Cost Analysis of a Hybrid-Movement-Based and Time-Based Location Update Scheme in Cellular Networks

A movement-based location update (MBLU) scheme is effective and has low operation complexity. On the other hand, cellular networks use periodic LUs that are intrinsically time-based LUs (TBLUs) to detect the presence of a user equipment (UE) to avoid wasting network resources to deliver incoming calls to an abnormally detached UE. When implemented in a cellular network, the MBLU scheme must incorporate TBLUs to detect the UE presence. Thus, a hybrid-movement-based and time-based LU (HMTBLU) scheme arises naturally. Under the HMTBLU scheme, an LU occurs either when the movement threshold for MBLUs is reached or when the time threshold for TBLUs is reached. In this paper, we develop an embedded Markov chain approach to calculate the signaling cost of the HMTBLU scheme. We derive analytical formulas for the signaling cost and formulas useful for designing an optimal paging scheme. The accuracy of these formulas is validated through simulation. Based on these formulas, we conduct a numerical study to investigate the influence of various parameters on the signaling cost. The derived formulas can guide the implementation of the HMTBLU scheme in cellular networks, including Long-Term Evolution (LTE). Moreover, the developed mathematical approach can be applied to studying other LU schemes such as the LU scheme used in LTE.