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Optimization Of Multiclass Queueing Networks with Changeover Times via the Achievable Region Approach: Part I, The Singlestation Case
, 1999
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The achievable region method in the optimal control of queueing systems; formulations, bounds and policies
 QUEUEING SYST
, 1995
"... We survey a new approach that the author and his coworkers have developed to formulate stochastic control problems (predominantly queueing systems) as mathematicalprogramming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., fi ..."
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Cited by 14 (4 self)
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We survey a new approach that the author and his coworkers have developed to formulate stochastic control problems (predominantly queueing systems) as mathematicalprogramming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable systems (multiclass single station queues and multiarmed bandit problems), restless bandit problems, polling systems, multiclass queueing and loss networks. These relaxations lead to bounds on the performance of an optimal policy. Using information from the relaxations we construct heuristic nearly optimal policies, The theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic control problems parallels efforts of the mathematical programming community in the last twenty years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and nearly optimal algorithms for restless bandit problems, polling systems, multiclass queueing and loss networks.
SelfControl of Traffic Lights and Vehicle Flows in Urban Road Networks
, 2008
"... Based on fluiddynamic and manyparticle (carfollowing) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of selforganized oscillations of pedestrian flows at bottlenecks [D. Helbing and P ..."
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Cited by 14 (3 self)
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Based on fluiddynamic and manyparticle (carfollowing) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of selforganized oscillations of pedestrian flows at bottlenecks [D. Helbing and P. Molnár, Phys. Rev. E 51 (1995) 4282–4286], we propose a selforganization approach to traffic light control. The problem can be treated as multiagent problem with interactions between vehicles and traffic lights. Specifically, our approach assumes a prioritybased control of traffic lights by the vehicle flows themselves, taking into account shortsighted anticipation of vehicle flows and platoons. The considered local interactions lead to emergent coordination patterns such as “green waves ” and achieve an efficient, decentralized traffic light control. While the proposed selfcontrol adapts flexibly to local flow conditions and often leads to noncyclical switching patterns with changing service sequences of different traffic flows, an almost periodic service may evolve under certain conditions and suggests the existence of a spontaneous synchronization of traffic lights despite the varying delays due to variable vehicle queues and travel times. The selforganized traffic light control is based on an optimization and a stabilization rule, each of which performs poorly at high utilizations of the road network, while their proper combination reaches a superior performance. The result is a considerable reduction not only in the average travel times, but also of their variation. Similar control approaches could be applied to the coordination of logistic and production processes.
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 14 (1 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...
Stochastic Scheduling of Parallel Queues with SetUp Costs
 QUEUEING SYSTEMS THEORY AND APPLICATIONS
, 1995
"... We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and a setup cost. The objective is to minimize the expected cost due to the waiting of jobs and t ..."
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Cited by 13 (3 self)
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We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and a setup cost. The objective is to minimize the expected cost due to the waiting of jobs and the switching of the server. A setup cost is required to effect an instantaneous switch from one queue to another. We partially characterize an optimal policy and provide a simple heuristic scheduling policy. The heuristic's performance is evaluated in the cases of two and three queues by comparison with a numerically obtained optimal policy. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances with four queues.
A SURVEY ON THE BANDIT PROBLEM WITH SWITCHING COSTS
, 2004
"... The paper surveys the literature on the bandit problem, focusing on its recent development in the presence of switching costs. Switching costs between arms makes not only the Gittins index policy suboptimal, but also renders the search for the optimal policy computationally infeasible. This survey w ..."
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Cited by 9 (0 self)
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The paper surveys the literature on the bandit problem, focusing on its recent development in the presence of switching costs. Switching costs between arms makes not only the Gittins index policy suboptimal, but also renders the search for the optimal policy computationally infeasible. This survey will first discuss the decomposability properties of the arms that make the Gittins index policy optimal, and show how these properties break down upon the introduction of costs on switching arms. Having established the failure of the simple index policy, the survey focus on the recent efforts to overcome the difficulty of finding the optimal policy in the bandit problem with switching costs: characterization of the optimal policy, exact derivation of the optimal policy in the restricted environments, and lastly approximation of optimal policy. The advantages and disadvantages of the above approaches are discussed.
The stochastic economic lot scheduling problem: heavy tra c analysis of dynamic cyclic policies. Sloan School of Management
, 1997
"... We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a nished goods inventory that services exogenous customer demand. Unsatis ed demand is backordered, and each class ha ..."
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Cited by 9 (2 self)
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We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a nished goods inventory that services exogenous customer demand. Unsatis ed demand is backordered, and each class has its own general service time distribution, renewal demand process, and holding and backordering cost rates. In the rst problem, a setup cost is incurred when the server switches class, and the setup cost is replaced by a setup time in the second problem. In both problems we employ a longrun average cost criterion and restrict ourselves to a class of dynamic cyclic policies, where idle periods and lot sizes are statedependent, but the N classes must be served in a xed sequence. Motivated by existing heavy tra c limit theorems, we make a time scale decomposition assumption that allows us to approximate these scheduling problems by di usion control problems. Our analysis of the approximating setup cost problem yields a closedform dynamic lotsizing policy and a computational procedure for an idling threshold. We derive structural results and an algorithmic procedure for the setup time problem. A computational study compares the proposed policy and several alternative policies to the numerically computed optimal policy. We consider a queueing system scheduling problem that is motivated by a situation commonly found in maketostock manufacturing. The system consists of a single server, or machine, and multiple customer classes, which will be referred to as products. Each product has its
Dynamic Server Assignment in a TwoQueue Model
 European Journal of Operational Research
, 1997
"... We consider a polling model of two M=G=1 queues, served by a single server. The service policy for this polling model is of threshold type. Service at queue 1 is exhaustive. Service at queue 2 is exhaustive unless the size of queue 1 reaches some level T during a service at queue 2; in the latte ..."
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Cited by 5 (1 self)
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We consider a polling model of two M=G=1 queues, served by a single server. The service policy for this polling model is of threshold type. Service at queue 1 is exhaustive. Service at queue 2 is exhaustive unless the size of queue 1 reaches some level T during a service at queue 2; in the latter case the server switches to queue 1 at the end of that service. Both zero and nonzero switchover times are considered. We derive exact expressions for the joint queue length distribution at customer departure epochs, and for the steadystate queuelength and sojourn time distributions. In addition, we supply a simple and very accurate approximation for the mean queue lengths, which is suitable for optimization purposes. AMS Subject Classification (1991): Primary: 60K25, Secondary: 90B22 Keywords & Phrases: Queueing, polling, ATM, threshold service, queue length distribution. 1 Introduction In this paper we consider a model of two M=G=1 queues, which are served by a single serve...
Mean value analysis for polling systems in heavy traffic
 In Proceedings of ValueTools, Pisa Article
, 2006
"... In this paper we present a new approach to derive heavytraffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general servicetime and switchover time distributions, and study its behavior when the load tends to one. F ..."
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Cited by 4 (2 self)
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In this paper we present a new approach to derive heavytraffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive service at each queue, and with general servicetime and switchover time distributions, and study its behavior when the load tends to one. For this model, we explore the recently proposed mean value analysis (MVA), which takes a new view on the dynamics of the system, and use this view to provide an alternative way to derive closedfrom expressions for the expected asymptotic delay; the expressions were derived earlier in [32], but in a different way. Moreover, the MVAbased approach enables us to derive closedform expressions for the heavytraffic limits of the covariances between the successive visit periods, which are key performance metrics in many application areas. These results, which have not been obtained before, reveal a number of insensitivity properties of the covariances with respect to the system parameters under heavytraffic assumptions, and moreover, lead to simple approximations for the covariances between the successive visit times for stable systems. Numerical examples demonstrate that the approximations are accurate when the load is close enough to one.
Multiproduct systems with both setup times and costs: Fluid bounds and schedules
 Operations Research
, 2004
"... 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 m ..."
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Cited by 4 (0 self)
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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 static, but is only an approximation when scheduling is dynamic. Heavytraffic analysis yields a refined bound that includes secondmoment terms. The fluid bound suggests both dynamic and static scheduling In this paper we consider a production environment where a number of different products are produced on a single machine and setup activities are necessary when switches of product type are made. These setup activities require both time and cost that depend on the specific product type. Throughout the paper we assume that the setups do not depend on the previous product produced