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Wireless sensor networks are a new class of ad hoc networks that will find increasing deployment in coming years, as they enable reliable monitoring and analysis of unfamiliar and untested environments. The advances in technology have made it possible to have extremely small, low powered sensor devices equipped with programmable computing, multiple parameter sensing, and wireless communication capability. Because of their inherent limitations, the protocols designed for such sensor networks must efficiently use both limited bandwidth and battery energy. We develop an M/G/1 model to analytically determine the delay incurred in handling various types of queries using our enhanced APTEEN (Adaptive Periodic Threshold-sensitive Energy Efficient sensor Network protocol) protocol. Our protocol uses an enhanced TDMA schedule to efficiently incorporate query handling, with a queuing mechanism for heavy loads. It also provides the additional flexibility of querying the network through any node in the network. To verify our analytical results, we have simulated a temperature sensing application with a Poisson arrival rate for queries on the network simulator ns-2. As the simulation and analytical results match perfectly well, this can be said to be the first step towards analytically determining the delay characteristics of a wireless sensor network.