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Queueing dynamics and maximal throughput scheduling in switched processing systems. Queueing systems
"... Abstract. We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the ..."
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Cited by 49 (14 self)
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Abstract. We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the most workloadintensive input traffic traces (arrival processes). Stability preserves the job inflow–outflow balance at each queue on the traffic traces. Two key families of service policies are shown to maximize throughput, under the mild condition that traffic traces have longterm average workload rates. In the first family of cone policies, the service mode is chosen based on the system backlog state belonging to a corresponding cone. Two distinct policy classes of that nature are investigated, MaxProduct and FastEmpty. In the second family of batch policies (BatchAdapt), jobs are collectively scheduled over adaptively chosen horizons, according to an asymptotically optimal, robust schedule. The issues of nonpreemptive job processing and nonnegligible switching times between service modes are addressed. The analysis is extended to cover feedforward networks of such processing systems/nodes. The approach taken unifies and generalizes prior studies, by developing a general tracebased modeling framework (samplepath approach) for addressing the queueing stability problem. It treats the queueing structure as a deterministic dynamical system and analyzes directly its evolution trajectories. It does not require any probabilistic superstructure, which is
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
Optimal control of a highvolume assembletoorder system
 Mathematics of Operations Research
, 2006
"... For an assembletoorder system with a high volume of prospective customers arriving per unit time, we show how to set nominal component production rates, quote prices and maximum leadtimes for products, and then, dynamically, sequence orders for assembly and expedite components. (Components must b ..."
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Cited by 16 (6 self)
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For an assembletoorder system with a high volume of prospective customers arriving per unit time, we show how to set nominal component production rates, quote prices and maximum leadtimes for products, and then, dynamically, sequence orders for assembly and expedite components. (Components must be expedited if necessary to fill an order within the maximum leadtime). We allow for updating of the prices, maximum leadtimes, and nominal component production rates in response to periodic, random shifts in demand and supply conditions. Assuming expediting costs are large, we prove that our proposed policy maximizes infinite horizon expected discounted profit in the high volume limit. For a more general assembletoorder system with arbitrary cost of expediting and the option to salvage excess components, we show how to solve an approximating Brownian control problem and translate its solution into an effective control policy. 1
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 # .
Near Optimal Control of Queueing Networks over a Finite Time Horizon
, 2007
"... We propose a novel approach for controlling queueing networks that minimizes weighted holding costs over a finite time horizon. Our approach approximates the discrete problem by a fluid system for which an optimization problem is formulated. This problem is a separated continuous linear program, it ..."
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Cited by 12 (10 self)
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We propose a novel approach for controlling queueing networks that minimizes weighted holding costs over a finite time horizon. Our approach approximates the discrete problem by a fluid system for which an optimization problem is formulated. This problem is a separated continuous linear program, it is solved optimally using a simplex based algorithm of Weiss. The solution consists of piecewise constant allocations of the activities, with a finite number of breakpoints over the time horizon. Once solved, we associate a multiclass queueing network with infinite virtual queues with each interval of the fluid solution, and this measures the deviations of the original system from the fluid solution. We then track the fluid solution by using an adaptation of Dai and Lin’s maximum pressure policy that keeps these deviations rate stable. This procedure is asymptotically optimal as we scale up the number of jobs and the processing speed. We illustrate the details of the approach on a simple example composed of two servers and three queues. Simulation results confirm that the system performance is near optimal when the network is scaled up.
Management of DemandDriven Production Systems
 IEEE TRANS. AUTOMAT. CONTROL
, 2004
"... Controlsynthesis techniques are developed for demand driven production systems. The resulting policies are timeoptimal for a deterministic model, and approximately timeoptimal for a stochastic model. Moreover, they are easily adapted to take into account a range of issues that arise in a realisti ..."
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Cited by 10 (6 self)
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Controlsynthesis techniques are developed for demand driven production systems. The resulting policies are timeoptimal for a deterministic model, and approximately timeoptimal for a stochastic model. Moreover, they are easily adapted to take into account a range of issues that arise in a realistic, dynamic environment. In particular, control synthesis techniques are developed for models in which resources are temporarily unavailable. This may be due to failure, maintenance, or an unanticipated change in demand. These conclusions are based upon the following development...
Capacity Realization in Stochastic BatchProcessing Networks Using DiscreteReview Policies
, 1999
"... We present difficulties with realizing the capacity of queueing networks with batch servers under well known scheduling disciplines. We introduce a family of scheduling policies called discretereview policies, which not only guarantee capacity realization for queueing networks with batch servers, b ..."
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Cited by 4 (0 self)
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We present difficulties with realizing the capacity of queueing networks with batch servers under well known scheduling disciplines. We introduce a family of scheduling policies called discretereview policies, which not only guarantee capacity realization for queueing networks with batch servers, but also contain among them policies that allow us to realize desired behavior on "fluid" scale, including asymptotically optimal policies. In this family of policies system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed, which is then executed in openloop fashion. We outline a proof of capacity realization for every policy in this family, and provide results of simulation studies that establish the usefulness of the proposed family of policies.