Our focus is on a class of Markov chains which have a polyhedral translation invariance property for the transition probabilities. This class can be used to model several applications of interest which feature complexities not found in usual models of queueing networks, for example failure prone manufacturing systems which are operating under hedging point policies, or enhanced wafer fab models featuring batch tools and setups or affine index policies. We present a new family of performance bounds which is more powerful both in expressive capability as well as the quality of the bounds than some earlier approaches.

One of the primary tools in establishing the stability of a fluid network is to construct a Lyapunov function. In this paper, we establish the sufficiency in the use of a Lyapunov function. Specifically, we show that a necessary and sufficient condition for the stability of a generic fluid network (GFN) is the existence of a Lyapunov function for its fluid level process. Then by applying this result to various specific fluid networks, including a fluid network under all work-conserving service disciplines, a fluid network under a priority service discipline, and a fluid network under a FIFO service discipline, we establish the existence of a Lyapunov function for their fluid level processes is a necessary and sufficient condition for their stabilities. The result is also applied to various fluid limit models and a linear Skorohod problem.

We provide a state-of-the-art survey of results concerning stability issues for routing in communication networks, and corresponding protocols. Roughly speaking, a distributed routing protocol is stable on some particular network if the protocol maintains a bounded number of packets in the network at all times, under some suitable assumptions on the fashion of injecting packets into the network. Fundamental questions that pose themselves in such a setting include: What is the e ect of the injection pattern on stability? Which protocols are stable on which networks? What can be said about an algorithmic characterization of stability? In this survey, we summarize some of the known answers to these questions, and some questions for which noanswers are yet known, as a collection of current challenges for the distributed computing community. Partially supported by funds from the Joint Program of Scienti c and Technological Collaboration between

This paper studies the stability of a three-station fluid network. We prove that the global stability region of our three-station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three-station network. The linear program proposed by Bertsimas, Gamarnik and Tsitsiklis [1] does not characterize either the global stability region or even the monotone global stability region of our three-station network.

this paper we investigate the stability of a class of two-station multiclass uid networks with proportional routing. We obtain explicit necessary and sucient conditions for the global stability of such networks. By virtue of a stability theorem of Dai [14], these results also give sucient conditions for the stability of a class of related multiclass queueing networks. Our study extends the results of Dai and VandeVate [19], who provided a similar analysis for uid models without proportional routing, which arise from queueing networks with deterministic routing. The models we investigate include uid models which arise from a large class of two-station queueing networks with probabilistic routing. The stability conditions derived turn out to have an appealing intuitive interpretation in terms of virtual stations and push-starts which were introduced in earlier work on multiclass networks. Keywords: Multiclass queueing network, uid mod

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This paper contains more general results than are used here and applies to all two-server balanced networks with certain types of non-idling service disciplines. It proves that the policy proposed by Harrison and Wein [14] is asymptotically optimal. Let U