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Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies
 ANN. APPL. PROBAB
, 2005
"... We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks ..."
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Cited by 23 (0 self)
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We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks
Approximation and Limit Results for Nonlinear Filters over an Infinite Time Interval: Part II, Random Sampling Algorithms
"... The paper is concerned with approximations to nonlinear filtering problems that are of interest over a very long time interval. Since the optimal filter can rarely be constructed, one needs to compute with numerically feasible approximations. The signal model can be a jumpdiffusion, reflected or no ..."
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Cited by 22 (9 self)
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The paper is concerned with approximations to nonlinear filtering problems that are of interest over a very long time interval. Since the optimal filter can rarely be constructed, one needs to compute with numerically feasible approximations. The signal model can be a jumpdiffusion, reflected or not. The observations can be taken either in discrete or continuous time. The cost of interest is the pathwise error per unit time over a long time interval. In a previous paper of the authors [2], it was shown, under quite reasonable conditions on the approximating filter and on the signal and noise processes that (as time, bandwidth, process and filter approximation, etc.) go to their limit in any way at all, the limit of the pathwise average costs per unit time is just what one would get if the approximating processes were replaced by their ideal values and the optimal filter were used. When suitable approximating filters cannot be readily constructed due to excessive computational requirem...
Heavy Traffic Analysis of Controlled Multiplexing Systems
 SIAM J. Control and Optimization
, 1997
"... The paper develops the mathematics of the heavy traffic approach to the control and optimal control problem for multiplexing systems, where there are many mutually independent sources which feed into a single channel via a multiplexer (or of networks composed of such subsystems). Due to the widely v ..."
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Cited by 12 (2 self)
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The paper develops the mathematics of the heavy traffic approach to the control and optimal control problem for multiplexing systems, where there are many mutually independent sources which feed into a single channel via a multiplexer (or of networks composed of such subsystems). Due to the widely varying bit rates over all sources, control over admission, bandwidth, etc., is needed to assure good performance. Optimal control and heavy traffic analysis has been shown to yield systems with greatly improved performance. Indeed, the heavy traffic approach covers many cases of great current interest, and provides a useful and practical approach to problems of analysis and control arising in modern high speed telecommunications. Past works on the heavy traffic approach to the multiplexing problem concentrated on the uncontrolled system or on the use of the heavy traffic limit control problem for applications, and did not provide details of the proofs. This is done in the current paper. The ...
Diffusion Approximations for a Single Node Accessed by CongestionControlled Sources
 IEEE Transactions on Automatic Control
, 1999
"... We consider simple models of congestion control in highspeed networks and develop diffusion approximations which could be useful for resource allocation. We first show that, if the sources are ONOFF type with exponential ON and OFF times, then, under a certain scaling, the steadystate distribution ..."
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Cited by 11 (5 self)
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We consider simple models of congestion control in highspeed networks and develop diffusion approximations which could be useful for resource allocation. We first show that, if the sources are ONOFF type with exponential ON and OFF times, then, under a certain scaling, the steadystate distribution of the number of active sources can be described by a combination of two appropriately truncated and renormalized normal distributions. For the case where the source arrival process is Poisson and the service times are exponential, the steadystate distribution consists of appropriately normalized and truncated Gaussian and exponential distributions. We then consider the case where the arrival process is a general renewal process with finite coefficient of variation and servicetime distributions that are phasetype and show the impact of these distributions on the steadystate distribution of the number of sources in the system. We also establish an insensitivity to servicetime distributi...
Ergodic Rate Control Problem for Single Class Queueing Networks
"... Abstract: We consider critically loaded single class queueing networks with infinite buffers in which arrival and service rates are state (i.e., queue length) dependent and may be dynamically controlled. An optimal rate control problem for such networks with an ergodic cost criterion is studied. It ..."
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Cited by 6 (5 self)
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Abstract: We consider critically loaded single class queueing networks with infinite buffers in which arrival and service rates are state (i.e., queue length) dependent and may be dynamically controlled. An optimal rate control problem for such networks with an ergodic cost criterion is studied. It is shown that the value function (i.e., optimum value of the cost) of the rate control problem for the network converges, under a suitable heavy traffic scaling limit, to that of an ergodic control problem for certain controlled reflected diffusions. Furthermore, we show that near optimal controls for limit diffusion models can be used to construct asymptotically near optimal rate control policies for the underlying physical queueing networks. The expected cost per unit time criterion studied here is given in terms of an unbounded holding cost and a linear control cost (“cost for effort”). Time asymptotics of a related uncontrolled model are studied as well. We establish convergence of invariant measures of scaled queue length processes to that of the limit reflecting diffusions. Our proofs rely on infinite time horizon stability estimates that are uniform in control and the heavy traffic parameter, for the scaled queue length processes. Another key ingredient, and a result of independent interest, in the proof of convergence of value functions is the existence of continuous near optimal feedback controls for the diffusion control model.
Robustness and Convergence of Approximations to Nonlinear Filters for JumpDiffusions
 Computational and Applied Math
, 1996
"... The paper treats numerical approximations to the nonlinear filtering problem for jumpdiffusion processes. This is a key problem in stochastic systems analysis. The processes are defined, and the optimal filters described. In the general nonlinear case, the optimal filters cannot be computed, and s ..."
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Cited by 4 (2 self)
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The paper treats numerical approximations to the nonlinear filtering problem for jumpdiffusion processes. This is a key problem in stochastic systems analysis. The processes are defined, and the optimal filters described. In the general nonlinear case, the optimal filters cannot be computed, and some numerical approximation is needed. Then the weak conditions that are required for the convergence of the approximations are given and the convergence is proved. Examples of useful approximations which satisfy the conditions are given. Quite weak conditions are given under which the approximating filter is continuous in the observation function, and it is shown that our canonical methods satisfy the conditions. Such continuity is essential if the approximations are to be used with confidence on actual physical data. Finally, we prove the convergence of monte carlo methods for approximating the optimal filters, and also show that the optimal filter is continuous in the parameters of the si...
Critical Branching Processes, (ii)Large Deviation Properties of Weakly Interacting Processes, (iii)Multiscale Diffusion Approximations for Stochastic Networks in Heavy Traffic, (iv) Adaptive Ergodic Control of Markov Chains, (v)Controlled Stochastic Netwo
, 2010
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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington