The recent research has established an analogy between successive interference cancellation in slotted ALOHA framework and iterative belief-propagation erasure-decoding, which has opened the possibility to enhance random access protocols by utilizing theory and tools of erasure-correcting codes. In this paper we present a generalization of the and-or tree evaluation, adapted for the asymptotic analysis of the slotted ALOHA-based random-access protocols, for the case when the contending users experience different channel conditions, resulting in packet loss probability that varies across users. We apply the analysis to the example of frameless ALOHA, where users contend on a slot basis. We present results regarding the optimal access probabilities and contention period lengths, such that the throughput and probability of user resolution are maximized.