  Motivated by the need to provide differentiated quality-of-service (QoS) in
grant-free uplink transmissions in 5G networks and beyond, we extend the
probabilistic analysis of coded Poisson receivers (CPR) to the setting with
multiple classes of users and receivers. For such a CPR system, we prove (under
certain technical conditions) that there is a region, called the stability
region in this paper. Each transmitted packet can be successfully received with
probability 1 when the offered load to the system is within the stability
region. On the other hand, if the offered load is outside the stability region,
there is a nonzero probability that a packet will fail to be received. We then
extend the stability region to the $\epsilon$-stability region for CPR systems
with decoding errors. We also demonstrate the capability of providing
differentiated QoS in such CPR systems by comparing the stability regions under
various parameter settings.
