An Embedded Markov Chain Modeling Method for Movement-Based Location Update Scheme

Abstract

In this paper, an embedded Markov chain model is proposed to analyze the signaling cost of the Movement-Based Location Update (MBLU) scheme under which a Location Update (LU) occurs whenever the number of cells crossed reaches a threshold, called movement threshold. Compared with existing literature, this paper has the following advantages. 1) This paper proposes an embedded Markov chain model in which the cell residence time follows Hyper-Erlang distribution. 2) This paper considers the Location Area (LA) architecture. 3) This paper emphasize the dependency between the cell and LA residence times using a fluid flow model. Close-form expressions for the signaling cost produced by LU and paging operations are derived, and their accuracy is validated by simulation. Based on the derived analytical expressions, we conduct numerical studies to investigate the impact of diverse parameters on the signaling cost. Index Terms—Embedded markov chain, hyper-erlang distribution, Location Management (LM), Movement-Based Location Update (MBLU).