Stephen D. Patek

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The deterministic network calculus offers an elegant framework for determining delays and backlog in a network with deterministic service guarantees to individual traffic flows. This paper addresses the problem of extending the network calculus to a probabilistic framework with statistical service guarantees. Here, the key difficulty relates to expressing,(More)
We consider dynamic, two-player, zero-sum games where the \minimizing" player seeks to drive an underlying nite-state dynamic system to a special terminal state along a least expected cost path. The \maximizer" seeks to interfere with the minimizer's progress so as to maximize the expected total cost. We consider, for the rst time, undiscounted nite-state(More)
We consider a class of undiscounted terminating Markov decision processes with a risk-averse exponential objective function and compact constraint sets. After assuming the existence of an absorbing cost-free terminal state , positive transition costs away from , and continuity of the transition probability and cost functions, we establish (i) the existence(More)
We analyze a class of partially observed stochastic shortest path problems. These are terminating Markov decision process with imperfect state information that evolve on an innnite time horizon and have a total cost criterion. For well-posedness, we make reasonable stochastic shortest path type assumptions: (1) the existence of a policy that guarantees(More)
The network calculus offers an elegant framework for determining worst-case bounds on delay and backlog in a network. This paper extends the network calculus to a probabilistic framework with statistical service guarantees. The notion of a statistical service curve is presented as a probabilistic bound on the service received by an individual flow or an(More)
Recent research on statistical multiplexing has provided many new insights into the achievable multiplexing gain in QoS networks, however, generally only in terms of the gain experienced at a single switch. Evaluating the statistical multiplexing gain in a general network remains a difficult challenge. In this paper we describe two distinct network designs(More)
Scalability concerns of QoS implementations have stipulated service architectures where QoS is not provisioned separately to each flow, but instead to aggregates of flows. This paper determines stochastic bounds for the service experienced by a single flow when resources are managed for aggregates of flows and when the scheduling algorithms used in the(More)
Modern networks have become increasingly complex over the past years in terms of control algorithms, applications and service expectations. Since classical theories for the analysis of telephone networks were found inadequate to cope with these complexities, new analytical tools have been conceived as of late. Among these, the stochastic network calculus(More)
Modularity plays a key role in many engineering systems, allowing for plug-and-play integration of components, enhancing flexibility and adaptability, and facilitating standardization. In the control of diabetes, i.e., the so-called "artificial pancreas," modularity allows for the step-wise introduction of (and regulatory approval for) algorithmic(More)