We propose new methods to solve simulation optimization problems over multidimensional discrete sets. The proposed methods are based on extending the objective function from a discrete domain to a continuous domain and applying stochastic approximation to the extended function. The extension of the objective function is constructed as a piecewise linear interpolation of the original objective function over a particular partition of ℝ d . The advantage of the proposed approach lies in that stochastic approximation is applied to the extension, not the original function, over ℝ d , so the estimated optimal solution at each iteration of the proposed methods is not restricted to be an integer point. Rather, we are free to approach the optimal solution aggressively by moving toward the direction of the steepest descent, thereby skipping over intervening points, thereby resulting in fast convergence in the early stage of the procedures. We provide a set of sufficient conditions under which the proposed methods guarantee the almost sure (a.s.) convergence to the optimal solution. One of such conditions is the multimodularity or L ♮ -convexity of the objective function, which arises in various inventory systems and queueing networks with controlled admission. Numerical examples illustrate the effectiveness of the proposed methods in such settings.

In Operations Research and Management Science (OR/MS), Discrete Event Simulation (DES) models are typically created using commercial off-the-shelf simulation packages (CSPs) such as AnyLogic™, Arena™, Flexsim™, Simul8™, SLX™, Witness™, and so on. A DES ...

State-dependent importance sampling algorithms based on mixtures are considered. The algorithms are designed to compute tail probabilities of a heavy-tailed random walk. The increments of the random walk are assumed to have a regularly varying distribution. Sufficient conditions for obtaining bounded relative error are presented for rather general mixture algorithms. Two new examples, called the generalized Pareto mixture and the scaling mixture, are introduced. Both examples have good asymptotic properties and, in contrast to some of the existing algorithms, they are very easy to implement. Their performance is illustrated by numerical experiments. Finally, it is proved that mixture algorithms of this kind can be designed to have vanishing relative error.

Quantiles, which are also known as values-at-risk in finance, frequently arise in practice as measures of risk. This article develops asymptotically valid confidence intervals for quantiles estimated via simulation using variance-reduction techniques (VRTs). We establish our results within a general framework for VRTs, which we show includes importance sampling, stratified sampling, antithetic variates, and control variates. Our method for verifying asymptotic validity is to first demonstrate that a quantile estimator obtained via a VRT within our framework satisfies a Bahadur-Ghosh representation. We then exploit this to show that the quantile estimator obeys a central limit theorem (CLT) and to develop a consistent estimator for the variance constant appearing in the CLT, which enables us to construct a confidence interval. We provide explicit formulae for the estimators for each of the VRTs considered.

Low-discrepancy sequences provide a way to generate quasi-random numbers of high dimensionality with a very high level of uniformity. The nearly orthogonal Latin hypercube and the generalized Halton sequence are two popular methods when it comes to generate low-discrepancy sequences. In this article, we propose to use evolutionary algorithms in order to find optimized solutions to the combinatorial problem of configuring generators of these sequences. Experimental results show that the optimized sequence generators behave at least as well as generators from the literature for the Halton sequence and significantly better for the nearly orthogonal Latin hypercube.

Radio signal strength estimation is essential in many applications, including the design of military radio communications and industrial wireless installations. For scenarios with large or richly featured geographical volumes, parallel processing is required to meet the memory and computation time demands. Here, we present a scalable and efficient parallel execution of the sequential model for radio signal propagation recently developed by Nutaro et al. [2008]. Starting with that model, we (a) provide a vector-based reformulation that has significantly lower computational overhead for event handling, (b) develop a parallel decomposition approach that is amenable to reversibility with minimal computational overheads, (c) present a framework for transparently mapping the conservative time-stepped model into an optimistic parallel discrete event execution, (d) present a new reversible method, along with its analysis and implementation, for inverting the vector-based event model to be executed in an optimistic parallel style of execution, and (e) present performance results from implementation on Cray XT platforms. We demonstrate scalability, with the largest runs tested on up to 127,500 cores of a Cray XT5, enabling simulation of larger scenarios and with faster execution than reported before on the radio propagation model. This also represents the first successful demonstration of the ability to efficiently map a conservative time-stepped model to an optimistic discrete-event execution.

Stroke disease places a heavy burden on society, incurring long periods of hospital and community care. Also stroke is a highly complex disease with heterogeneous outcomes and multiple strategies for therapy and care. In this article we develop a modeling framework that clusters patients with respect to their length of stay (LOS); phase-type models are then used to describe patient flows for each cluster. In most cases, there are multiple outcomes, such as discharge to normal residence, nursing home, or death. We therefore derive a novel analytical model for the distribution of LOS in such situations. A model of the whole care system is developed, based on Poisson admissions to hospital, and results obtained for expected numbers in different states of the system at any time. We can thus describe the whole integrated system of stroke patient care, which will facilitate planning of services. We also use the basic model to build a discrete-event simulation, which incorporates back-up queues to model delayed discharge. Based on stroke patients' data from the Belfast City Hospital, various scenarios are explored with a focus on the potential efficiency gains if LOS, prior to discharge to a private nursing home, can be reduced. Predictions for bed occupancy are also provided. The overall modeling framework characterizes the behavior of stroke patient populations, with a focus on integrated system-wide planning, encompassing hospital and community services. Within this general framework we can develop either analytic or simulation models that take account of patient heterogeneity and multiple care options.

The Emergency Department (ED) of a modern hospital is a highly complex system that gives rise to numerous managerial challenges. It spans the full spectrum of operational, clinical, and financial perspectives, over varying horizons: operational—a few hours or days ahead; tactical—weeks or a few months ahead; and strategic, which involves planning on monthly and yearly scales. Simulation offers a natural framework within which to address these challenges, as realistic ED models are typically intractable analytically. We apply a general and flexible ED simulator to address several significant problems that arose in a large Israeli hospital. The article focuses mainly, but not exclusively, on workforce staffing problems over these time horizons. First, we demonstrate that our simulation model can support real-time control, which enables short-term prediction and operational planning (physician and nurse staffing) for several hours or days ahead. To this end, we present a novel simulation-based technique that implements the concept of offered-load and discover that it performs better than a common alternative. Then we evaluate ED staff scheduling that adjusts for midterm changes (tactical horizon, several weeks or months ahead). Finally, we analyze the design and staffing problems that arose from physical relocation of the ED (strategic yearly horizon). Application of the simulation-based approach led to the implementation of our design and staffing recommendations.

We develop an efficient importance sampling algorithm for estimating the tail distribution of heavy-tailed compound sums, that is, random variables of the form S M = Z 1 +…+ Z M where the Z i 's are independently and identically distributed (i.i.d.) random variables in R and M is a nonnegative, integer-valued random variable independent of the Z i 's. We construct the first estimator that can be rigorously shown to be strongly efficient only under the assumption that the Z i 's are subexponential and M is light-tailed. Our estimator is based on state-dependent importance sampling and we use Lyapunov-type inequalities to control its second moment. The performance of our estimator is empirically illustrated in various instances involving popular heavy-tailed models.

Most popular simulation and emulation tools use high-level models of forwarding behavior in switches and routers, and give little guidance on setting model parameters such as buffer sizes. Thus, a myriad of papers report results that are highly sensitive to the forwarding model or buffer size used. Incorrect conclusions are often drawn from these results about transport or application protocol performance, service provisioning, or vulnerability to attacks. In this article, we argue that measurement-based models for routers and other forwarding devices are necessary. We devise such a model and validate it with measurements from three types of Cisco routers and one Juniper router, under varying traffic conditions. The structure of our model is device-independent, but the model uses device specific parameters. The compactness of the parameters and simplicity of the model make it versatile for high-fidelity simulations that preserve simulation scalability. We construct a profiler to infer the parameters within a few hours. Our results indicate that our model approximates different types of routers significantly better than the default ns-2 simulator models. The results also indicate that queue characteristics vary dramatically among the devices we measure, and that backplane contention can be a factor.