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In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution. [ABSTRACT FROM AUTHOR]

We study a system of two queues with boundary assistance, represented as a continuous-time Quasi-Birth-and-Death process (QBD). Under our formulation, this QBD has a 'doubly infinite' number of phases. We determine the convergence norm of Neuts' R-matrix and, consequently, the interval in which the decay rate of the infinite system can lie. We next consider four sequences of finite-phase approximations to the original system in which the Nth approximation has 2 N+1 phases; one is derived by truncating the infinite system without augmentation, the others are obtained by using different augmentation schemes that ensure that the generator of the QBD remains conservative. The sequences of matrices { R} for the truncated system without augmentation and one of the sequences with augmentation have monotonically increasing spectral radii that approach the convergence norm of the infinite-phase R as the truncation point tends to infinity; the two other sequences of matrices { R} have spectral radii that are constant irrespective of the truncation size, and not equal to the convergence norm of the infinite R. [ABSTRACT FROM AUTHOR]

The existence of product form solutions in networks of queues has been known for many years. Recently the authors have shown that there is a class of stochastic Petri nets (SPN's), distinct from queueing networks, which also have a product form equilibrium distribution. Most practical SPN's, however, do not fall within this class. In this paper the class of SPN's which can be analyzed using these methods is extended in several directions. Using embedded discrete time processes we study a class of SPN's which have a closed form equilibrium distribution. These SPN's have probabilistic output bags, colored tokens, and alternating periods of arbitrarily distributed enabling and firing times (periods of time between transitions becoming enabled and absorption of tokens and between transitions absorbing tokens and depositing them in output places, respectively.) In addition an aggregation procedure is proposed which, in certain nets, not only reduces a complex SPN to a much simpler skeleton SPN but obtains results for the skeleton SPN which are exact marginal distributions for the original SPN. [ABSTRACT FROM AUTHOR]

Introduces a batch service discipline, called assemble-transfer batch service, for continuous-time open queueing networks with batch movements. Assumption of a Markovian setting for the arrival process, service times and routing; Geometric product form of the stationary distribution of the queue length.