relationship between perturbation realization factors with queueing models and markov models perturbation realization factor is an important concept in perturbation analysis of both queueing systems and markov systems a perturbation realization factor measures the effect of a perturbation on the system performance this concept is important for the performance sensitivity and performance optimization of these systems since the perturbations in queueing systems are continuous in nature and those in markov systems are discrete it is not straightforward to establish the relationship between these two types of fundamental concepts this note solves this long standing problem we find a formula that links these two types of perturbation realization factors in gordon newell and open jackson networks together the results enhance our understanding of perturbation analysis and lead to new research directions

optimal selection and control strategies for a flexible manufacturing and assembly system abstract this paper deals with the selection control problem of a system which consists of a flexible manufacturing cell m production lines and an assembly machine the flexible manufacturing cell feeds the production lines and the production lines feed the assembly machine sufficient conditions on optimal feedback selection control strategies that maximize the expected value of the total time that all the buffers concerned are simultaneously nonempty are derived also a simple feedback selection control strategy is proposed

stability and finite element approximation of phase change models for natural convection in porous media abstract in this paper we study a phase change problem for non isothermal incompressible viscous flows the underlying continuum is modelled as a viscous newtonian fluid where the change of phase is either encoded in the viscosity itself or in the brinkman boussinesq approximation where the solidification process influences the drag directly we address these and other modelling assumptions and their consequences in the simulation of differentially heated cavity flows of diverse type a second order finite element method for the primal formulation of the problem in terms of velocity temperature and pressure is constructed and we provide conditions for its stability we finally present several numerical tests in 2d and 3d corroborating the accuracy of the numerical scheme as well as illustrating key properties of the model

error estimates of finite element methods for nonstationary thermal convection problems with temperature dependent coefficients general error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature dependent coefficients these variable coefficients turn the diffusion and the buoyancy terms to be nonlinear which increases the nonlinearity of the problems an argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions error estimates are also provided for schemes modified by approximate coefficients which are used conveniently in practical computations

three dimensional finite element methods for the stokes problem the tetrahedral finite element approximation of the stokes problem is analyzed by means of polynomials piecewise of degree k 1 for the velocity and continuous piecewise of degree k for the pressure a stability result is given for every k ge 1

a projection based stabilized finite element method for steady state natural convection problem abstract we formulate a projection based stabilization finite element technique for solving steady state natural convection problems in particular we consider heat transport through combined solid and fluid media this stabilization does not act on the large flow structures based on the projection stabilization idea finite element error analysis of the problem is investigated and optimal errors for the velocity temperature and pressure are established we also present some numerical tests which both verify the theoretical predictions and demonstrate the method s promise

analysis of a conforming finite element method for the boussinesq problem with temperature dependent parameters abstract in this paper we analyze a conforming finite element method for the numerical simulation of non isothermal incompressible fluid flows subject to a heat source modeled by a generalized boussinesq problem with temperature dependent parameters we consider the standard velocity pressure formulation for the fluid flow equations which is coupled with a primal mixed scheme for the convection diffusion equation modeling the temperature in this way the unknowns of the resulting formulation are given by the velocity the pressure the temperature and the normal derivative of the latter on the boundary hence assuming standard hypotheses on the discrete spaces we prove existence and stability of solutions of the associated galerkin scheme and derive the corresponding cea s estimate for small and smooth solutions in particular any pair of stable stokes elements such as hood taylor elements for the fluid flow variables continuous piecewise polynomials of degree k 1 for the temperature and piecewise polynomials of degree k for the boundary unknown becomes feasible choices of finite element subspaces finally we derive optimal a priori error estimates and provide several numerical results illustrating the performance of the conforming method and confirming the theoretical rates of convergence

the performance of some manufacturing queueing networks when some of the machines are in the failure mode abstract using the theory of right continuous markov processes with values in n k an optimal control problem concerning the performance of manufacturing queueing networks when some of the machines are in the failure mode is dealt with

on the accuracy of the rotation form in simulations of the navier stokes equations the rotation form of the navier stokes equations nonlinearity is commonly used in high reynolds number flow simulations it was pointed out by a few authors and not widely known apparently that it can also lead to a less accurate approximate solution than the usual email protected u form we give a different explanation of this effect related to i resolution of the bernoulli pressure and ii the scaling of the coupling between velocity and pressure error with respect to the reynolds number we show analytically that i the difference between the two nonlinearities is governed by the difference in the resolution of the bernoulli and kinematic pressures and ii a simple linear grad div stabilization ameliorates much of the bad scaling of the velocity error with respect to re the rotation form does have superior conservation properties to the alternatives and it appears to be amenable to more efficient preconditioners thus the rotational form with grad div stabilization is a promising method we also give experiments that show bad velocity approximation is tied to poor pressure resolution in either form

policy iteration for customer average performance optimization of closed queueing systems we consider the optimization of queueing systems with service rates depending on system states the optimization criterion is the long run customer average performance which is an important performance metric different from the traditional time average performance we first establish with perturbation analysis a difference equation of the customer average performance in closed networks with exponentially distributed service times and state dependent service rates then we propose a policy iteration optimization algorithm based on this difference equation this algorithm can be implemented on line with a single sample path and does not require knowing the routing probabilities of queueing systems finally we give numerical experiments which demonstrate the efficiency of our algorithm this paper gives a new direction to efficiently optimize the customer centric performance in queueing systems

max min optimality of service rate control in closed queueing networks in this technical note we discuss the optimality properties of service rate control in closed jackson networks we prove that when the cost function is linear to a particular service rate the system performance is monotonic w r t with respect to that service rate and the optimal value of that service rate can be either maximum or minimum we call it max min optimality when the second order derivative of the cost function w r t a particular service rate is always positive negative which makes the cost function strictly convex concave the optimal value of such service rate for the performance maximization minimization problem can be either maximum or minimum to the best of our knowledge this is the most general result for the optimality of service rates in closed jackson networks and all the previous works only involve the first conclusion moreover our result is also valid for both the state dependent and load dependent service rates under both the time average and customer average performance criteria

stationary solutions for generalized boussinesq models abstract we study the existence regularity and conditions for uniqueness of solutions of a generalized boussinesq model for thermally driven convection the model allows temperature dependent viscosity and thermal conductivity

optimization of queues using an infinitesimal perturbation analysis based stochastic algorithm with general update times convergence with probability one of a stochastic optimization algorithm for a single server queue is proved the parameter to be optimized is updated using an infinitesimal perturbation analysis estimate of the gradient of the performance measure and the updates are performed at general times first an algorithm in which the parameter is updated before each customer begins service is considered then it is shown how this analysis can be extended to an algorithm that updates at certain stopping times the analysis suggests that the sample path behavior of the algorithm is similar to that of an algorithm that updates at the start of every busy period

smoothed conditional perturbation analysis of discrete event dynamical systems a new sample path analysis approach based on the smoothing property of conditional expectation for estimating the performance sensitivity of discrete event dynamical systems is proposed several examples are presented to show how this approach overcomes a difficulty of the ordinary infinitesimal perturbation analysis the basic message is that one can get more knowledge about the system performance by observing and analyzing the sample path than by using the conventional simulation approach it is also pointed out that the classical queueing theory approach for getting the performance sensitivity and the sample path based infinitesimal perturbation analysis approach can be unified in the framework of the new approach the smoothed conditional perturbation analysis

stabilized finite element approximations for a generalized boussinesq problem a posteriori error analysis abstract the purpose of this work is the design and analysis of a posteriori error estimators for low order stabilized finite element approximations of a generalized boussinesq problem we consider standard stabilization procedures over conforming finite element spaces and a nonconforming one that delivers a divergence free discrete velocity field the analysis that is valid for two and three dimensional domains relies on a smallness assumption on the solution and is based on a technique that involves the ritz projection of the residuals the devised a posteriori error estimators are proven to be globally reliable and locally efficient three dimensional numerical experiments reveal a competitive performance of adaptive procedures driven by the designed a posteriori error estimators

an optimal selection policy for a flexible manufacturing cell feeding several production lines abstract this paper deals with the selection problem of a flexible manufacturing cell feeding several production lines sufficient conditions on optimal selection policies which maximize the total amount of time that all the production lines are simultaneously active are derived a procedure for computing a suboptimal feedback selection policy is also proposed

dual mixed finite element methods for the stationary boussinesq problem abstract we propose and analyze two mixed approaches for numerically solving the stationary boussinesq model describing heat driven flows for the fluid equations the velocity gradient and a bernoulli stress tensor are introduced as auxiliary unknowns for the heat equation we consider primal and mixed primal formulations the latter incorporating additionally the normal component of the temperature gradient on the dirichlet boundary both dual mixed formulations exhibit the same classical structure of the navier stokes equations we derive a priori estimates and the existence of continuous and discrete solutions for the formulations in addition we prove the uniqueness of solutions and optimal order error estimates provided the data is sufficiently small numerical experiments are given which back up the theoretical results and illustrate the robustness and accuracy of both methods for a classic benchmark problem

decentralized control of service rates in a closed jackson network the authors consider a closed jackson network with m nodes the service rate at each node is controllable in a decentralized manner i e it will be controlled based on local information extracted from that node only for each node there is a holding cost and an operating cost it is assumed that both costs are time homogeneous and that the operating cost is a linear function of the service rate however both costs are arbitrary functions of the number of jobs at the node the objective is to minimize the time average expected total cost it is shown that there exists an optimal control characterized by a set of thresholds one for each node such that it is optimal for each node to serve at zero rates if the number of jobs there is below or at the threshold and serve at maximum allowed rates when the number of jobs exceeds the threshold this structure of the optimal control is identified by using the product form solution of the jackson network and the duality theory of linear programming

a monolithical fluid structure interaction algorithm applied to the piston problem abstract an investigation of time marching computational fluid structure interaction algorithms is presented the analysis is applied to the piston problem attention is focussed on the time integration properties of the coupling algorithms the staggered scheme is first investigated where fluid and structure are alternately integrated by separate solvers in a predictor corrector fashion this algorithm suffers from a time lag between the integration of the fluid and structure the influence of the time lag is investigated by the comparison of different predictions for the structure a novel monolithical algorithm is then introduced in order to annihilate the time lag this algorithm integrates fluid structure and interaction as a single system by an implicit algorithm linear acoustic as well as nonlinear euler equations for gas dynamics are investigated the numerical results of the staggered scheme reveal a non physical deviation of the mean position of the piston at higher cfl numbers the deviation of the mean position is not present in the calculation with the monolithical scheme stability analysis shows the unconditional stability of the monolithical scheme for the acoustic equations whereas the staggered scheme has a limited domain of stability this domain can be enlarged by an improvement of the structural prediction analysis of the damping shows an energy production in the staggered scheme while the monolithical scheme has no energy production term the analyses lead to the formulation of the interaction consistency law which prescribes the relation for the time discretisation between fluid and structure solvers and their boundary conditions

perturbation realization potentials and sensitivity analysis of markov processes two fundamental concepts and quantities realization factors and performance potentials are introduced for markov processes the relations among these two quantities and the group inverse of the infinitesimal generator are studied it is shown that the sensitivity of the steady state performance with respect to the change of the infinitesimal generator can be easily calculated by using either of these three quantities and that these quantities can be estimated by analyzing a single sample path of a markov process based on these results algorithms for estimating performance sensitivities on a single sample path of a markov process can be proposed the potentials in this paper are defined through realization factors and are shown to be the same as those defined by poisson equations the results provide a uniform framework of perturbation realization for infinitesimal perturbation analysis ipa and non ipa approaches to the sensitivity analysis of steady state performance they also provide a theoretical background for the pa algorithms developed in recent years

conservative load projection and tracking for fluid structure problems the loose coupling of computational fluid dynamics and computational structural dynamics solvers introduces some problems related to the information transfer between the codes some techniques developed to solve the problems of the load transfer and interface surface tracking are presented the main criterion is to achieve conservation of total loads and total energy the load projection scheme is based on gaussian integration and fast interpolation algorithms for unstructured grids the surface tracking algorithm also based on interpolation is important for many applications including aeroelastic deformation of wings due to aerodynamic loads the methodologies not only improve present fluid structure interaction simulations but also increase the range of their applicability these techniques are of general character and can be used in other multidisciplinary applications as well

a mixed formulation of boussinesq equations analysis of nonsingular solutions this paper is concerned with the mixed formulation of the boussinesq equations in two dimensional domains and its numerical approximation the paper deals first with existence and uniqueness results as well as the description of the regularity of any solution the problem is then approximated by a mixed finite element method where the gradient of the velocity and the gradient of the temperature quantities of practical importance are introduced as new unknowns an existence result for the finite element solution and convergence results are proved near a nonsingular solution quasi optimal error estimates are finally presented

optimal intensity control of a queueing system with state dependent capacity limit a general single state queueing system in which the input and output processes are modeled as point processes with stochastic intensities is studied the problem is to control both the input and the output intensities subject to some state dependent capacity limits and the objective is to maximize a discounted value function with reasonable assumptions on the capacity limits it is shown that there exists an optimal control that is of the threshold type characterized by a finite upper barrier the lower barrier being zero the results developed provide theoretical justification for the optimality of the threshold control which is widely applied in practice