A G/G/1 Queue with Nova-Distributed Interarrival and Service Times

Abstract

The reliance on exponential assumptions in classical queueing models often leads to a misrepresentation of real-world systems where service and interarrival times exhibit more complex variability. This paper introduces the Nova distribution, a novel one-parameter lifetime distribution developed as a mixture of exponential and gamma components. We derive its fundamental statistical properties and demonstrate its applicability by modeling interarrival and service times in a G/G/1 queueing system. Using real-world data from a banking service facility, we show that the Nova distribution provides a superior fit compared to established one-parameter models like Lindley and Shanker, as measured by Akaike and Bayesian Information Criteria. By integrating the Nova distribution into a G/G/1 framework, we derive essential performance measures and an associated economic cost model. The results confirm that the Nova-based queueing model offers a more accurate and cost-effective tool for analyzing and optimizing service systems, particularly under the high-utilization conditions typical in many real-world scenarios.