Closed-Form Approximations for the URLLC CapacityUsingG/G/sQueues

Efficient operation of resource management algorithms in modern ultra-reliablelow-latency communication (URLLC) systems requires fast and accurate estimation of the sys-tem capacity, i.e., the maximum traffic volume per second that can be served under strictquality of service requirements such as low latency and high reliability of data delivery. Queue-ing theory is helpful in this task; however, due to the variability of communication systemsand their operating conditions, queueing theory has to operate with general distributions, i.e.,to considerG/G/squeues. For such queues, obtaining a precise analytical solution is eitherimpossible in a closed-form or computationally expensive, so approximations forG/G/smodels 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 usingG/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