Estimation of Channel Holding Timedistribution in Cellular Telephone

In estimating the channel holding time distribution in cellular telephone systems, the pdf of the fraction of two non-negative random variables, distance and speed, has to be determined. Instead of the repeated application of numerical integration we show that the pdf of the holding time is the solution of an initial value problem of a non-linear ordinary diierential equation, which can be solved very eeciently. Many traac models have been proposed for the performance analysis of cellular telephone systems, mainly relied on simulation models 1]. When we make a traac model into a mathematical expression, only a few models have a known closed-form solution under special conditions 2], and usually the traac models cannot be solved in a closed-form. Therefore a simulation or approximating method has to be used to solve the problems. The channel holding time of a mobile user in cellular telephone systems is important for system design and radio resource allocation. The distribution of this parameter can be computed by a double integral of the moving distance and speed of a mobile in a cell 2]. Although the cumulative distribution functions of the distance and the speed are derived as a closed-form solution, in most cases the double integrals are not solved analytically. In this paper, we propose a method for deriving the cannel holding time distribution and we apply this method to the analysis of cannel holding time for the traac model of a soft handoo call which has non-closed-form solution. We also perform computer simulations to check the results of the non-closed-form application. We assume that the origination of a new call is uniformly distributed over a service area. The speed and the direction of the call are uniformly distributed, and they are unchanged during the call. We also assume that the speed and the direction are independent of each other. Soft handoo allows that a mobile station is connected to a new base station before it is disconnected from the old base station during handoo. Thus when a mobile station is in the soft handoo state, two cell sites are connected to use with diversity 3]. Due to this overlapped region, one more boundary exists in a soft handoo traac model 4]. A circular-shaped cell is