This paper presents a method of employing a priority scheme in a rando
m access environment. A prioritized nonblocked stack collision resolut
ion algorithm with binary feedback is developed and tested using simul
ations. The algorithm accommodates an n-level priority scheme which ma
kes it attractive in mobile data systems. The effectiveness of the alg
orithm is described on its ability to first, reject the lowest priorit
y class when the system load is near or on the maximum value and secon
d, minimize the delay spread of the higher class users. The performanc
e of the algorithm is characterized using the through-put/delay and cu
mulative delay for each class of users.