In this work, we investigate the problem of RRM and Call Admission Control (CAC) in the downlink channel of multi-rate CDMA systems. We introduce an accurate approach to characterize the system power outage probability considering all the network parameters and environmental random variables. A new mathematical paradigm is systematized to characterize the total traffic power as a function of the system parameters as well as the random variables controlling the shadowing and signal path loss phenomenon. The effect of the shadow fading and path loss on a transmission is represented by a random variable whose distribution is approximated in three different ways. These probability distributions are used derive the probability distribution of the accumulative shadow fading and path loss yields from all the transmissions in the system. Eventually, we formulate a novel probabilistic model for the for the call admission probability upon adding a new transmission to the system. The comparison with Monte-Carlo simulations results show that the developed scheme provides a good accuracy for different network settings with different shadow fading and path loss behaviors.