In provisioning packet data service on wireless cellular networks, a scheme of altering connection status between mobile and base stations appeared with an effort to utilize resource during idle periods. A critical issue in such scheme of sojourn and transition on the connection states is to determine a maximum time to sojourn at each state. An excessive sojourn time leads to resource invasion by inactive stations, while a high cost of re-establishing connection components is imposed by an insufficient sojourn. Thus, the maximum sojourn times must be optimized in consideration of the two conflicting arguments. In this paper, we consider a generic scheme of connection status transitions and formulate a decision problem to determine maximum sojourn times by introducing a loss function which reflects the cost of connection re-establishment as well as the loss induced by inefficient resource usage. From the decision problem, we derive an optimal value for maximum sojourn time, identified as Bayes rule, by observing the delay time of last packet to have posterior information about the length of upcoming idle period. From the analytical results, we show the Bayes sojourn time is trivial under a constraint on loss coefficients when packet arrivals follow a Poisson process.

In this Letter, an analytic method to calculate the cumulative distribution function (cdf) of the cell sojourn time with various distributions of a mobile velocity (constant, uniform, or Gaussian distribution) is presented. Gaussian pdf and cdf are estimated through curve-fitting. The cdf of the cell sojourn time is calculated through a numerical method. It is shown that the simulated result matches very close to the calculated result.