Future 5G/6G cellular Internet of Things (CIoT) technologies need to be able to multiplex a number of traffic types having different arrival patterns, resource requirements, and directions. To this aim, the random access (RA) and data transmission (DT) phases in such technologies should be appropriately optimized. In this paper, we develop a service model accounting for successive service and both random access and data transmission phases and the different nature of traffic types in uplink and downlink directions multiplexed over the data transmission phase. The uplink traffic requires both phases to get service while the downlink one shall pass the data transmission phase only. We establish the stability criterion for the considered system and then utilize this model to investigate the performance of the system serving asynchronous arrivals in the uplink direction and software updates in the downlink one. Our results show that modern CIoT systems such as NB-IoT are not optimized for wide ranges of load conditions. Specifically, even in the presence of software updates constituting 3% or less of the overall load, RA phase may bottleneck the whole system. The optimal division of resources may drastically vary depending on the uplnk and downlink traffic load. The model developed in this paper allows optimal tuning RA and DT phases for any offered load conditions in the uplink and downlink directions. © 2024 IEEE.