Optimal control of two interacting service stations

Optimal controls described by switching curves in the two-dimensional state space are shown to exist for the optimal control of a Markov network with two service stations and linear cost. The controls govern routing and service priorities. Finite horizon and long run average cost problems are considered and value iteration is a key tool. Nonconvex value functions are shown to exist for slightly more general networks. Nonconvex value functions are also shown to arise for a simple single station control problem in which the instantaneous cost is convex but not monotone. Nevertheless, optimality of threshold policies is established for the single station problem. The proof is based on a novel use of stochastic coupling and policy iteration.     

Optimal attitude control of two pivotally connected bodies in the supportless phase of motion

The motion of two pivotally connected bodies in the supportless phase (weightlessness) is investigated. The minimization and maximization of the slew time from a given initial position to the given terminal position is solved. It is assumed that the angular momentum of the system about its center of mass is distinct from zero. This problem is a simple model of attitude control of a hopping machine in the supportless phase of the hop.     

Optimal threshold control of empty vehicle redistribution in two depot service systems

In this note, we consider the empty vehicle redistribution problem in a two-depot service system with random demands and uncertain transportation times. It is shown that the optimal stationary policy is of threshold control-type when the long-run average cost is to be minimized. The explicit form of the average cost under threshold controls is presented, which can be used to calculate the optimal threshold values. The sufficient and necessary conditions for the existence of the steady-state are provided. The results are then used to construct suboptimal policies for a more realistic model.     

一类排队服务系统的最优控制策略研究

建立一个双阈值排队服务模型, 用来协调顾客的等待时间和服务系统的运行成本. 采用一种精细的概率分解方法获得瞬态和稳态队长的概率分布性质; 再根据系统稳态性能指标, 建立系统营运利润函数, 并设计一种针对双离散变量函数的全局优化收索算法来研究最优控制策略; 进一步的数值实验揭示出双重阈值策略的优越性.     

Optimal control of a queueing system with two heterogeneous servers

The problem considered is that of optimally controlling a queueing system which consists of a common buffer or queue served by two servers. The arrivals to the buffer are Poisson and the servers are both exponential, but with different mean service times. It is shown that the optimal policy which minimizes the mean sojourn time of customers in the system is of threshold type. The faster server should be fed a customer from the buffer whenever it becomes available for service, but the slower server should be utilized if and only if the queue length exceeds a readily computed threshold value.     

可变服务率模式下基于需求驱动的传送带给料加工站系统的优化控制

本文主要研究可变服务率模式下基于需求驱动的传送带给料加工站(CSPS)系统的优化控制问题,主要目标是对系统的随机优化控制问题进行建模和提供解决方案.论文以缓冲库和成品库剩余容量为联合状态,以站点前视距离和工件服务率为控制变量,将其最优控制问题描述为半马尔科夫决策过程(SMDP)模型.该模型为利用策略迭代等方法求解系统在平均准则或折扣准则下的最优控制策略提供了理论基础,特别地,据此可引入基于模拟退火思想的Q学习算法等优化方法来寻求近似解,以克服理论求解过程中的维数灾和建模难等困难.仿真结果说明了本文建立的数学模型及给出的优化方法的有效性.     

Optimal use of an extra server in a two station tandem queueingnetwork

A two station tandem queueing system with given numbers of customers initially at each station and no arrivals is considered. There is a fixed server at each station, but also an additional server that can be dynamically allocated to wherever its use will do most good. There are differing linear holding costs at each station, and the aim is to use the extra server to minimize the expected total holding cost incurred until the system empties. It is shown that if either the extra server can be switched between the two stations at any time, or if it is restricted in use to just one station, where it can be turned on or off, then the optimal use of the server is such that after a service completion at one station, the effort devoted there never increases, and the effort devoted to the other station never decreases     

Optimal control of service in tandem queues

Customers arrive in a Poisson stream into a network consisting of twoM/M/1service stations in tandem. The service rateu in [0, a]at station 1 is to be selected as a function of the state (x_{1}, x_{2}) where xiis the number of customers at stationiso as to minimize the expected total discounted or average cost corresponding to the instantaneous costc_{1}x_{1} + c_{2}x_{2}. The optimal policy is of the formu=aoru=0according asx_{1} < S(x_{2}) or x_{1} geq S(X_{2})andSis a switching function. For the case of discounted cost, the optimal process can be nonergodic, but it is ergodic for the case of average cost.     

Optimal control of multiclass parallel service systems

We consider routing and scheduling systems consisting of a number of parallel homogeneous servers with finite capacities. Assuming that jobs belong to multiple classes, we represent the interconnection of arrival streams (servers) to stations by abipartite graph, called therouting (resp.scheduling) digraph. By developing an algebraic structure on the interconnection pattern embedded in the digraph, we identify certain classes of symmetric routing and scheduling systems for which a simple control policy such as theShortest Queue policy can be shown to be optimal in the sense of optimizing the departure and loss counting processes. A counterexample is shown for systems described by digraphs with a cyclic structure.     

服务率不确定的单站点传送带给料加工站系统鲁棒优化控制

研究了服务率不确定情况下的单站点传送带给料加工站(CSPS)系统的鲁棒优化控制问题。在仅知服务率区间的条件下,以CSPS系统的前视距离作为控制变量,将鲁棒优化控制问题建模成不确定参数的半马尔可夫决策过程(SMDP)的极大极小优化问题,在状态相关的情况下,给出全局优化算法进行鲁棒控制策略求解。首先,运用遗传算法求解固定策略下的最差性能值;其次,根据求解得到的最差性能值,运用模拟退火算法求解最优鲁棒控制策略。仿真结果表明,服务率不确定的CSPS系统的最优鲁棒性能代价与服务率固定为区间中值系统的最优性能代价相差不大,并且随着不确定区间的缩小,两者的差值越小,说明了全局优化算法的有效性。     

Optimal management for infinite capacity N-policy M/G/1 queue with a removable service station

In this article, we consider an infinite capacity N-policy M/G/1 queueing system with a single removable server. Poisson arrivals and general distribution service times are assumed. The server is controllable that may be turned on at arrival epochs or off at service completion epochs. We apply a differential technique to study system sensitivity, which examines the effect of different system input parameters on the system. A cost model for infinite capacity queueing system under steady-state condition is developed, to determine the optimal management policy at minimum cost. Analytical results for sensitivity analysis are derived. We also provide extensive numerical computations to illustrate the analytical sensitivity properties obtained. Finally, an application example is presented to demonstrate how the model could be used in real applications to obtain the optimal management policy.     

Relative equilibrium stability of a space station consisting of two solid bodies connected by an elastic rod

The problem is considered for stability of a relative equilibrium of a mechanical system in orbit that consists of two solid bodies connected by a thin inextensible elastic rod. The problem for stability of a relative equilibrium position reduces to the problem of a minimum of a changed potential system energy comprising the potential energy of elastic, gravitational and centrifugal forces.     

Optimal control of service for facilities holding inventory

This paper addresses the problem of optimally controlling service rates for an inventory system of service facilities. We consider a finite capacity system with Poisson arrivals and exponentially distributed leadtimes and service times. For given values of maximum inventory and reorder levels, we determine the service rates to be employed at each instant of time so that the long-run expected cost rate is minimized. The problem is modelled as a semi-Markov decision problem. We establish the existence of a stationary optimal policy and we solve it by employing linear programming. Several instances of a numerical example, which provide insight into the behaviour of the system, are presented.Scope and purposeIn this article we discuss the problem of inventory control of service parts at a service facility where there is only a limited waiting space for customers. If a customer enters the service facility and sees all the waiting spaces occupied he/she will leave the facility, which results in both intangible losses (loss of goodwill) and tangible losses (loss in profit). Hence, the service provider aims at obtaining an optimal rate at which service is to be provided by balancing costs due to waiting time and limited waiting spaces against costs due to ordering and overheads due to storing items. We develop an algorithm that controls the service rate as a function of the number of customers waiting for service.     

Optimal routing into two heterogeneous service stations withdelayed information

The problem of optimal routing of messages into two parallel queues is considered in the framework of discrete-time Markov decision processes with countable state space and unbounded costs. We assume that the controller has a delayed state information, the delay being equal to one time slot. Both discount and average optimal policies are shown to be monotone and of threshold type     

Optimal control of a water distribution network by two multilevel methods

The problem of daily controlling a water distribution network, including pumping devices and storage capacities, in order to supply the consumers at the lowest cost is formulated as a constrained optimal control problem. Discrete Dynamic Programming seems the only way to overcome the particular difficulties of this problem but the dimensionality prevents one using it on the global problem. Two approaches are considered. The first one consists in tearing up the network into several subnetworks and to use an algorithm of coordination. It succeeds in case of weak coupling between subnetworks. The second one uses an original approach of aggregation and disaggregation iteratively. Presently available experiments with the latter method showed its satisfactory behaviour.     

中心站点和普通站点完全服务排队系统分析

通过对具有最高优先级的排队轮询系统的分析,用物理方法及其机理原理,提出最高优先级及普通队列都采用完全服务的统一服务机制,得出系统平均排队长和平均查询周期的解析式。     

Optimal motion control for a system of two bodies on a straight line

The optimal control problem for motions of a system of two rigid bodies on an inclined straight line in a plane that are periodic in velocity is solved. The external body (frame) moves on a plane under the action of a force from the inner body in the course of its motions relative to the frame under dry friction between the frame and plane. The acceleration of the inner body relative to the outer one is the control whose absolute value is bounded. An optimal control that maximizes the average velocity of the system motion for a given period is found. It is shown that optimal relative acceleration of the inner body has three intervals of constancy on this period, and the outer body is in the state of rest on a part of the period (in the case of horizontal straight line, it is in a state of rest on half a period), and during the rest of the period, it moves in the desired direction and never performs a reversion. It is established that, for the found control law and under an additional constraint on the amplitude of oscillations of the inner body, it is possible to make the motion velocity of the system arbitrarily large under arbitrarily large accelerations of the inner body and an under arbitrarily large frequency of its oscillations simultaneously.     

Dynamic admission control in a call center with one shared and two dedicated service facilities

Admission control of a call center is addressed through a Markovian loss system with two classes of calls and three stations, one dedicated for each class, and one shared station. Each class is identified by different revenues, service and arrival rates. We show that serving a call in its dedicated station, whenever possible, is optimal. For the shared station, we establish the existence of optimal monotone thresholds, and of preferred class(es) under certain conditions.     

Optimal energy-dissipation control for SOC based balancing in series connected Lithium-ion battery packs

Multimedia Tools and Applications - Since the state-of-charge (SOC) based balancing can prolong the battery pack’s life and maximize its capacity, implementing the balancing process in the...