Results 1  10
of
65
Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic,”
 Annals of Applied Probability,
, 2004
"... ..."
(Show Context)
Dynamic Scheduling of a System with Two Parallel Servers in Heavy Traffic with Resource Pooling: Asymptotic Optimality of a Threshold Policy
 Annals of Applied Probability
, 1999
"... This paper concerns a dynamic scheduling problem for a queueing system that has two streams of arrivals to infinite capacity buffers and two (nonidentical) servers working in parallel. One server can only process jobs from one buffer, whereas the other server can process jobs from either buffer. Th ..."
Abstract

Cited by 112 (6 self)
 Add to MetaCart
(Show Context)
This paper concerns a dynamic scheduling problem for a queueing system that has two streams of arrivals to infinite capacity buffers and two (nonidentical) servers working in parallel. One server can only process jobs from one buffer, whereas the other server can process jobs from either buffer. The service time distribution may depend on the buffer being served and the server providing the service. The system manager dynamically schedules waiting jobs onto available servers. We consider a parameter regime in which the system satisfies both a heavy traffic condition and a resource pooling condition. Our cost function is a mean cumulative discounted cost of holding jobs in the system, where the (undiscounted) cost per unit time is a linear function of normalized (with heavy traffic scaling) queue length. We first review the analytic solution of the Brownian control problem (formal heavy traffic approximation) for this system. We "interpret" this solution by proposing a threshold contro...
Scheduling flexible servers with convex delay costs: Heavytraffic optimality of the generalized cμrule
 OPER. RES
, 2004
"... ..."
Brownian models of open processing networks: Canonical representation of workload
 Ann. Appl. Probab
, 2003
"... ar ..."
(Show Context)
On Dynamic Scheduling of a Parallel Server System with Complete Resource Pooling
 In Analysis of Communication Networks: Call Centres, Traffic and Performance
, 2000
"... scientific noncommercial use only for individuals, with permission from the authors. We consider a parallel server queueing system consisting of a bank of buffers for holding incoming jobs and a bank of flexible servers for processing these jobs. Incoming jobs are classified into one of several dif ..."
Abstract

Cited by 66 (5 self)
 Add to MetaCart
(Show Context)
scientific noncommercial use only for individuals, with permission from the authors. We consider a parallel server queueing system consisting of a bank of buffers for holding incoming jobs and a bank of flexible servers for processing these jobs. Incoming jobs are classified into one of several different classes (or buffers). Jobs within a class are processed on a firstinfirstout basis, where the processing of a given job may be performed by any server from a given (classdependent) subset of the bank of servers. The random service time of a job may depend on both its class and the server providing the service. Each job departs the system after receiving service from one server. The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs to available servers. We consider a parameter regime in which the system satisfies both a heavy traffic and a complete resource pooling condition. Our cost function is an expected cumulative discounted cost of holding jobs in the system, where the (undiscounted) cost per unit time is a linear function of normalized (with heavy traffic scaling) queue length. In a prior work [40], the second author proposed a continuous review threshold control policy for use in such a parallel server system. This policy was advanced as an “interpretation ” of the analytic solution to an associated Brownian control problem (formal heavy
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 ..."
Abstract

Cited by 61 (19 self)
 Add to MetaCart
(Show Context)
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.
Sequencing and routing in multiclass queueing networks part I: Feedback regulation
 SIAM J. Control Optim
"... Abstract. Part II continues the development of policy synthesis techniques for multiclass queueing networks based upon a linear fluid model. The following are shown: (i) A relaxation of the fluid model based on workload leads to an optimization problem of lower dimension. An analogous workloadrelax ..."
Abstract

Cited by 55 (12 self)
 Add to MetaCart
(Show Context)
Abstract. Part II continues the development of policy synthesis techniques for multiclass queueing networks based upon a linear fluid model. The following are shown: (i) A relaxation of the fluid model based on workload leads to an optimization problem of lower dimension. An analogous workloadrelaxation is introduced for the stochastic model. These relaxed control problems admit pointwise optimal solutions in many instances. (ii) A translation to the original fluid model is almost optimal, with vanishing relative error as the networkload ρ approaches one. It is pointwise optimal after a short transient period, provided a pointwise optimal solution exists for the relaxed control problem. (iii) A translation of the optimal policy for the fluid model provides a policy for the stochastic networkmodel that is almost optimal in heavy traffic, over all solutions to the relaxed stochastic model, again with vanishing relative error. The regret is of order  log(1 − ρ).
Dynamic Pricing Strategies for Multiproduct Revenue Management Problems
, 2006
"... ..."
(Show Context)
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 ..."
Abstract

Cited by 46 (26 self)
 Add to MetaCart
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.
Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities
, 2002
"... We introduce a class of models, called newsvendor networks, that allow for multiple products and multiple processing and storage points and investigate how their singleperiod properties extend to dynamic settings. Such models provide a parsimonious framework to study various problems of stochastic ..."
Abstract

Cited by 43 (7 self)
 Add to MetaCart
We introduce a class of models, called newsvendor networks, that allow for multiple products and multiple processing and storage points and investigate how their singleperiod properties extend to dynamic settings. Such models provide a parsimonious framework to study various problems of stochastic capacity investment and inventory management, including assembly, commonality, distribution, flexibility, substitution and transshipment. Newsvendor networks are stochastic models with recourse that are characterized by linear revenue and cost structures and a linear inputoutput transformation. While capacity and inventory decisions are locked in before uncertainty is resolved, some managerial discretion remains via expost inputoutput activity decisions. Expost decisions involve both the choice of activities and their levels and can result in subtle benefits. This discretion in choice is captured through alternate or "nonbasic" activities that can redeploy inputs and resources to best respond to resolved uncertain events. Nonbasic activities are never used in a deterministic environment; their value stems from discretionary flexibility to meet stochastic demand deviations from the operating point. The optimal capacity and inventory decisions balance overages with underages. Continuing the classic newsvendor analogy, the optimal balancing conditions can be interpreted as