Donald L. Iglehart

Bio: Donald L. Iglehart is an academic researcher from Stanford University. The author has contributed to research in topics: Markov chain & Queueing theory. The author has an hindex of 28, co-authored 69 publications receiving 4137 citations.

Importance sampling for stochastic simulations

Abstract: Importance sampling is one of the classical variance reduction techniques for increasing the efficiency of Monte Carlo algorithms for estimating integrals. The basic idea is to replace the original...

Multiple channel queues in heavy traffic. I

Abstract: The queueing systems considered in this paper consist of r independent arrival channels and s independent service channels, where as usual the arrival and service channels are independent. Arriving customers form a single queue and are served in the order of their arrival without defections. We shall treat two distinct modes of operation for the service channels. In the standard system a waiting customer is assigned to the first available service channel and the servers (servers ≡ service channels) are shut off when they are idle. Thus the classical GI/G/s system is a special case of our standard system. In the modified system a waiting customer is assigned to the service channel that can complete his service first and the servers are not shut off when they are idle. While the modified system is of some interest in its own right, we introduce it primarily as an analytical tool. Let λ i denote the arrival rate (reciprocal of the mean interarrival time) in the ith arrival channel and μ j the service rate (reciprocal of the mean service time) in the jth service channel. Then is the total arrival rate to the system and is the maximum service rate of the system. As a measure of congestion we define the traffic intensity ρ = λ/μ.

Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem

Abstract: The optimal ordering policy for a n-period dynamic inventory problem in which the ordering cost is linear plus a fixed reorder cost and the other one-period costs are convex is characterized by a pair of critical numbers, (sn, Sn); see Scarf, [4]. In this paper we give bounds for the sequences {sn} and {Sn} and discuss their limiting behavior. The limiting (s, S) policy characterizes the optimal ordering policy for the infinite horizon problem. Similar results are obtained if there is a time-lag in delivery.

Simulating Stable Stochastic Systems: III. Regenerative Processes and Discrete-Event Simulations

Abstract: This paper shows that a previously developed technique for analyzing simulations of GI/G/s queues and Markov chains applies to discrete-event simulations that can be modeled as regenerative processes. It is possible to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of observations that produces independent identically distributed blocks in the course of the simulation. This grouping allows one to obtain confidence intervals for a general function of the steady-state distribution of the process being simulated and for the asymptotic cost per unit time. The technique is illustrated with a simulation of a retail inventory distribution system.

Multiple channel queues in heavy traffic. II: sequences, networks, and batches

Abstract: : Sequences of queueing facilities with r parallel arrival channels and s parallel service channels are studied under the conditions of heavy traffic: the associated sequences of traffic intensities approaching a limit greater than or equal to one. Weak convergence is obtained for sequences of random functions induced in D(0,1) by the basic queueing processes. Sequences of queueing systems in heavy traffic which are networks of the facilities described above are also investigated. Furthermore, customers are allowed to arrive and be served in batches.

Dynamic Programming and Optimal Control

Abstract: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning.

Convergence of Probability Measures

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Modelling of extremal events in insurance and finance

Abstract: Extremal events play an increasingly important role in stochastic modelling in insurance and finance. Over many years, probabilists and statisticians have developed techniques for the description, analysis and prediction of such events. In the present paper, we review the relevant theory which may also be used in the wider context of Operation Research. Various applications from the field of insurance and finance are discussed. Via an extensive list of references, the reader is guided towards further material related to the above problem areas.

Practical Markov Chain Monte Carlo

Abstract: Markov chain Monte Carlo using the Metropolis-Hastings algorithm is a general method for the simulation of stochastic processes having probability densities known up to a constant of proportionality. Despite recent advances in its theory, the practice has remained controversial. This article makes the case for basing all inference on one long run of the Markov chain and estimating the Monte Carlo error by standard nonparametric methods well-known in the time-series and operations research literature. In passing it touches on the Kipnis-Varadhan central limit theorem for reversible Markov chains, on some new variance estimators, on judging the relative efficiency of competing Monte Carlo schemes, on methods for constructing more rapidly mixing Markov chains and on diagnostics for Markov chain Monte Carlo.

Robust Optimization of Large-Scale Systems

Abstract: Mathematical programming models with noisy, erroneous, or incomplete data are common in operations research applications. Difficulties with such data are typically dealt with reactively-through sensitivity analysis-or proactively-through stochastic programming formulations. In this paper, we characterize the desirable properties of a solution to models, when the problem data are described by a set of scenarios for their value, instead of using point estimates. A solution to an optimization model is defined as: solution robust if it remains "close" to optimal for all scenarios of the input data, and model robust if it remains "almost" feasible for all data scenarios. We then develop a general model formulation, called robust optimization RO, that explicitly incorporates the conflicting objectives of solution and model robustness. Robust optimization is compared with the traditional approaches of sensitivity analysis and stochastic linear programming. The classical diet problem illustrates the issues. Robust optimization models are then developed for several real-world applications: power capacity expansion; matrix balancing and image reconstruction; air-force airline scheduling; scenario immunization for financial planning; and minimum weight structural design. We also comment on the suitability of parallel and distributed computer architectures for the solution of robust optimization models.