A discrete-argument stochastic process is presented. The process is a gener
alization of the Cinlar semiregenerative process [5] and process eta (t) gi
ven in [17], For this process, the theorem, which is similar to the Smith r
egenerative process theorem, is given. We use this theorem to find the tran
smission rate and mean packet delay for stack and part-and-try random multi
ple access algorithms in their supercritical regions. For part-and-try algo
rithm, the results are new, For stack algorithm, we give a new method of fi
nding the rate and delay.