Control of systems with flexible multi-server pools: a shadow routing approach

A general model with multiple input flows (classes) and several flexible multi-server pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queueing system. We study the behavior of our scheme in the Halfin–Whitt (or, QED) asymptotic regime, when server pool sizes and the input rates are scaled up simultaneously by a factor r growing to infinity, while keeping the system load within \(O(\sqrt{r}\,)\) of its capacity.The main results are as follows. (i) We show that, in general, a system in a stationary regime has at least \(O(\sqrt{r}\,)\) average queue lengths, even if the so called null-controllability (Atar et al., Ann. Appl. Probab. 16, 1764–1804, 2006) on a finite time interval is possible; strategies achieving this \(O(\sqrt{r}\,)\) growth rate we call order-optimal. (ii) We show that some natural algorithms, such as MaxWeight, that guarantee stability, are not order-optimal. (iii) Under the complete resource pooling condition, we prove the diffusion limit of the arrival processes into server pools, under the Shadow routing. (We conjecture that result (iii) leads to order-optimality of the Shadow routing algorithm; a formal proof of this fact is an important subject of future work.) Simulation results demonstrate good performance and robustness of our scheme.     

Rigid–flexible interactive dynamics modelling approach

Dynamics modelling of multi-body systems composed of rigid and flexible elements is elaborated in this article. The control of such systems is highly complicated due to severe underactuated conditions caused by flexible elements and an inherent uneven non-linear dynamics. Therefore, developing a compact dynamics model with the requirement of limited computations is extremely useful for controller design, simulation studies for design improvement and also practical implementations. In this article, the rigid–flexible interactive dynamics modelling (RFIM) approach is proposed as a combination of Lagrange and Newton–Euler methods, in which the motion equations of rigid and flexible members are separately developed in an explicit closed form. These equations are then assembled and solved simultaneously at each time step by considering the mutual interaction and constraint forces. The proposed approach yields a compact model rather than a common accumulation approach that leads to a massive set of equations in which the dynamics of flexible elements is united with the dynamics equations of rigid members. The proposed RFIM approach is first detailed for multi-body systems with flexible joints, and then with flexible members. Then, to reveal the merits of this new approach, few case studies are presented. A flexible inverted pendulum is studied first as a simple template for lucid comparisons, and next a space free-flying robotic system that contains a rigid main body equipped with two manipulating arms and two flexible solar panels is considered. Modelling verification of this complicated system is vigorously performed using ANSYS and ADAMS programs. The obtained results reveal the outcome accuracy of the new proposed approach for explicit dynamics modelling of rigid–flexible multi-body systems such as mobile robotic systems, while its limited computations provide an efficient tool for controller design, simulation studies and also practical implementations of model-based algorithms.     

Allocating flexible servers in serial systems with switching costs

Consider a firm that operates a make-to-order serial production system and employs a cross-trained workforce. We model such a firm as a tandem queuing system in which flexible servers can be allocated across stations, and assume that a switching cost is charged when servers move between stations. We show that even in the two-station two-server case the optimal policy follows a complex state-dependent structure that may be difficult to implement in practice. We propose three alternate heuristic policies and assess their performance. We show that a simpler policy which only moves one server can achieve close to optimal results.     

Mixed convection heat transfer by nanofluids in a cavity with two oscillating flexible fins: A fluid–structure interaction approach

This study investigated the effects of two oscillating fins on the heat transfer rate and flow characteristics of a nanofluid inside a square enclosure. Both fins were attached to the hot wall and both fins oscillated at the same frequencies and amplitudes. The finite element method implemented in the arbitrary Lagrangian–Eulerian (ALE) technique was used to solve the equations describing the interactions and movements of the nanofluid and fins. Comparisons of our results and those reported in previous studies demonstrated that the modeling and numerical investigations were valid and reliable. The results showed that the increase in the heat transfer rate was due to the oscillation of the fins. In addition, the increasing trend in the heat transfer rate due to the oscillating fins decreased as the ratio of the thermal conductivity of the fins relative to the nanofluid increased. Increasing the thermal conductivity and viscosity parameters enhanced and weakened the heat transfer rate, respectively.     

A flexible block classical Gram–Schmidt skeleton with reorthogonalization

We investigate a variant of the reorthogonalized block classical Gram–Schmidt method for computing the QR factorization of a full column rank matrix. Our aim is to bound the loss of orthogonality even when the first local QR algorithm is only conditionally stable. In particular, this allows the use of modified Gram–Schmidt instead of Householder transformations as the first local QR algorithm. Numerical experiments confirm the stable behavior of the new variant. We also examine the use of non-QR local factorization and show by example that the resulting variants, although less stable, may also be applied to ill-conditioned problems.     

Inventory based allocation policies for flexible servers in?serial systems

Motivated by an industry example, we study a two-station serial system in which we allocate flexible servers in order to maximize throughput. We investigate two cases which are different in the way that servers work together when at the same station; namely collaboratively or non-collaboratively. For the collaborative case we prove the optimal policy to be such that the servers work together at a single station at any point in time. In addition to the policy being state-dependent, it also follows a switching-curve structure. In the non-collaborative case, on the other hand, it may be optimal to allocate servers to different stations. Some numerical examples and results regarding policy assignments, switching curves, and system throughput are presented.     

Необходимое условие полноты системы экспонент в прострaнстве квaдрaтично интегрируемых функций со степенным весом

A necessary condition is obtained for the completeness of the system of exponents $$e(\Lambda ) = \left\{ {e^{ - \lambda _n t} :\lambda _n \in \left\{ {z:0 < \operatorname{Re} z < A \in \mathbb{R}^ + ,0 < \operatorname{Im} z < 2\pi } \right\}} \right\}$$ in the space of square integrable functions with the power weight t ^?? , where ?1 < ?? < 0.     

Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation

In this paper, the developed model of an N-flexible-link mobile manipulator with revolute-prismatic joints is presented for the cooperative flexible multi mobile manipulator. In this model, the deformation of flexible links is calculated by using the assumed modes method. In additions, non-holonomic constraints of the robots’ mobile platforms that bound its locomotion are considered. This limitation is alleviated through the concurrent motion of revolute and prismatic joints, although it results in computational complexity and changes the final motion equations to time-varying form. Not only is the proposed dynamic model implemented for the multi-mobile manipulators with arms having independent motion, but also for multi-mobile manipulators in cooperation after defining gripper's kinematic constraints. These constraints are imported to the dynamic equations by defining Lagrange multipliers. The recursive Gibbs–Appell formulation is preferred over other similar approaches owing to the capability of solving the equations without the need to use Lagrange multipliers for eliminating non-holonomic constraints in addition to the novel optimized process of obtaining system equations. Hence, cumbersome simultaneous computations for eliminating the constraints of platform and arms are circumvented. Therefore, this formulation is improved for the first time by importing Lagrange multipliers for solving kinematic constrained systems. In the simulation section, the results of forward dynamics solution for two flexible single-arm manipulators with revolute-prismatic joints while carrying a rigid object are presented. Inverse dynamics equations of the system are also presented to obtain the maximum dynamic load-carrying capacity of the two-rigid-link mobile manipulators on a predefined path. Two constraints, namely the capacity of joint motors torque and robot motion stability are considered as the limitation criteria. The concluded motion equations are used to accurately control the movement of sensitive bodies, which is not achievable through the use of one platform.     

Active vibration control of unbalanced flexible rotor–shaft systems parametrically excited due to base motion

Rotor vibrations caused by large time-varying base motion are of considerable importance as there are a good number of rotors, e.g., the ship and aircraft turbine rotors, which are often subject to excitations, as the rotor base, i.e. the vehicle, undergoes large time varying linear and angular displacements as a result of different maneuvers. Due to such motions of the base, the equations of vibratory motion of a flexible rotor–shaft relative to the base (which forms a non-inertial reference frame) contains terms due to Coriolis effect as well as inertial excitations (generally asynchronous to rotor spin) generated by different system parameters. Such equations of motion are linear but time-varying in nature, invoking the possibility of parametric instability under certain frequency–amplitude combinations of the base motion. An investigation of active vibration control of an unbalanced rotor–shaft system on moving bases is attempted in this work with electromagnetic control force provided by an actuator consisting of four electromagnetic exciters, placed on the stator in a suitable plane around the rotor–shaft. The actuator does not levitate the rotor or facilitate any bearing action, which is provided by the conventional suspension system. The equations of motion of the rotor–shaft continuum are first written with respect to the non-inertial reference frame (the moving base in this case) including the effect of rotor internal damping. A conventional model for the electromagnetic exciter is used. Numerical simulations performed on the flexible rotor–shaft modelled using beam finite elements shows that the control action is successful in avoiding the parametric instability, postponing the instability due to internal material damping and reducing the rotor response relative to the rigid base significantly, with sufficiently low demand of control current in comparison with the bias current in the actuator coils.     

Solving a Problem by Using a Diagram

Sketches and diagrams are sometimes useful in problem solving．For example,four runners are in a one-mile race:A,B,C,and D．Points are awarded only to the person finishing first or sec- ond．The first-place winner gets more points than the second-place winner．How many different arrangements of first-and second-place winner are possible?     

When is a Coalgebra a Generator?

Let C be a coalgebra over a field k. The aim of this paper is to study the following problem : (P) If C is a k-coalgebra such that C is a generator for the category of left comodules, is C a left quasi-co-Frobenius coalgebra ? The converse always holds. We show that if C has a finite coradical series, the answer is positive.     

When is a stochastic integral a time change of a diffusion?

We give necessary and sufficient conditions that a time change of ann-dimensional Ito stochastic integralX _t of the form

Using a Table to Make a Generalization

A generalization is a statement that is true about many instances.The following story is aboutmaking a generalization.Francie lives in Phoenix.She has a telephone in her room.She pays for all long-distance callsshe makes.One Sunday she called her cousin Meg in San Diego.As they talked,Francie forgot     

Draining a polygon—or—rolling a ball out of a polygon

We introduce the problem of draining water (or balls representing water drops) out of a punctured polygon (or a polyhedron) by rotating the shape. For 2D polygons, we obtain combinatorial bounds on the number of holes needed, both for arbitrary polygons and for special classes of polygons. We detail an $O(n^2\log n)$ algorithm that finds the minimum number of holes needed for a given polygon, and argue that the complexity remains polynomial for polyhedra in 3D. We make a start at characterizing the 1-drainable shapes, those that only need one hole.     

角a、a/2、2a终边位置的研究报告

(~责审余炯沛)a终边位置一象限二象限三象限一四象限一注释代数表示 Zk兀相似文献   

On a universal Σ-function over a tree

We obtain a sufficient condition for the absence of any universal ??-function in an admissible set (a hereditarily finite admissible set). We construct a tree T of height 4 such that no universal ??-function exists in the hereditarily finite admissible set ? $\mathbb{F} $ (T) over T.     

Exit Time of a Hyperbolic α-Stable Process from a Halfspace or a Ball

For a hyperbolic α-stable process in the hyperbolic space \(\mathbb {H}^{d}, d\ge 2\), we prove that the mean exit time from a halfspace \(H(a)=\{x_{d}>a\}\subset \mathbb {H}^{d} \) is equal to \(\mathbb {E}^{x} \tau _{H(a)} = c(\alpha , d) \delta ^{\alpha /2}_{H(a)} (x),\) where δ_D(x) is the (hyperbolic) distance of x to D^c. Based on this exact result we provide a sharp estimate of the mean exit time from a hyperbolic ball B(x₀,R) of radius R and center x₀: \(\mathbb {E}^{x}\tau _{B(x_{0},R)}\approx (\delta _{B(x_{0},R)}(x) \tanh R)^{\alpha /2}, x\in \mathbb {H}^{d}\). By usual isomorphism argument the same estimate holds in any other model of real hyperbolic space.     

Turán Number of the Family Consisting of a Blow-up of a Cycle and a Blow-up of a Star

Let F={H₁,...,H_k}(k> 1) be a family of graphs.The Turán number of the family F is the maximum number of edges in an n-vertex {H₁,...,H_k)-free graph,denoted by ex(n,F) or ex(n,{H₁,H₂,...,H_k}).The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different.In this paper we determine the Turán number of the family cons...     

Recovering a Lamé kernel in a viscoelastic system

In the equation of viscoelasticity related to a geometric cylinder, we recover the spatial part p of a factorized Lamé kernel depending on two spatial sectional variables. More explicitly, we determine sufficient conditions on the data ensuring the (local) uniqueness of p and its continuous dependence on the data in suitable metrics.