Abstract <p>This paper presents a novel analytical approach for the steady-state analysis of a multiserver queueing system in which arriving tasks may require simultaneous service from several servers. The system comprises a finite number of identical servers, and each task demands a random number of servers for service. Tasks in the queue are served on a first-come, first-served basis, with service beginning only when the required number of servers becomes available. A stochastic model is constructed and balance equations are derived to characterize the system’s steady-state behavior. The proposed model and its results have potential applications in distributed computing systems, cloud computing environments, and other shared-resource systems where tasks may require multiple computing resources simultaneously.</p>