Control Policies of an M/G/1 Queueing System with a Removable and Non-reliable Server

This paper considers a single non-reliable server in the ordinary M/G/1 queueing system whose arrivals form a Poisson process and service times are generally distributed. We also study a single removable and non-reliable server in the controllable M/G/1 queueing systems operating under the N policy, the T policy and the Min( N , T ) policy. It is assumed that the server breaks down according to a Poisson process and the repair time has a general distribution. In three control policies, we show that the probability that the server is busy in the steady-state is equal to the traffic intensity. It is shown that the optimal N policy and the optimal Min( N , T ) policy are always superior to the optimal T policy. Sensitivity analysis is also investigated.     

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。     

不完全柔性制造系统的最优控制

考虑具有随机需求的不完全柔性制造系统的最优控制，系统在各种产品间的切换时间是不可忽略的。运用马尔可夫最优决策过程归纳方法，导出机器服务率的最优控制策略。通过分析最优值函数的性质，证明最优策略具有简单的阈值结构，从而可得到次优生产策略--阈值控制策略。     

Scheduling with asynchronous service opportunities withapplications to multiple satellite systems

A single server is assigned to M parallel queues with independent Poisson arrivals. Service times are constant, but the server has the opportunity to initiate service at a given queue only at times forming a Poisson process. Four related scheduling policies are investigated: a simple first-come, first-serve policy for which the stability region is determined: a policy with maximum throughput, but requiring the server to have advance knowledge of service opportunities; a policy of threshold type, which is shown to be optimal among nonlookahead policies with preemption; and an adaptive policy, which when M=2 is shown to provide stability for all arrival rate vectors for which stability is possible under any nonlookahead policy with preemption. The work is motivated by the problem of transmission scheduling for a packet-switched, low-altitude, multiple-satellite system     

Optimal control of a queueing system with two interacting servicestations and three classes of impatient tasks

The problem of task selection and service priority is studied for a queueing network with two interacting service stations and three classes of impatient tasks. By using stochastic dynamic programming, a functional equation for the optimal, state-dependent priority assignment policy is derived. Properties of the optimal cost-to-go functions and the optimal policy are established through inductive proofs. It is shown that the optimal policy is governed by two switching surfaces in the three-dimensional state space (one dimension for each task class). For the infinite-time-horizon case, the optimal policy is shown to be stationary. In this case, the optimal cost-to-go function and switching surfaces are obtained numerically by using the overrelaxed Gauss-Seidel method. Sensitivities of the optimal policy with respect to key system parameters are also investigated     

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.     

Flexible secure inter-domain interoperability through attribute conversion

The access control policy of an application that is composed of interoperating components/services is defined in terms of the access control policies enforced by the respective services. These individual access control policies are heterogenous in the sense that the services may be independently developed and managed and it is not practical to assume that all policies are defined with respect to some uniform domain vocabulary of policy attributes. A framework is described that provides a domain mapping for heterogenous policies. A fuzzy-based conversion mechanism determines the degree to which an access control attribute of one (service) policy may safely interoperate with an access control attribute of another (service) policy. The approach is scalable in the sense that it is not necessary to a priori specify every pairwise policy interoperation relationship, rather, where obvious interpretations exist then policy relationships are specified, while other relationships are inferred using the fuzzy mechanism.     

A Method for Performance Analysis of Earliest-Deadline-First Scheduling Policy

This paper introduces an analytical method to approximate the fraction of jobs missing their deadlines in a soft real-time system when the earliest-deadline-first (EDF) scheduling policy is used. In the system, jobs either all have deadlines until the beginning of service (DBS) and are non-preemptive, or have deadlines until the end of service (DES) and are preemptive. In the former case, the system is represented by an M/M/m/EDF+G model, i.e., a multi-sever queue with Poisson arrival, exponential service, and generally distributed relative deadlines. In the latter case, it is represented by an M/M/1/EDF+G model, i.e., a single-server queue with the same specifications as before. EDF is known to be optimal in both of the above cases. The optimality property of EDF scheduling policy is used for the estimation of a key parameter, namely the loss rate when there are n jobs in the system. The estimation is possible by assuming an upper bound and a lower bound for this parameter and then linearly combining these two bounds together. The resulting Markov chains can then be easily solved numerically. Comparing numerical and simulation results, we find that the existing errors are relatively small.     

输入随机的不可靠串行生产线的反馈控制

对于具有随机输入和随机需求的一类串行生产纡系统,利用转移率一致化技术和随机动态规划方法,给出了输入率和服务率分配的最优反馈控制策略,指出 最优控制具有邦一邦形式的开关结构。仿真例子验证了方法的有效性。     

输入随机的不可靠柔性制造系统的反馈控制

对于具有随机输入和随机需求的一类不可靠柔性制造系统,利用转移率一致化技术和随机动态规划方法,给出了输入率和服务率分配的最优反馈控制策略,指出系统的最优控制具有bang-bang形式的天关结构,数值例子验证了文中的结果。     

基于软件定义网络的媒体分发网络的接入控制

针对软件定义网络（SDN）环境下的媒体分发网络的接入控制问题,提出了一种综合考虑服务节点和传输链路服务性能优化问题的接入控制方案。该方案利用SDN控制器对路由器的直接管控和对全网的感知能力,对应用层上服务节点服务性能和网络层上服务节点到用户之间的传输链路的服务性能进行联合优化,减少了链路拥塞对数据传输和用户服务质量的影响。首先,为SDN服务系统的接入控制过程建立部分可观Markov决策过程（POMDP）模型;然后,使用基于观测的随机策略作为系统的接入控制策略;最后,通过策略梯度算法对接入控制策略进行优化,求解出模型的最优策略。仿真结果表明,与尽力而为的服务策略相比,基于POMDP模型的最优接入控制策略使系统性能提高了10%,验证了所提方法的有效性。     

The optimal control of an M/G/1 queueing system with server vacations, startup and breakdowns

This paper studies the control policy of the N policy M/G/1 queue with server vacations, startup and breakdowns, where arrivals form a Poisson process and service times are generally distributed. The server is turned off and takes a vacation whenever the system is empty. If the number of customers waiting in the system at the instant of a vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N customers in the system, he requires a startup time before providing service until the system is again empty. It is assumed that the server breaks down according to a Poisson process and his repair time has a general distribution. The system characteristics of such a model are analyzed and the total expected cost function per unit time is developed to determine the optimal threshold of N at a minimum cost.     

随机需求不可靠制造系统的最优服务率分配策略

本文讨论了一类随机需求不可靠制造系统的最优服务率控制问题。所研究的系统能同时生产多类产品，但生产能力受常数限制。目标是通过最小化库顾和欠缺的期望折扣费用，寻找最优服务率分配策略，本文证明了最优策略具有开关结构，并针对生产单类和两类产品的系统详细研究了最优控制策略的结构性质，最后以数值例子验证了本文的结论。     

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.     

Adaptive control of service in queueing systems

We consider the service-rate selection problem in an M/G/1 queueing system with unknown arrival rate and average cost criterion. An optimal adaptive policy is determined using recently developed results on parameter estimation and adaptive control of semi-Markov processes.     

Optimal multi-layered congestion based pricing schemes for enhanced QoS

Pricing is an effective tool to control congestion and achieve quality of service (QoS) provisioning for multiple differentiated levels of service. In this paper, we consider the problem of pricing for congestion control in the case of a network of nodes with multiple queues and multiple grades of service.We present a closed-loop multi-layered pricing scheme and propose an algorithm for finding the optimal state dependent price levels for individual queues, at each node. This is different from most adaptive pricing schemes in the literature that do not obtain a closed-loop state dependent pricing policy. The method that we propose finds optimal price levels that are functions of the queue lengths at individual queues. Further, we also propose a variant of the above scheme that assigns prices to incoming packets at each node according to a weighted average queue length at that node. This is done to reduce frequent price variations and is in the spirit of the random early detection (RED) mechanism used in TCP/IP networks.We observe in our numerical results a considerable improvement in performance using both of our schemes over that of a recently proposed related scheme in terms of both throughput and delay performance. In particular, our first scheme exhibits a throughput improvement in the range of 67–82% among all routes over the above scheme.     

Sensitivity analysis of the optimal management policy for a queuing system with a removable and non-reliable server

The management policy of an M/G/1 queue with a single removable and non-reliable server is considered. The decision-maker can turn the single server on at any arrival epoch or off at any service completion. It is assumed that the server breaks down according to a Poisson process and the repair time has a general distribution. Arrivals form a Poisson process and service times are generally distributed. In this paper, we consider a practical problem applying such a model. We use the analytic results of the queueing model and apply an efficient Matlab program to calculate the optimal threshold of management policy and some system characteristics. Analytical results for sensitivity analysis are obtained. We carry out extensive numerical computations for illustration purposes. An application example is presented to display how the Matlab program could be used. The research is useful to the analyst for making reliable decisions to manage the referred queueing system.     

Event-based optimization of admission control in open queueing networks

In this paper, we use the event-based optimization framework to study the admission control problem in an open Jackson network. The external arriving customers are controlled by an admission controller. The controller makes decision only at the epoch when an event of customer arrival happens. Every customer in the network obtains a fixed reward for each service completion and pays a cost with a fixed rate during its sojourn time (including waiting time and service time). The complete information of the system state is not available for the controller. The controller can observe only the number of total customers in the network. Based on the property of closed form solution of Jackson networks, we prove that the system performance is monotonic with respect to the admission probabilities and the optimal control policy has a threshold form. That is, when the number of total customers is smaller than a threshold, all of the arriving customers are admitted; otherwise, all are rejected. The sufficient condition and necessary condition of optimal policy are also derived. Furthermore, we develop an iterative algorithm to find the optimal policy. The algorithm can be executed based on a single sample path, which makes the algorithm online implementable. Simulation experiments are conducted to demonstrate the effectiveness of our approach.     

Optimization analysis for an infinite capacity queueing system with multiple queue-dependent servers: genetic algorithm

This paper considers an M/M/r queueing system with infinite capacity, in which the number of working servers changes depending on the queue length. The steady-state probability distributions and the expected number of customers in the system are derived, which are used to construct a cost function. In order to minimize the expected cost of the system, we use the genetic algorithm to find the best thresholds of queue length in activating servers and their corresponding service rate. Some illustrative examples are provided to demonstrate how the process of this algorithm works for the optimal management policy of the multi-server queueing system.     

模态跳变概率可控的Markov跳变线性系统的优化

研究模态跳变概率可控的Markov跣变线性二次模型的最优控制问题,考虑两类模态跳变控制策略:开环模态控制和闭环模态控制,应用策略迭代和性能势的概念,给出了最优的闭环模态控制优于最优的开环模态控制的充分条件,以指导最优控制器的设计,在已知最优的开环模态控制策略的基础上,应用策略迭代给出了构造闭环模态控制策略的方法,以进一步改善系统的性能.