The QNET method for two-moment analysis of closed manufacturing systems
The so-called QNET method for two-moment analysis of steady-state characteristics of multiclass closed queueing network with Markovian routes and one-channel nodes is developed. Wide manufacturing applications of such model is discussed in detail. The method is analogous to one for open networks and is based on the algorithm for computing the stationary distribution of corresponding reflected Brownian motion (RBM) approximation of the basic processes (total workload and queue-size ones) under heavy traffic conditions. The following treatment of closed networks having wide applications is used: there is an infinite external queue of ``replacement'' jobs and the job enters to the network each time an active job completes its route. The main restriction is: Service time distribution is the same for all classes of customers at the given node. The paper is organized as follows: description and motivation of model; Brownian models for open and closed multiclass networks (renewal type assumptions and functional central limit theorem for scaled input process formal Brownian approximation for basic processes, reduction of queue- size process approximation to RBM in a simplex); steady-state analysis of RBM in a simplex (the existence of a unique absolutely continuous distribution, computation of the stationary distribution); closed network models of the generalized Jackson type network (connection with classical results); some examples and numerical results (symmetric cyclic queue, a multiproduct two-station network); some extensions.
scientific article; zbMATH DE number 496236