Nowadays, operators offer telecommunication services at a very high level. For the support of the best quality of service it would be reasonable to implement a handover to another radio access network cell in the same territory, a so-called vertical handover (VHO), by transferring the user connection and IP session from the current access network to a new network. In this paper, we analyze vertical handovers from an untrusted WLAN network to an LTE network. This type of handover from an untrusted WLAN network is the most difficult because of the many nodes of an LTE network related to authorization and resource allocation. The paper includes a synthesis of the basic procedures for the session setup and LTE resource allocation. Unlike other papers, we represent a complicated VHO procedure as a sequence of at least 40 signalling messages from the discovery of a new network for the VHO to its full completion at the target LTE network. We also propose a vertical handover time estimation method for the said VHO procedure. We perform numerical experiments on realistic data. © ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi,Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors).