Approximate Solution of Multiclass Queueing Networks with Region Constraints

Among existing modeling techniques, queueing networks with "finite capacity regions" have largely proven to be effective in characterizing push-back effects and simultaneous resource possession in which a request holds more resources simultaneously. Queueing network models with finite capacity regions impose upper bounds on the number of jobs that can simultaneously reside in a set of service centers. For this reason they can be used to model application constraints. However, since they do not satisfy product-form assumptions, they are difficult to treat. In this paper we propose a novel approximate method for closed multiclass queueing networks containing finite capacity regions and shared constraints. Our approach is based on Norton's theorem for queueing networks where a region is replaced by a single Flow Equivalent Service Center (FESC). We propose a population-mix driven definition of FESCs service rates which provides increased accuracy with respect to existing methods. We solve the resulting non-product-form network with a new approximate variant of the convolution algorithm proposed in the paper. A comparison with simulation shows that the algorithm typically has a 4% approximation error.