Analysis of a Fork/Join Station With Inputs from a Finite Population: Sub-Network With Multi-Server Stations

This paper presents an exact analysis of a fork/join station with inputs from stations composed of multiple exponential servers. The queue length process at the input buffers is analyzed exactly in terms of the underlying Markov process. The semi-Markov kernel characterizing the departure process is analyzed to derive expressions for the marginal and joint distributions of inter-departure times from the fork/join station. These analyses are used to study the effect of inputs from multiple servers on key performance measures at a fork/join station. Comparison studies show that replacing the multiple servers by a single server with equivalent capacity could result in significantly different estimates of throughput, synchronization delays and queue lengths at the individual buffers. These insights could lead to better representation of synchronization constraints in closed queuing net- work models of computer networks, fabrication/assembly systems and material control strategies for manufacturing systems.