Abstract
An open acyclic fork-join queueing network is considered. When a job arrives from a source into the network, it is split to be serviced into a given constant number of associated tasks. The tasks are routed between service-nodes independently of each other and independently of tasks associated with other jobs. Upon leaving the queuing network, all tasks enter a node called the join-node, where associated tasks join into a job. A method is proposed for calculating the mean time spent by a task in the join-node and the mean response time in the fork-join queueing network. For the case of so-called uniform workload distribution in the queueing network, the calculation of the mean response time in the queueing network is described. Uniform workload distribution is determined by equal route lengths of tasks in the queuing network, equal probabilities of these routes, as well as equal service rates in the service-nodes, proportional to the number of tasks associated with jobs. A comparison of numerical results obtained in computational experiments using analytical and simulation models of a fork-join queueing network is presented. The results can be used to evaluate the time characteristics of the operation of multiprocessor systems, cloud computing systems and other stochastic systems modeled by fork-join queueing networks.