SUMMARY
Wireless sensor networks (WSNs) still attract the attention of researchers, users and the private sector despite their low power and low range tendency for malfunction. This attraction towards WSNs results from their low cost structure and the solutions they offer for many prevalent problems. Many conditions, which remain unforeseen or unexpected during the design of the system, may arise after the initialization of the system. Similarly, many situations where security vulnerabilities take place may emerge in time in WSNs operating normally. In this study, we called nodes which enter sleeping mode without any further waking up and causing a sparser number of nodes in the network without any function in data transmission as Long-Term Sleep Nodes (LT-SN); and considered energy spaces caused by such nodes as a problem; and established two Linear Programming (LP) models based on the efficiency of the present nodes. We offered two different models which present the effect of sensor nodes, which were initially operating in wireless sensor network environment and did not wake up following sleep mode, on network lifetime. The results of the present study report that as the number of LT-SN increases, the lifetime of the network decreases.