shift of the nodes from their initial location $x_i^0=i$, i.e., $x_i=i-d_i$.