Nowadays, wireless sensor networks (WSNs) and Internet of Things (IoT) employ the IEEE 802.15.4 media access control (MAC) protocol in many applications. In time critical applications with periodic traffic model when the packets have a specified time to live (TTL), if the packet stays in the queue of a sensor node more than time to live, the node should drop that packet, which called reneging packet, to improve the network performance. This paper presents a new analytical Markov model for the IEEE 802.15.4 protocol in non-beacon enabled mode for the periodic traffic considering the reneging packets. The proposed model is applied to the both acknowledged and non-acknowledged modes under heterogeneous traffic for time critical sensor network applications. We obtain the probability distribution function (PDF) of packet delay (PD) and packet delivery ratio (PDR) under periodic and high data rate traffic model. The effects of packet generation period and reneging packets on the performance of sensor network is investigated. The results confirm that dropping an unusable reneging packet increases the network performance, and the non-acknowledged mode can be used for high data rate applications in which the delay is more critical than the packet delivery ratio.