[Paper Review] Multihop Adjustment for the Number of Nodes in Contention-Based MAC Protocols for Wireless Ad hoc Networks

Ash Mohammad Abbas|arXiv (Cornell University)|Aug 19, 2011

Wireless Networks and Protocols7 references3 citations

TL;DR

This paper proposes a multihop adjustment factor to accurately estimate the effective number of contending neighbors in contention-based MAC protocols for multihop wireless ad hoc networks. By modeling overlapping carrier sense ranges along a path using geometric probability, it derives an analytical adjustment factor χ = 2.1521/π(1 − 1/h), which reduces overestimation of contention and improves delay and throughput modeling for multi-hop paths.

ABSTRACT

The number of contending neighbors of a node in a multihop ad hoc network has to be adjusted while analyzing the performance of the network such as computing the end-to-end delays along a path from a given source to a destination. In this paper, we describe a method to adjust the number of contending neighbors of a node in a multihop wireless ad hoc network. Our method is based on the minimum number of neighbors that has to be common between two consecutive nodes along a path. We derive an analytical expression for the adjustment factor.

Motivation & Objective

• To address the inaccuracy in modeling end-to-end delay and throughput in multihop ad hoc networks when using single-hop MAC performance models.
• To quantify how overlapping carrier sense ranges among consecutive nodes along a path reduce the effective number of contending nodes.
• To derive a closed-form analytical expression for the adjustment factor that corrects overestimation of contention due to overlapping contention areas.
• To enable more accurate performance evaluation of CSMA/CA-based MAC protocols like IEEE 802.11 DCF and EDCA in multihop scenarios.

Proposed method

• Uses geometric probability to model the union of carrier sense ranges of h consecutive nodes along a multihop path.
• Applies the inclusion-exclusion principle to compute the total area of overlapping contention regions.
• Defines the adjustment factor χ as the ratio of overlapping area to total area of individual contention regions.
• Derives χ = 2.1521/π(1 − 1/h) for h ≥ 2, based on the average intersection area of adjacent nodes' carrier sense ranges.
• Validates the formula via mathematical induction and numerical examples for h = 5 and h = 6 nodes.
• Uses node density ζ, transmission range r, and carrier sense range rcs = βr (β = 2) as key system parameters.

Experimental results

Research questions

• RQ1 How does the effective number of contending neighbors change along a multihop path due to overlapping carrier sense ranges?
• RQ2 What is the analytical expression for the adjustment factor that corrects for overcounting of contending nodes in multihop paths?
• RQ3 How does the adjustment factor vary with the number of hops in a path?
• RQ4 To what extent does the adjustment factor diminish as the number of hops increases?

Key findings

• The adjustment factor is χ = 2.1521/π(1 − 1/h), which decreases with increasing h, indicating diminishing returns in contention reduction.
• For h = 5, the adjustment factor is χ = 4 × 2.1521 / (5π) ≈ 0.555, reducing contention by ~44.5%.
• For h = 6, χ = 5 × 2.1521 / (6π) ≈ 0.555, showing minimal incremental change from h = 5.
• The incremental increase in χ drops from 33.33% (h=2 to h=3) to 12.5% (h=3 to h=4), indicating diminishing returns.
• The adjustment factor asymptotically approaches 2.1521/π ≈ 0.685 as h → ∞, meaning contention is reduced by up to ~31.5% in long paths.
• The model corrects the naive assumption that end-to-end delay is simply h × single-hop delay, by accounting for overlapping contention.