In this paper, we consider two different classes of IoT sensors with high and low priorities in which both classes send their data to a Monitoring Center (MC) equipped with one server and a buffer to store the arrival packets waiting in the queue, representing an M/M/1/2 system. An error-free channel predominates the link between the sensors and MC. We assume a non-preemptive scheme applying priorities on the buffer in MC so that the packets with lower priority in the queue can be replaced by more urgent higher priority packets but not in the service, as well. The arrival packets are specified by deadline characteristic due to the great demand for fresh data. The deadline is provided to free the buffer and let the monitoring center be updated by the latest data. As significant parameters in calculating the throughput and freshness of data, Rate of Information () and system-s Age of Information (AoI) are investigated in the MC. Our goal is to study the effect of priority and packet deadlines on the rate and status update of the system. Thus, a Markov model is applied to derive the closed form expressions considering deterministic deadlines and the impact of high and low priority packets. Also, a new metric named the Age to Rate Ratio of Information (ARRoI) is introduced and discussed for better realization of the relation between effective arrival rate and AoI. Simulation results for various parameters confirm the analytical results and show that the newly introduced metric, ARRoI, could be employed in finding proper transmission rates.