Geodesic
Analysis of fork/join and related queueing systems
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2017), pp. 43-58

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This article introduces a generalization of the classical parallel-server fork-join queueing networks. We consider open fork-join queueing networks with an arbitrary topology. There are three types of nodes in the queueing networks (service-nodes, fork-nodes, join-nodes). We focus on the infinite server case, in which each service-node is a queueing system with infinite servers. An arriving job is split (at fork-nodes) into a number of independent tasks that are serviced in parallel (at multiple service-nodes). Each task can be split at fork-nodes repetitively. These tasks synchronize (at join-nodes) before they leave the network. A method, which allows to obtain the sojourn time distribution, was developed.
Keywords: fork-join networks, queueing network, sojourn time distribution, performance evaluation, synchronization, parallel processing, PH-distribution. 
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     author = {O. Osipov and I. E. Tananko},
     title = {Analysis of fork/join and related queueing systems},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {43--58},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_4_a3/}
}
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O. Osipov; I. E. Tananko. Analysis of fork/join and related queueing systems. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2017), pp. 43-58. http://geodesic.mathdoc.fr/item/VTPMK_2017_4_a3/