Upper Bound on Network Utilization under Fair-Access in Multi-hop Wireless Grid Sensor Networks with 3-4 Rows

In a typical wireless sensor network, one of the primary tasks of sensor nodes is to gather data and give accurate measurements of sensing environment. Thus, obtaining a fair amount of data from each sensor node plays a key role to achieve this objective. In this paper, we investigate upper bounds on network utilization of multi-hop wireless grid sensor networks with 3-4 rows. We adopt a fair-access criterion requiring that sensor nodes have an equal rate of frame delivery to a base station. Under the constraint of fair access, we derive tight upper bounds on network utilization for specific grid topologies. Furthermore, we prove that these bounds are tight and can be achieved by a version of time division multiple access (TDMA) protocol. The significance of these upper bounds is that they hold for any medium access control protocol employing a fair-access criterion.