Analysis of a fork/join station with inputs from a finite population subnetwork with multi-server stations

Abstract

Forks/join stations are commonly used to model synchronization constraints in queuing networks. 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 using 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 inputs from multiple servers have a significant effect on performance measures such as throughput, synchronization delays and queue lengths at the individual buffers. These insights are important to obtain better representation of synchronization constraints in closed queuing network models of computer networks, fabrication/assembly systems and material control strategies for manufacturing systems.