Optimal control of single-server fluid networks

We consider a stochastic single server fluid network with both a discounted reward and a cost structure. It can be shown that the optimal policy is a priority index policy. The indices coincide with the optimal indices in a Semi-Markovian Klimov problem. Several special cases like single server re-entrant fluid lines are considered. The approach we use is based on sample path arguments and Pontryagins maximum principle

Review on the Research for Separated Continuous Linear Programming: With Applications on Service Operations

We give a review on the research for a class of optimization model—separated continuous linear programming (SCLP). SCLP takes several similar forms and can be used to find the dynamic control of a multiclass fluid network. We review the duality theory and solution methods for it. We also present application examples of SCLP on service operations

Correction. Brownian models of open processing networks: canonical representation of workload

Due to a printing error the above mentioned article [Annals of Applied Probability 10 (2000) 75--103, doi:10.1214/aoap/1019737665] had numerous equations appearing incorrectly in the print version of this paper. The entire article follows as it should have appeared. IMS apologizes to the author and the readers for this error. A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an ``equivalent workload formulation'' of a Brownian network model. Denoting by $Z(t)$ the state vector of the original Brownian network, one has a lower dimensional state descriptor $W(t)=MZ(t)$ in the equivalent workload formulation, where $M$ can be chosen as any basis matrix for a particular linear space. This paper considers Brownian models for a very general class of open processing networks, and in that context develops a more extensive interpretation of the equivalent workload formulation, thus extending earlier work by Laws on alternate routing problems. A linear program called the static planning problem is introduced to articulate the notion of ``heavy traffic'' for a general open network, and the dual of that linear program is used to define a canonical choice of the basis matrix $M$. To be specific, rows of the canonical $M$ are alternative basic optimal solutions of the dual linear program. If the network data satisfy a natural monotonicity condition, the canonical matrix $M$ is shown to be nonnegative, and another natural condition is identified which ensures that $M$ admits a factorization related to the notion of resource pooling.Comment: Published at http://dx.doi.org/10.1214/105051606000000583 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Fuzzy Nonlinear Programming Approach for Optimizing the Performance of a Four-Objective Fluctuation Smoothing Rule in a Wafer Fabrication Factory

In theory, a scheduling problem can be formulated as a mathematical programming problem. In practice, dispatching rules are considered to be a more practical method of scheduling. However, the combination of mathematical programming and fuzzy dispatching rule has rarely been discussed in the literature. In this study, a fuzzy nonlinear programming (FNLP) approach is proposed for optimizing the scheduling performance of a four-factor fluctuation smoothing rule in a wafer fabrication factory. The proposed methodology considers the uncertainty in the remaining cycle time of a job and optimizes a fuzzy four-factor fluctuation-smoothing rule to sequence the jobs in front of each machine. The fuzzy four-factor fluctuation-smoothing rule has five adjustable parameters, the optimization of which results in an FNLP problem. The FNLP problem can be converted into an equivalent nonlinear programming (NLP) problem to be solved. The performance of the proposed methodology has been evaluated with a series of production simulation experiments; these experiments provide sufficient evidence to support the advantages of the proposed method over some existing scheduling methods

Dynamic Server Allocation at Parallel Queues

We explore whether dynamically reassigning servers to parallel queues in response to queue imbalances can reduce average waiting time in those queues. We use approximate dynamic programming methods to determine when servers should be switched, and we compare the performance of such dynamic allocations to that of a pre-scheduled deterministic allocation. Testing our method on both synthetic data and data from airport security checkpoints at Boston Logan International Airport, we find that in situations where the uncertainty in customer arrival rates is significant, dynamically reallocating servers can substantially reduce waiting time. Moreover, we find that intuitive switching strategies that are optimal for queues with homogeneous entry rates are not optimal in this setting. Keywords: control of queues, fluid queues, approximate dynamic programming, dynamic server allocation, workforce management

Dobrushin's approach to queueing network theory

R.L. Dobrushin (1929-1995) made substantial contributions to Queueing Network Theory (QNT). A review of results from QNT which arose from his ideas or were connected to him in other ways is given. We also comment on various related open problems.Peer Reviewe