6,371 research outputs found

    Estimation of linear stochastic systems over a queueing network

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    In this paper, we consider the standard state estimation problem over a congested packet-based network. The network is modeled as a queue with a single server processing the packets. This provides a framework to consider the effect of packet drops, packet delays and bursty losses on state estimation. We use a modified Kalman Filter with buffer to cope with delayed packets. We analyze the stability of the estimates with varying buffer length and queue size. We use high order Markov chains for our analysis. Simulation examples are presented to illustrate the theory

    A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning

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    In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay-aware resource control in wireless systems. They have their relative pros and cons in terms of performance, complexity and implementation issues. For each of the approaches, the problem setup, the general solution and the design methodology are discussed. Applications of these approaches to delay-aware resource allocation are illustrated with examples in single-hop wireless networks. Furthermore, recent results regarding delay-aware multi-hop routing designs in general multi-hop networks are elaborated. Finally, the delay performance of the various approaches are compared through simulations using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201

    The Value-of-Information in Matching with Queues

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    We consider the problem of \emph{optimal matching with queues} in dynamic systems and investigate the value-of-information. In such systems, the operators match tasks and resources stored in queues, with the objective of maximizing the system utility of the matching reward profile, minus the average matching cost. This problem appears in many practical systems and the main challenges are the no-underflow constraints, and the lack of matching-reward information and system dynamics statistics. We develop two online matching algorithms: Learning-aided Reward optimAl Matching (LRAM\mathtt{LRAM}) and Dual-LRAM\mathtt{LRAM} (DRAM\mathtt{DRAM}) to effectively resolve both challenges. Both algorithms are equipped with a learning module for estimating the matching-reward information, while DRAM\mathtt{DRAM} incorporates an additional module for learning the system dynamics. We show that both algorithms achieve an O(Ļµ+Ī“r)O(\epsilon+\delta_r) close-to-optimal utility performance for any Ļµ>0\epsilon>0, while DRAM\mathtt{DRAM} achieves a faster convergence speed and a better delay compared to LRAM\mathtt{LRAM}, i.e., O(Ī“z/Ļµ+logā”(1/Ļµ)2))O(\delta_{z}/\epsilon + \log(1/\epsilon)^2)) delay and O(Ī“z/Ļµ)O(\delta_z/\epsilon) convergence under DRAM\mathtt{DRAM} compared to O(1/Ļµ)O(1/\epsilon) delay and convergence under LRAM\mathtt{LRAM} (Ī“r\delta_r and Ī“z\delta_z are maximum estimation errors for reward and system dynamics). Our results reveal that information of different system components can play very different roles in algorithm performance and provide a systematic way for designing joint learning-control algorithms for dynamic systems

    Probabilistic Inference in Queueing Networks

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    Although queueing models have long been used to model the performance of computer systems, they are out of favor with practitioners, because they have a reputation for requiring unrealistic distributional assumptions. In fact, these distributional assumptions are used mainly to facilitate analytic approximations such as asymptotics and large-deviations bounds. In this paper, we analyze queueing networks from the probabilistic modeling perspective, applying inference methods from graphical models that afford significantly more modeling flexibility. In particular, we present a Gibbs sampler and stochastic EM algorithm for networks of M/M/1 FIFO queues. As an application of this technique, we localize performance problems in distributed systems from incomplete system trace data. On both synthetic networks and an actual distributed Web application, the model accurately recovers the systemā€™s service time using 1 % of the available trace data.

    Arrival first queueing networks with applications in kanban production systems

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    In this paper we introduce a new class of queueing networks called {\it arrival first networks}. We characterise its transition rates and derive the relationship between arrival rules, linear partial balance equations, and product form stationary distributions. This model is motivated by production systems operating under a kanban protocol. In contrast with the conventional {\em departure first networks}, where a transition is initiated by service completion of items at the originating nodes that are subsequently routed to the destination nodes (push system), in an arrival first network a transition is initiated by the destination nodes of the items and subsequently those items are processed at and removed from the originating nodes (pull system). These are similar to the push and pull systems in manufacturing systems

    Importance Sampling Simulation of Population Overflow in Two-node Tandem Networks

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    In this paper we consider the application of importance sampling in simulations of Markovian tandem networks in order to estimate the probability of rare events, such as network population overflow. We propose a heuristic methodology to obtain a good approximation to the 'optimal' state-dependent change of measure (importance sampling distribution). Extensive experimental results on 2-node tandem networks are very encouraging, yielding asymptotically efficient estimates (with bounded relative error) where no other state-independent importance sampling techniques are known to be efficient The methodology avoids the costly optimization involved in other recently proposed approaches to approximate the 'optimal' state-dependent change of measure. Moreover, the insight drawn from the heuristic promises its applicability to larger networks and more general topologies
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