A wireless sensor network (WSN) is a group of specialized sensor nodes with a communication infrastructure intended to monitor and record conditions at diverse locations. The critical issue in WSNs is represented by the limited availability of energy within the network and hence optimizing energy consumption is very important. One important existing technique used to prolong the network lifetime of WSN is the Energy Minimization Scheme (EMS) using N-Policy Model (NPM) based on queue threshold but this technique increases mean delay. This paper proposes a Modified Energy Minimization Scheme (MEMS) which reduces the mean delay and average energy consumption of individual nodes in the cluster based heterogeneous sensor network using queue threshold based on M/D/1 Priority Queueing Model (PQM) in order to prolong the network lifetime. The expression for the optimal value of queue threshold for which the node consumes minimum energy using PQM is also derived. Results show that the mean delay is highly reduced in PQM when compared to the NPM and the trade-off exist between the average energy consumption and mean delay is explored. We perform simulations and the results obtained show that the simulation results match with the analytical results thus validating the accuracy of the approach.