Bayes Rule for MAC State Sojourn Time Supporting Packet Data Service in CDMA Wireless Celluar Networks

MAC state models appeared with an effort to overcome technical demerits of CDMA in provisioning packet data service. In the scenario of sojourn and transition on MAC states, the design of state sojourn time is a critical issue for an efficient utilization of limited recource; a longer sojourn time leads to more resource being preserved for inactive stations, while more connection components should be recovered with a shorter sojourn time. Thus, the sojourn time at each MAC state must be optimized in consideration of these two conflicting arguments. In this paper, we first present a generic MAC state model. Secondly, based on the generic model, we reveal a relation of inactive period and the delay time of the last packet served in pre- ceding active period and specify a loss function reflect-ing two antinomic features that result from a change of state sojourn time. Using the proposed loss function, we construct a decision problem to find an optima3 rule for state sojourn times. Finally, we present a way of computing Bayes rule by use of the posterior distribution of inactivity duration for given observation on the delay time of last packet. Furthermore, Bayes rules are explicitly expressed for special arrival processes and investigated with respect to traffic load and loss parameters.