An approximation method for a class of queueing systems

We consider a queueing system with an ordered hunt. Specifically, we consider a communication system in which messages arrive at a node that has n output links numbered 1,…,n, and an arriving message is processed by the lowest numbered idle link. Obtaining such steady-state parameters as the expected delay of an arbitrary message and the utilization factor of each link requires knowledge of the complete state space of the system and the solution of 2ⁿ linear equations. In this paper we develop a method of computing the approximate values of these parameters without the need for the knowledge of the complete state space and the solution of 2ⁿ linear equations.     

Optimal resource allocation for time-reservation systems

This paper studies the optimal resource allocation in time-reservation systems. Customers arrive at a service facility and receive service in two steps; in the first step information is gathered from the customer, which is then sent to a pool of computing resources, and in the second step the information is processed after which the customer leaves the system. A central decision maker has to decide when to reserve computing power from the pool of resources, such that the customer does not have to wait for the start of the second service step and that the processing capacity is not wasted due to the customer still being serviced at the first step. The decision maker simultaneously has to decide on how many processors to allocate for the second processing step such that reservation and holding costs are minimized. Since an exact analysis of the system is difficult, we decompose the system into two parts which are solved sequentially leading to nearly optimal solutions. We show via dynamic programming that the near-optimal number of processors follows a step function with as an extreme policy the bang-bang control. Moreover, we provide new fundamental insights in the dependence of the near-optimal policy on the distribution of the information gathering times. Numerical experiments demonstrate that the near-optimal policy closely matches the performance of the optimal policy of the original problem.     

一类脉冲切换系统的最优控制

研究一类脉冲依赖于状态的脉冲切换系统的最优控制问题. 考虑了目标函数的两种情况: 当目标函数光滑时, 通过将跳跃瞬间转化为一个新的待优化参数, 得到了该脉冲切换系统的必要最优性条件; 当目标函数不光滑时, 利用非光滑分析的知识, 得到了广义微分形式的必要最优性条件. 算例分析验证了所提出方法的有效性.     

Optimal power allocation for homogeneous and heterogeneous CA-MIMO systems

Carrier aggregation (CA) technique has been adopted by 3GPP LTE-Advanced due to its ability of enhancing the spectrum efficiency and peak data rates through aggregating multiple component carriers (CCs). Two main factors make power control optimization very essential for CA-MIMO radio link: the different channel characteristics in multiple CCs, and multiple power constraint conditions (per-CC, per-antenna and pertransmitter power constraints) in the actual CA system deployment. This paper firstly derives the degenerate conditions of optimal power allocation for a single-transmitter CA-MIMO system. Stemming from the derived degenerate conditions, we propose a modified hybrid gradient optimal power allocation(MHGOPA) algorithm to maximize the system performance. Simulation results verify the validity of the proposed resource allocation approach by comparing with baseline average power allocation algorithm. Finally, we extend the MHGOPA algorithm into a heterogeneous CA network with multiple transmitters working simultaneously.     

Optimal buffer allocation in finite closed networks with multiple servers

In this study, we present an optimal buffer allocation procedure for closed queueing networks with finite buffers. The performance measures are evaluated using the expanded mean value analysis, and the solution procedure is incorporated into a nonlinear optimization scheme to arrive at the sub-optimal buffer space vector. The effectiveness of the method is demonstrated through several numerical experiments. Discussions on convergence and computational complexity are also included.     

一类离散线性切换系统的最优控制

研究了一类离散线性切换系统在切换时间、切换次数固定的情况下的二次最优控制问题.利用离散动态规划的方法,将多级决策过程分解成一系列易于求解的单级决策过程,求出最优控制序列和最优切换序列,并给出算法.最后通过一个数值例子来说明所提出的方法的有效性.     

Optimal nonlinear estimation for a class of discrete-time stochastic systems

Recursive estimation for nonlinear discrete-time stochastic systems with additive white Gaussian observation noise is investigated. It is proved that for certain classes of systems, described either by finite Volterra series expansions or by state-linear realizations under certain algebraic conditions, the optimal conditional mean estimator is recursive and of fixed finite dimension. An example is presented to illustrate the structure of the estimators.     

Optimal capacitor allocation in power systems

Static capacitors are installed at specific locations in large power systems for minimising power losses and to ensure quality of the supply system. It has been found that the number of units in each capacitor bank can be considerably reduced by suitable choice of transformer tap settings and generator voltage magnitudes, thereby reducing the cost of installation of capacitors. This paper presents an efficient method for finding the optimal values for the number of units in each capacitor bank and their locations for the purpose of reducing power losses and for ensuring the quality of the supply system. This is accomplished by optimal allocation of all reactive power sources in the system in a coordinated fashion by varying the number of units in each capacitor bank and generator voltage magnitudes and transformer tap setting positions.The problem is formulated as an optimisation problem with the objective function representing the revenue resulting from reduction in power losses, taking into account the cost due to interest and depreciation on the static capacitor installation and the constraints based on physical and technical limitations on the system. The problem falls in the category of Mixed Integer Linear Programming (M.I.L.P.) and is solved by decomposing the problem into two smaller subproblems viz., a pure integer programming problem in binary variables and a linear programming problem. The solutions of these subproblems are coordinated to get the solution of the original problem. Very fast convergence is obtained by preventing zigzagging of the solution about the optimal point. All these result in considerable savings in computer time and memory. The proposed model has been applied to sample systems and the results presented and discussed.     

Optimal buffer allocation of serial production lines with quality inspection machines

Using Taylor series expansion and probability generating function technique, we present an approximation method for the analysis of the average steady state throughput of serial production lines with unreliable machines, finite buffers and quality inspection machines. Employing the approximation method, we propose an analytic method for the optimal buffer allocation to achieve a desired throughput. The proposed methods are validated by computer simulations.     

一类混杂系统的最优控制

研究了一类脉冲依赖于状态的混杂系统的最优控制问题.与传统的变分方法不同,通过将跳跃瞬间转化为一个新的待优化参数,得到了该混杂系统的必要最优性条件,从而将最优控制问题转化为一边界值问题,该边界值问题可由数值方法或解析方法解决.此外,利用广义微分的理论,将该必要最优性条件推广到Frechet微分形式.结论表明,在混杂动态系统运行的连续部分,最优解所满足的必要性条件和传统的连续系统相同.在混杂动态系统的脉冲点处,哈密尔顿函数满足连续性条件,协态变量则满足一定的跳跃条件.最后,通过两个实例分析,表明该方法是有效的.     

Optimal control of a class of distributed systems

A procedure consisting of two iterative schemes is developed for the optimal control of quasi-static distributed systems. The procedure, which is based on singular perturbation techniques and calculus of variations, is illustrated for a diffusive system.     

Optimal addition of servers for a time-dependent queueing process

Necessary conditions for optimal control of systems containing a time delay that is a function of the state of the system and of time are derived by utilizing calculus of variations. The time delay may be in the state vector and in the control vector. The state vector and the control vector can be constrained by inequality constraints. A transformation to eliminate state variable inequality constraints by increasing the dimensions of state space, developed by Jacobson for an undelayed system, is extended to a system with time delays. Necessary conditions to obtain an optimal delay are shown, and an example of finding an optimal delay is included. A gradient algorithm for systems with state dependent time delays has been developed.     

Target-pursuing scheduling and routing policies for multiclass queueing networks

We propose a parametric class of myopic scheduling and routing policies for open and closed multiclass queueing networks. In open networks, they steer the state of the system toward a predetermined and fixed target, while, in closed networks they steer instantaneous throughputs toward a fixed target. In both cases, the proposed policies measure distance from the target using a weighted norm. In open networks, we establish that for an L2 norm the corresponding policies are stable. In closed networks, we establish that with proper target selection the corresponding policy is efficient, that is, attains bottleneck throughput in the infinite population limit. In both open and closed networks, the proposed policies are amenable to distributed implementation using local state information. We exploit the work in a previous paper to select appropriate parameter values and outline how optimal parameter values can be computed. We report numerical results indicating that we obtain near-optimal policies (when the optimal can be computed) and significantly outperform heuristic alternatives. This work has applications in a number of areas including optimizing the processing of information in sensor networks.     

Optimal control of a class of hybrid systems

We present a modeling framework for hybrid systems intended to capture the interaction of event-driven and time-driven dynamics. This is motivated by the structure of many manufacturing environments where discrete entities (termed jobs) are processed through a network of workcenters so as to change their physical characteristics. Associated with each job is a temporal state subject to event-driven dynamics and a physical state subject to time-driven dynamics. Based on this framework, we formulate and analyze a class of optimal control problems for single-stage processes. First-order optimality conditions are derived and several properties of optimal state trajectories (sample paths) are identified which significantly simplify the task of obtaining explicit optimal control policies     

On the complexity of buffer allocation in message passing systems

Message passing programs commonly use message buffers to avoid unnecessary synchronizations and to improve performance by overlapping communication with computation. Unfortunately, using buffers can introduce portability problems and can lead to deadlock problems on systems without a sufficient number of message buffers.We explore a variety of problems related to buffer allocation for safe and efficient execution of message passing programs. We show that determining the minimum number of message buffers or verifying that each process has a sufficient number of message buffers are intractable problems. However, we give a polynomial time algorithm to determine the minimum number of message buffers needed to ensure that no send operation is unnecessarily delayed due to lack of message buffers. We extend these results to several different buffering schemes, which in some cases make the problems tractable.     

Optimal allocation for partially replicated database systems onring networks

Considers a distributed database with partial replication of data objects located on a ring network. Certain placements of replicated objects are shown to optimize the probability of read-only success and the probability of write-only success. We also obtain optimal placements for k-terminal reliability and expected minimal path length for read-only and write-only operations     

一类含阶跃干扰的切换系统最优控制

研究了一类含阶跃干扰的切换系统的二次最优控制问题,其中切换系统的切换序列、切换次数固定、采用动态规划方法,利用多级决策和改进的遗传算法来得到最优切换时刻和最优控制输入．最后通过一个数值例子说明了本文方法的有效性．