A process algebra for wireless mesh networks used for modelling, verifying and analysing AODV

We propose AWN (Algebra for Wireless Networks), a process algebra tailored to the modelling of Mobile Ad hoc Network (MANET) and Wireless Mesh Network (WMN) protocols. It combines novel treatments of local broadcast, conditional unicast and data structures. In this framework we present a rigorous analysis of the Ad hoc On-Demand Distance Vector (AODV) protocol, a popular routing protocol designed for MANETs and WMNs, and one of the four protocols currently standardised by the IETF MANET working group. We give a complete and unambiguous specification of this protocol, thereby formalising the RFC of AODV, the de facto standard specification, given in English prose. In doing so, we had to make non-evident assumptions to resolve ambiguities occurring in that specification. Our formalisation models the exact details of the core functionality of AODV, such as route maintenance and error handling, and only omits timing aspects. The process algebra allows us to formalise and (dis)prove crucial properties of mesh network routing protocols such as loop freedom and packet delivery. We are the first to provide a detailed proof of loop freedom of AODV. In contrast to evaluations using simulation or model checking, our proof is generic and holds for any possible network scenario in terms of network topology, node mobility, etc. Due to ambiguities and contradictions the RFC specification allows several interpretations; we show for more than 5000 of them whether they are loop free or not, thereby demonstrating how the reasoning and proofs can relatively easily be adapted to protocol variants. Using our formal and unambiguous specification, we find shortcomings of AODV that affect performance, e.g. the establishment of non-optimal routes, and some routes not being found at all. We formalise improvements in the same process algebra; carrying over the proofs is again easy

Classification comparison.

<p>Prevalence by standard deviation cutoffs for weight-for-height and arm circumference-for-age z-scores for single and means of repeated measures among children 0–4.9 years of age.</p

Mean z-score, standard deviation, and test of equal variance between age groups for height-for-age (HAZ), weight-for-height (WHZ), weight-for-age (WAZ), arm circumference-for-age (ACZ), and head circumference-for-age (HCZ) from manual measurements (n = 474), BINA 2017.

<p>Mean z-score, standard deviation, and test of equal variance between age groups for height-for-age (HAZ), weight-for-height (WHZ), weight-for-age (WAZ), arm circumference-for-age (ACZ), and head circumference-for-age (HCZ) from manual measurements (n = 474), BINA 2017.</p

Terminal digit preference expressed as percentage of anthropometrists’ first measurement for height, head circumference and arm circumference ending in .0 to .9 compared to the expected 10% among children 0–4.9 years (n = 948 observations from 474 children), BINA 2017.

<p>Terminal digit preference expressed as percentage of anthropometrists’ first measurement for height, head circumference and arm circumference ending in .0 to .9 compared to the expected 10% among children 0–4.9 years (n = 948 observations from 474 children), BINA 2017.</p

Measurement reliability.

<p>Closest two manual measures from single observer (intra-observer) and measurement reliability in average of closest two manual measures between two observers (inter-observer) for stature, head circumference (HC) and arm circumference (MUAC) among children 0–4.9 years of age (intra-observer n = 948, inter-observer n = 474).</p

Sample characteristics.

<p>Sample characteristics.</p

Additional file 1: of Validity of gestational age estimates by last menstrual period and neonatal examination compared to ultrasound in Vietnam

Analytic Dataset. (XLSX 123 kb

Individual-level factors of study population by prevalence of iron and folic acid receipt and consumption.

<p>^a It should be noted that all women in the study population received at least one ANC visit. Those who did not attend ANC were not asked about IFA receipt or consumption;</p><p>^b Early enrollment: 1^st trimester, Late enrollment: 2^nd-3^rd trimester; ANC: Antenatal care; IFA: Iron and Folic Acid</p><p>Individual-level factors of study population by prevalence of iron and folic acid receipt and consumption.</p

Characteristics and rotated factor loadings for antenatal care factors^a^a.

<p>^a Factor loadings ≤|0.5| are not shown; ANC: Antenatal care</p><p>Characteristics and rotated factor loadings for antenatal care factors^{<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120404#t001fn001" target="_blank">a</a>}^a.</p

Characteristics and rotated factor loadings for Health Sub-Center factors^a^a.

<p>^a Factor loadings ≤|0.35| are not shown;</p><p>HSC: Health Sub-Center; PHC: Primary Health Center; VHSC: Village Health and Sanitation Committee</p><p>Characteristics and rotated factor loadings for Health Sub-Center factors^{<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0120404#t002fn001" target="_blank">a</a>}^a.</p