Predicting departure times in multi-stage queueing systems

We develop an approximation model for the state-dependent sojourn time distribution of customers or orders in a multi-stage, multi-server queueing system, when interarrival and service times can take on general distributions. The model can be used to make probabilistic statements about the departure time of a customer or order, given the number and location of customers currently in process or waiting, and these probabilities can be recomputed while waiting at any point during the sojourn time. The model uses phase-type distributions and a new method to estimate the remaining processing times of customers in service when the sojourn time distribution is computed.     

Accuracy of approximating queueing network departure processes with independent renewal processes

A distributed and fully symmetric solution is presented for the distributed termination problem. In contrast to the existing solutions, the above solution does not require a predesignated process to detect termination. The case of asynchronous communications is also discussed.     

The queueing equivalence to a manufacturing system with failures

The authors consider optimal production rate control in a failure prone manufacturing system. It is well known that the hedging point policy is the optimum controller for such a system. They show that under the hedging point policy the system can be treated as an M/M/1 queue. Therefore, existing results in queuing theory can be readily applied to obtaining the steady-state probability density function of the production surplus, based on which the optimal hedging point policy can be computed. To a large extent, the approach is based on sample path analysis. It not only provides an alternative way to solve the problem but also reveals some interesting insights     

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.     

Optimal assignments in a markovian queueing system

A generalization of the Hypercube queueing model for exponential queueing systems is presented which allows for distinguishable servers and multiple types of customers. Given costs associated with each server-customer pair, the determination of the assignment policy which minimizes time-averaged costs is formulated as a Markov decision problem. A characterization of optimal policies is obtained and used in an efficient algorithm for determining the optimum. The algorithm combines the method of successive approximations and “Howard's method” in a manner which is particularly applicable to Markov decision problems having large, sparse transition matrices.     

Optimal control of admission to a queueing system

Congestion in a queueing system can sometimes be controlled by restricting arrivals, either by "closing a gate" or by charging an entrance fee or toll. We review both static (open-loop) and dynamic (closed-loop) models for control of admission to a queueing system. The main emphases are on the difference between socially optimal and individually optimal (equilibrium) controls and on the use of dynamic-programming inductive analysis to show that an optimal control is monotonic or characterized by one or more "critical numbers." We discuss the potential for use of these models in the analysis of computer/ communication systems and compare the results to certain others in the literature.     

Filtering of a semi-Markov queueing system with retrials

A recursive differential equation for the conditional probability of the number of waiting customers is derived for the M_wrM|G|1 queue with continuous monitoring of the server state.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 169–173, July–August, 1991.     

基于视频的高速车道偏离预警系统

在驾驶过程中发生非意识车道偏离时,偏离预警系统采用报警方式保障行车安全。针对高速公路频发的车道偏离事故,设计和实现了基于视频处理的高速车道偏离预警系统(Highway Departure Warning System,HDWS)。算法处理上,分别进行感兴趣区域(Area of Interest,AOI)设定、图像预处理和Otsu自适应阈值二值化,应用直线模型和改进Hough变换提取车道线,采用像素距离与车道线斜率信息融合的偏离决策,并在MATLAB R2015a上仿真测试。仿真结果表明,该系统能提前1.2 s报警,准确率高于95%,漏报率低于3%,满足高速道路环境下偏离预警性能要求。     

Departure process of a single server queueing system with Markov renewal input and general service time distribution

The independence of processes in queueing systems is generally assumed when developing queueing models. However, real systems often involve several process dependencies, and failure to take these into consideration can lead to serious underestimation of the performance measures. We consider herein a single server queueing system with a Markov renewal process (MRP) for its arrival process and a general service time distribution, and derive the distribution function and correlation coefficient of the departure process. Since the departure process also often corresponds to an arrival process in downstream queues, the results obtained here can be used to derive a better approximation of the performance measures of a non-product form general queueing network.     

Perturbation analysis of a multiclass queueing system withadmission control

A service facility with multiple customer classes is considered. Each class forms an independent Poisson arrival process with admission controlled by a threshold parameter and is characterized by a general service time distribution. Gradient estimators are derived for performance measures of the system (mean system time, throughput, blocking probabilities) using perturbation analysis techniques. The approach is based on exploiting alternative sample path representations of generalized semi-Markov process models of the system, such that the resulting sample functions are continuous with respect to parameters of interest. The unbiasedness of the estimators is proved. Simulation examples are included to illustrate their properties     

The departure process of an N/G/1 queue

The departure process of an N/G/1 queue is investigated. The arrival process called an N process is a versatile point process and includes, for example, a Markov-modulated Poisson process, which is comprised of models of packetized voice and video traffic arrival processes. The first passage analysis yields LSTs of distributions of the interdeparture times. Emphasis is on the interdeparture times of an N/D/1 queue. Numerical examples show that correlation of interarrival times is likely to be preserved in interdeparture times, and that the departure of a voice packet multiplexer can be expected to be smoothed for a normal load. The result in this paper enables evaluation of the smoothing effect of burst traffic through nodes in Asynchronous Transfer Mode networks.     

基于OpenCV的嵌人式车辆驾驶偏离报警系统

为减少因驾驶员无意识偏离车道行驶造成的交通事故,基于ARM和OpenCV建立嵌入式车道偏离报警系统。重点介绍了系统的设计、平台的搭建和算法处理流程。该系统通过摄像头采集获取图像信息,并应用OpenCV对图像进行预处理,通过提取图像中车道线信息,评估车辆行驶状态是否偏离车道中心位置,根据车辆的行驶状态,发出报警,提醒车辆驾驶人员当前行驶偏离情况,以达到辅助安全驾驶的目的。     

Optimal intensity control of a queueing system with state-dependentcapacity 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     

Infinitesimal perturbation analysis of a queueing system with bursty traffic

We study aG/G/1 queueing system with a bursty arrival process. Based on a general model for such a bursty process, we derive infinitesimal perturbation analysis (IPA) derivative estimators of the mean system time with respect to various parameters of interest. The cases of both complete and partial state information are considered. To ensure unbiasedness and strong consistency of the estimators, different sample path representations are developed such that sample functions are continuous with respect to the particular parameter of interest. Some of these representations are applicable to a wider class of gradient estimation problems where sample path discontinuities arise. Simulation results are included to compare the convergence rates and variance properties of the different IPA estimators developed.     

Waiting time distribution of a queueing system with postservice activity

In this paper, we consider a queueing system with postservice activity. During the time when the server is engaged in the postservice activity (wrap-up time), the waiting customer, if any, cannot receive his or her service. This type of queueing system has been used to model automatic call distribution (ACD) systems. We consider the waiting time distribution of the queueing system. Using the Markovian point process that can be expressed by the so-called Markovian arrival process (MAP), we derive the waiting time distribution in terms of the representing matrices of a particular MAP. Then we apply the Baker-Hausdorff lemma to the matrices and derive the conditional waiting time distribution in closed form by exploiting the specific structure of the matrices. As a byproduct, we give an explicit solution of the number of arrivals for the MAP.     

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.