Fluid models of bilateral matching queues with time‐varying arrivals

Abstract The double‐ended matching queueing model has wide applicability across various real‐life scenarios. In this paper, we analyze fluid models of bilateral matching queues with time‐varying arrivals. The model contains fluid contents with general patience time distributions in a task queue and a worker queue, aiming to approximate the characteristics of bilateral queueing systems. We first prove the existence and uniqueness of the solution to the fluid model. When the arrival rates of both tasks and workers are constant, we determine the steady‐state queue lengths and abandonment proportions for both sides of the queueing system. Furthermore, we demonstrate that the solution converges to an equilibrium state starting from any initial state. For situations involving time‐varying arrival rates, satisfactory results from numerical experiments validate the reliability of the fluid model in describing the queueing system. Finally, we explore the matching problems within bilateral queueing systems and provide tailored solutions for various scenarios.