This paper establishes structural properties for the throughput of a large class of queueing networks with i.i.d. new-better-than-used service times. The main result obtained in this paper is applied to a wide range of networks, including tandems, cycles and fork-join networks with general blocking and starvation (as well as certain networks with splitting and merging of traffic streams), to deduce the concavity of their throughput as a function of system parameters, such as buffer and initial job configurations, and blocking and starvation parameters. These results have important implications for the optimal design and control of such queueing networks by providing exact solutions, reducing the search space over which optimization need be performed, or establishing the convergence of optimization algorithms. In order to obtain results for such disparate networks in a unified manner, we introduce the framework of constrained discrete event systems (CDES), which enables us to characterize any permutable and non-interruptive queueing network through its constraint set. The main result of this paper establishes comparison properties of the event occurrence processes of CDES as a function of the constraint sets, which are then translated into the above-mentioned concavity of the throughput as a function of system parameters in the context of queueing networks.

The primary objective in the present paper is to gain fundamental understanding of the performance achievable in ATM networks as a function of the various system characteristics. We derive limit theorems that characterize the achievable performance in terms of the offered traffic, the admissible region, and the revenue measure. The insights obtained allow for substantial simplifications in the design of real-time connection admission control algorithms. In particular, we describe how the boundaries of admissible regions with convex complements may be linearized - thus reducing the admissible region - so as to obtain a convenient loss network representation. The asymptotic results for the achievable performance suggest that the potential reduction in revenue is immaterial in high-capacity networks. Numerical experiments confirm that the actual reduction is typically negligible, even in networks of moderate capacity.

We study the expected delay in a cyclic polling model with mixtures of exhaustive and gated service in heavy traffic. We obtain closed-form expressions for the mean delay under standard heavy-traffic scalings, providing new insights into the behaviour of polling systems in heavy traffic. The results lead to excellent approximations of the expected waiting times in practical heavy-load scenarios and moreover, lead to new results for optimizing the system performance with respect to the service disciplines.