Effective Capacity Approximations for G/G/s/k Queues under Strict QoS

Modern digital systems impose increasingly stringent quality of service requirements. A key performance metric for such systems is the effective capacity, defined as the maximum arrival rate at which the system satisfies the given delay and reliability constraints. The effective capacity is often evaluated using queueing theory, namely, leveraging multi-server queueing models with a finite buffer (G/G/s/k). However, traditional analysis methods for these models work with a limited set of distributions, have low accuracy in the vicinity of low failure probabilities, or impose high computational complexity. This paper proposes an approximation formula for estimating the effective capacity for G/G/s/k queues that accounts for the finite buffer size and strict quality of service requirements while maintaining low computational complexity. A comparative analysis shows that the proposed method achieves high accuracy while avoiding the substantial estimation errors caused by neglecting the finite buffer. The proposed approximation has practical importance for the design of modern telecommunication and computing systems with strict requirements on latency and reliability.