A Hybrid Parallel-Sequential Service Model for Tandem Communication Networks with Load-Dependent and Time-Variant Behaviour

Abstract

Queueing models are vital analytical tools for examining a wide range of real-world scenarios, such as those found in communication networks, transportation systems, machine maintenance, and production lines. These systems often exhibit non-stationary arrival and service processes, reflecting their dynamic nature over time. In this study, we develop and evaluate a queueing model that integrates both sequential and parallel service mechanisms, characterized by non-stationary Poisson arrivals and time-dependent service rates. The model assumes the presence of two parallel queues, each serviced independently, which subsequently converge into a single queue connected to a downstream service station. Such configurations are commonly observed in manufacturing systems and network infrastructures. By employing differential equations, we derive the joint probability generating function for the queue lengths. Additionally, we obtain explicit expressions for key performance indicators, including the average no. of customers in the queue, the average waiting time, and the variation in queue size in response to changes in service station throughput. The results demonstrate that non-stationary arrival and service patterns have a significant effect on overall system performance. This investigation draws inspiration from earlier foundational models while extending their applicability to more complex and realistic scenarios.