  This article introduces a metric for performance evaluation of medium access
schemes in wireless ad hoc networks known as local capacity. Although deriving
the end-to-end capacity of wireless ad hoc networks is a difficult problem, the
local capacity framework allows us to quantify the average information rate
received by a receiver node randomly located in the network. In this article,
the basic network model and analytical tools are first discussed and applied to
a simple network to derive the local capacity of various medium access schemes.
Our goal is to identify the most optimal scheme and also to see how does it
compare with more practical medium access schemes. We analyzed grid pattern
schemes where simultaneous transmitters are positioned in a regular grid
pattern, ALOHA schemes where simultaneous transmitters are dispatched according
to a uniform Poisson distribution and exclusion schemes where simultaneous
transmitters are dispatched according to an exclusion rule such as node
coloring and carrier sense schemes. Our analysis shows that local capacity is
optimal when simultaneous transmitters are positioned in a grid pattern based
on equilateral triangles and our results show that this optimal local capacity
is at most double the local capacity of ALOHA based scheme. Our results also
show that node coloring and carrier sense schemes approach the optimal local
capacity by an almost negligible difference. At the end, we also discuss the
shortcomings in our model as well as future research directions.
