Asian Journal of Computer and Information Systems (ISSN: 2321 – 5658) Volume 02 – Issue 03, June 2014 Asian Online Journals (www.ajouronline.com ) 73 Development of an Access Point Positioning Algorithm under the Changing in Environment and Users’ density Estimation Twahir Kazema 1 , Michael Kisangiri 2 , Dina Machuve 3 Nelson Mandela Institute, School of Mathematica Computatinal and Communication Science and Engineering, Nambala, Arusha-Tanzania Twahir Kazema Email: kazemat {at} nm-aist.ac.tz _________________________________________________________________________________ ABSTRACT— In many wireless networks a single hop is all that is needed or in fact tolerable. The physical region where network is available is known as a coverage area. Generally, a transmitter and a receiver may exchange data by using one or more intermediate relays. In each case a path through the network must be found whereby each hop has a Signal to Interference Noise Ratio greater than ß. There are several ways to describe and compute network connectivity, but at the core, they all need that individual pairs are able to communicate, which is dictated by the SINR. This paper is going to develop an Access Point positioning algorithm by considering the changes of environment and users’ density estimation. Keywords--- SINR, beta, spatial, coverage _________________________________________________________________________________ 1. INTRODUCTION A stochastic process is noise signal whose amplitude varies in time (or is a random variable / number) drawn from some probability distributions but it is also defined as a time signal where the value at any given time is a random variable. The origins of stochastic geometry can be traced back to two different sources. These are, on one hand, geometric probabilities and integral geometry, with their intuitive problems and imagined experiments, and on the other hand the investigation of real-world materials by stochastic-geometric methods, which in the beginning were often heuristic and required sound mathematical foundations. Any stochastic process may be described by a probability distribution, and may be thought of as the mapping of a sequence of random variable to a new set of states. Examples of systems that may be modeled by a stochastic process are stock markets, images, Brownian motion, landscapes, galaxies, cellular networks and cosmological density _fields. Although the term process first brings to mind a time series it can be generalized to any suitable parameter space. When the space is a spatial volume we refer to it as a spatial random _field. 2. STOCHASTIC GEOMETRY IN WIRELESS COMMUNICATION- RELATED WORK Stochastic geometry is a powerful tool used to analyze and obtain the performance metrics of wireless networks with random topologies in a statistical manner. Stochastic geometry is a study of random spatial patterns such as:  point processes (Branch of stochastic geometry which is used to statistically describe the spatial distribution of the network nodes)  random tessellations  stereology Applications:  astronomy  communications  material science  forestry