Several UE energy consumption optimization techniques have been proposed for Machine Type Communication (MTC) devices. Extended Discontinuous Reception (eDRX) in idle mode is one such technique wherein an UE in idle mode wakes up only during its Paging Occasion (PO) to monitor paging messages from eNodeB (eNB). The PO is located within a Paging frame (PF). The PF is a function of System Frame Number (SFN) cycle of eNB. The paging messages may be sent asynchronously from multiple eNBs to a UE. Due to asynchronous operation of eNBs, SFN takes on different values at a given point in time and therefore a paging message is transmitted at different points in time from different eNBs. Due to this SFN misalignment between eNBs, an idle mode UE might receive and respond to the same paging message from different eNBs and/or miss a PO and thus the paging message. Due to this spread in time of SFN and PO, the actual handling of paging message by the UE becomes inefficient leading to increased UE energy consumption and decreased reachability. These issues, resulting from paging handling, will get amplified further if DRX period is extended longer (eDRX). In this study, we investigate the impact of eDRX cycles and mobility related parameters such as UE speed, cell size and size of SFN misalignment between eNBs on UE energy consumption, use of network resources and UE reachability. Receiving and responding to the same paging message results in increased energy consumption for UE and increased signaling between UE and the network. Missing a PO results in delayed paging reception and hence decreases UE reachability. As the DRX cycle lengths are increased from existing maximum of 2.56 seconds to 10.24 seconds and beyond, we see a reduction in UE energy consumption by more than 90%, but the network signaling and the delay to reach the UE increases linearly as a function of the DRX cycle length. We observe that the number of duplicate paging message receptions/missed POs is minuscule for DRX cycle lengths below 10.24 sec. At DRX cycle length of 10.24 seconds, UEs travelling across 500 m cell radius at speeds of 3, 50, 100 km/h the percentage of duplicate paging receptions are 0.07, 0.11, and 0.15 respectively. This duplicate paging message reception increases the UE energy consumption by 2.31, 6.15 and 12 percent of the total energy units respectively. Similarly, UE misses nearly 0.34, 0.39, and 0.405 percent of the total POs respectively. Depending on the number of consecutive PO misses, the UE reachability decreases. But by reducing the size of SFN misalignment between eNBs, we see that it’s possible to increase the reachability for UEs in eDRX. Further we have proposed solutions based on our analytical study to avoid duplicate paging message reception by UE, increase UE reachability and also reduce UE energy consumption using a windowing technique. We conclude that when a UE is configured with eDRX cycles, the tradeoff between battery lifetimes and UE reachability is based on mobility characteristics and service requirements.