State-based paging/registration: a greedy technique

For a mobile unit moving according to some ergodic stochastic process, we show how to minimize the expected average cost of paging and registration based on system state information. Specifically, we assume that both the system and mobile unit (user) have access to or can derive the following: the user location probability distribution as a function of time given the last location known to the system, and the time elapsed since this last known location. We then derive methods by which the user decides whether to register based on the following: current location (x), the time elapsed since last contact with the system (t), the paging cost F(x_t,x₀,t) to be incurred by the system at time t given the current location x_t and the last known location x₀, i.e., the user knows the paging strategy to be used by the system for each time t. If x and t define the system state, the method can be called “state based”. Since the optimization is based only on the current expected cost rate and not that of all registration intervals, the method is “greedy”. The greedy method was compared to a timer-based method using a simple diffusive motion process. Reductions in the average paging registration cost of approximately 10% were observed. The more striking improvement was a reduction in the variability of paging/registration costs by a factor of three. Thus, taking both cost and variability reduction as a performance measure, even suboptimal inclusion of location information in the registration decision affords substantial improvement