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We consider a tree network spanning a set of source nodes that generatemeasurement packets, a set of additional relay nodes that only forward packetsfrom the sources, and a data sink. We assume that the paths from the sources tothe sink have bounded hop count. We assume that the nodes use the IEEE 802.15.4CSMA/CA for medium access control, and that there are no hidden terminals. Inthis setting, starting with a set of simple fixed point equations, we derivesufficient conditions for the tree network to approximately satisfy certaingiven QoS targets such as end-to-end delivery probability and delay under agiven rate of generation of measurement packets at the sources (arrival ratesvector). The structures of our sufficient conditions provide insight on thedependence of the network performance on the arrival rate vector, and thetopological properties of the network. Furthermore, for the special case ofequal arrival rates, default backoff parameters, and for a range of values oftarget QoS, we show that among all path-length-bounded trees (spanning a givenset of sources and BS) that meet the sufficient conditions, a shortest pathtree achieves the maximum throughput.

An Approximate Inner Bound to the QoS Aware Throughput Region of a Tree  Network under IEEE 802.15.4 CSMA/CA and Application to Wireless Sensor  Network Design