Closed-Form Approximations for the URLLC Capacity Using \(G/G/s\) Queues

Efficient operation of resource management algorithms in modern ultra-reliable low-latency communication (URLLC) systems requires fast and accurate estimation of the system capacity, i.e., the maximum traffic volume per second that can be served under strict quality of service requirements such as low latency and high reliability of data delivery. Queueing theory is helpful in this task; however, due to the variability of communication systems and their operating conditions, queueing theory has to operate with general distributions, i.e., to consider $G/G/s$ queues. For such queues, obtaining a precise analytical solution is either impossible in a closed-form or computationally expensive, so approximations for $G/G/s$ models are in demand. However, existing approximation methods fail to account for URLLC features: low (but nonzero) delay thresholds and low probabilities of exceeding these thresholds, which results in significant errors in capacity estimation. We propose and investigate closed-form approximation formulas for estimating the URLLC capacity using $G/G/s$ queues. We analyze the accuracy of the proposed formulas and distinguish regions of acceptable capacity estimation errors. Finally, we show a specific asymptotics for the URLLC system capacity in a wide range of parameters and scenarios.