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Performance Evaluation and Policy Selection in Multiclass Networks
, 2002
"... This paper concerns modelling and policy synthesis for regulation of multiclass queueing networks. A 2parameter network model is introduced to allow independent modelling of variability and mean processingrates, while maintaining simplicity of the model. Policy synthesis is based on consideration ..."
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Cited by 46 (26 self)
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This paper concerns modelling and policy synthesis for regulation of multiclass queueing networks. A 2parameter network model is introduced to allow independent modelling of variability and mean processingrates, while maintaining simplicity of the model. Policy synthesis is based on consideration of more tractable workload models, and then translating a policy from this abstraction to the discrete network of interest. Translation is made possible through the use of safetystocks that maintain feasibility of workload trajectories. This is a wellknown approach in the queueing theory literature, and may be viewed as a generic approach to avoid deadlock in a discreteevent dynamical system. Simulation is used to evaluate a given policy, and to tune safetystock levels. These simulations are accelerated through a variance reduction technique that incorporates stochastic approximation to tune the variance reduction. The search for appropriate safetystock levels is coordinated through a cutting plane algorithm. Both the policy synthesis and the simulation acceleration rely heavily on the development of approximations to the value function through fluid model considerations.
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
Analysis of multiserver systems via dimensionality reduction of Markov chains
 School of Computer Science, Carnegie Mellon University
, 2005
"... The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chai ..."
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Cited by 22 (4 self)
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The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov
Control of Mobile Communications with Time Varying Channels in Heavy Traffic
 IEEE Trans. Automat. Control
, 2001
"... Consider a system with a xed number (K) of remote units and a single base transmitter with time varying (and perhaps correlated) connecting channels. Data to be transmitted to the remote units arrives according to some random process and is queued according to its destination. The forward link is tr ..."
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Cited by 22 (4 self)
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Consider a system with a xed number (K) of remote units and a single base transmitter with time varying (and perhaps correlated) connecting channels. Data to be transmitted to the remote units arrives according to some random process and is queued according to its destination. The forward link is treated. Power is to be allocated to the K channels in a queue and channel state dependent way to minimize some cost criterion. The modeling and control problem can be quite difficult. The channel time variations (fading) are fast and the bandwidth and data arrival rates are high. Owing to the complexity of the physical problem and the high speed of both the fading and arrival and service rates, an asymptotic or averaging method is promising. A heavy traffic analysis is done. By heavy traffic, we mean that on the average there is little server idle time and little spare power over the "average" requirements. Heavy traffic analysis has been very helpful in simplifying analysis of both controlled and uncontrolled problems in queueing and communications networks. It tends to eliminate unessential detail and focus on the fundamental issues of scaling and parametric dependencies. To illustrate the scope of the method, a variety of models are considered. The basic model assumes that the channel state is known or can be well estimated and that given the channel state there is a well defined rate of transmission per unit power. Then convergence of the controlled scaled queue lengths is shown. The scaling is different from the usual in heavy traffic work, and the limit Wiener process depends only on the channel state process and not on the...
Multiproduct systems with both setup times and costs: Fluid bounds and schedules.
 Operations Research,
, 2006
"... Abstract This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using ..."
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Cited by 18 (0 self)
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Abstract This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using a fluid model, we provide a closedform lower bound on system performance. This bound is also shown to provide a lower bound for stochastic systems when scheduling is local or static, but is only an approximation when scheduling is global or dynamic. The fluid bound suggests both local and global scheduling heuristics, which are tested for the stochastic system via a simulation study.
Reliability by Design in Distributed Power Transmission Networks
, 2005
"... The system operator of a large power transmission network must ensure that power is delivered whenever there is demand in order to maintain highly reliable electric service. To fulfill this mandate, the system operator must procure reserve capacity to respond to unforeseen events such as an unexpect ..."
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Cited by 17 (11 self)
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The system operator of a large power transmission network must ensure that power is delivered whenever there is demand in order to maintain highly reliable electric service. To fulfill this mandate, the system operator must procure reserve capacity to respond to unforeseen events such as an unexpected surge in demand. This paper constructs a centralized optimal solution for a power network model by generalizing recent techniques for the centralized optimal control of demanddriven production systems. The optimal solution indicates how reserves must be adjusted according to environmental factors including variability, and the rampingrate constraints on generation. Sensitivity to transmission constraints is addressed through the construction of an effective cost on an aggregate model.
Dynamic SafetyStocks for Asymptotic Optimality in Stochastic Networks
 Queueing Syst. Theory Appl
, 2004
"... This paper concerns control of stochastic networks using statedependent safetystocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the DaiWang reentrant line. In each case, a single policy is proposed that is independent of network load # . ..."
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Cited by 16 (7 self)
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This paper concerns control of stochastic networks using statedependent safetystocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the DaiWang reentrant line. In each case, a single policy is proposed that is independent of network load # .
Workload Models for Stochastic Networks: Value Functions and Performance Evaluation
, 2005
"... This paper concerns control and performance evaluation for stochastic network models. Structural properties of value functions are developed for controlled Brownian motion (CBM) and deterministic (fluid) workloadmodels, leading to the following conclusions: Outside of a nullset of network paramete ..."
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Cited by 16 (9 self)
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This paper concerns control and performance evaluation for stochastic network models. Structural properties of value functions are developed for controlled Brownian motion (CBM) and deterministic (fluid) workloadmodels, leading to the following conclusions: Outside of a nullset of network parameters, (i) The fluid valuefunction is a smooth function of the initial state. Under further minor conditions, the fluid valuefunction satisfies the derivative boundary conditions that are required to ensure it is in the domain of the extended generator for the CBM model. Exponential ergodicity of the CBM model is demonstrated as one consequence. (ii) The fluid valuefunction provides a shadow function for use in simulation variance reduction for the stochastic model. The resulting simulator satisfies an exact large deviation principle, while a standard simulation algorithm does not satisfy any such bound. (iii) The fluid valuefunction provides upper and lower bounds on performance for the CBM model. This follows from an extension of recent linear programming approaches to performance evaluation.
Stability and asymptotic optimality of generalized maxweight policies
 SIAM Journal on Control and Optimization
"... Abstract It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the "marginal disutility" at a buffer vanishes fo ..."
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Cited by 16 (2 self)
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Abstract It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the "marginal disutility" at a buffer vanishes for vanishingly small buffer population. This observation motivates the hMaxWeight policy, defined for a wide class of functions h. These policies share many of the attractive properties of the MaxWeight policy: (i) Arrival rate data is not required in the policy. (ii) Under a variety of general conditions, the policy is stabilizing when h is a perturbation of a monotone linear function, a monotone quadratic, or a monotone Lyapunov function for the fluid model. (iii) A perturbation of the relative value function for a workload relaxation gives rise to a myopic policy that is approximately averagecost optimal in heavy traffic, with logarithmic regret. The first results are obtained for a general Markovian network model. Asymptotic optimality is established for a general Markovian scheduling model with a single bottleneck, and homogeneous servers.