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48
MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic.
 Annals of Applied Probability
, 2004
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Scheduling flexible servers with convex delay costs: Heavytraffic optimality of the generalized cμrule
 OPER. RES
, 2004
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Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Network With Controllable Inputs
, 1989
"... Motivated by a factory scheduling problem, we consider the problem of input control (subject to a specified input mix) and priority sequencing in a multistation, multiclass queueing network with general service time distributions and a general routing structure. The objective is to minimize the long ..."
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Cited by 89 (6 self)
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Motivated by a factory scheduling problem, we consider the problem of input control (subject to a specified input mix) and priority sequencing in a multistation, multiclass queueing network with general service time distributions and a general routing structure. The objective is to minimize the longrun expected average number of customers in the system subject to a constraint on the longrun expected average output rate. Under balanced heavy loading conditions, this scheduling problem can be approximated by a control problem involving Brownian motion. Linear programming is used to reduce the
Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling
 QUEUEING SYSTEMS
, 1993
"... We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through th ..."
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Cited by 63 (5 self)
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We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian etwork models. Our main conclusion is that in many respects dynamic routing simplifies the behaviour of networks, and that under good control policies itmay well be possible to model the aggregate b haviour of a network quite straightforwardly.
Pathwise optimality of the exponential scheduling rule for wireless channels
 Advances in Applied Probability
, 2004
"... We consider the problem of scheduling transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a s ..."
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Cited by 61 (19 self)
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We consider the problem of scheduling transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a scheduling policy called Exponential scheduling rule, which was introduced in an earlier paper. Given a system with N users, and any set of positive numbers {an},n = 1,2,...,N, we show that in a heavytraffic limit, under a nonrestrictive complete resource pooling condition, this algorithm has the property that, for each time t, it (asymptotically) minimizes maxn an˜qn(t), where ˜qn(t) is user n queue length in the heavy traffic regime.
Dynamic routing in largescale service systems with heterogeneous servers
, 2005
"... Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is ..."
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Cited by 52 (12 self)
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Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is FSF which assigns customers to the Fastest Servers First. The asymptotic regime considered is the HalfinWhitt manyserver heavytraffic regime, which we refer to as the Quality and Efficiency Driven (QED) regime; it achieves high levels of both service quality and system efficiency by carefully balancing between the two. Additionally, expressions are provided for system limiting performance measures based on diffusion approximations. Our analysis shows that in the QED regime this heterogeneous server system outperforms its homogeneous server counterpart.
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.
Scheduling a multiclass queue with many exponential servers: Asymptotic optimality in heavytraffic
 THE ANNALS OF APPLIED PROBABILITY
, 2004
"... We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, line ..."
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Cited by 42 (14 self)
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We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavytraffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n ≈ r + β √ r for some scalar β. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.)
Heavy Traffic Limits for Some Queueing Networks
 Annals of Applied Probability
, 2001
"... Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under firstin firstout (FIFO), generalized headoftheline proportio ..."
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Cited by 33 (3 self)
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Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under firstin firstout (FIFO), generalized headoftheline proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines operating under firstbufferfirstserve (FBFS) and lastbufferfirstserve (LBFS) service disciplines; the last family consists of certain 2station, 5class networks operating under an SBP service discipline. Some of these heavy traffic limits have appeared earlier in the literature; our new proofs demonstrate the significant simplifications that can be achieved in the present setting.