Abstract
Fork/join stations are used to model synchronization constraints between entities in a queuing network. The fork/join station of interest in this chapter consists of a server with zero service times and two input buffers. As soon as there is one entity in each buffer, an entity from each of the buffers is removed and joined together. The joined entity exits the fork/join station instantaneously. Subsequent to its departure, the joined entity forks back into the component entities, which then each get routed to other parts of the network. Fork/join stations find many applications in queuing models of manufacturing and computer systems. In queuing models of assembly systems, the assembly station is typically modeled using a fork/join station (Harrison [7], Latouche [17], Hopp and Simon [8], Rao and Suri [23] Rao and Suri [24]). Fork/join stations are also used model the synchronization constraints in models of material control strategies for multi-stage manufacturing systems (Buzacott and Shanthikumar [5], Di Mascolo et al. [6], Krishnamurthy et al. [11]). In computer systems analysis, queuing networks with fork/join stations have been studied in the context of parallel processing, database concurrency control, and communication protocols (Baccelli et al. [3], Prabhakar et al. [21], Varki [37]).
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Krishnamurthy, A., Suri, R., Vernon, M. (2003). Two-Moment Approximations for Throughput and Mean Queue Length of a Fork/Join Station with General Inputs from Finite Populations. In: Shanthikumar, J.G., Yao, D.D., Zijm, W.H.M. (eds) Stochastic Modeling and Optimization of Manufacturing Systems and Supply Chains. International Series in Operations Research & Management Science, vol 63. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0373-6_5
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