A Queueing System with Two Operation Modes and a Disaster Flow: Its Stationary State Probability Distribution

This paper is concerned with a controllable queueing in which the operation mode changes, depending on the current queue length, and an additional flow of diasters arrive. A disaster may completely empty the system, i.e., all customers, including the customer under service, may quit the system. Its stationary state probability distribution is determined, which is helpful in optimizing the threshold control of the operation of the system.     

On a Multi-Channel Retrial Queueing System

The paper considers Markov multi-channel queueing systems with a single retrial attempt to begin service process. The authors establish the conditions of the existence of stationary mode and propose efficient algorithms for calculation of the stationary probabilities with the use of continued fractions and explicit vector-matrix formulas.     

On the Stability of a Queueing System with Uncountably Branching Fluid Limits

It is known that in many queueing systems uid limits are deterministic functions. Models and conditions which lead to random uid limits have not received much attention. This paper is devoted to a study of a queueing network whose uid limits admit a random and uncountable branching at certain points. Stability conditions for this model are investigated by the use of recent results from the theory of branching processes.     

Stationary Probabilities of States of a Queuing System with an Inverse Discipline and Demands of Three Types

Formulas are derived for probabilities of stationary states of a queuing system with demands of different types and a discipline of the inverse type with interrupts. Later on, the service of an interrupted demand is completed or such a demand is served again with a new (or with an old) length depending on its type.     

On a Retrial Single-Server Queueing System with Finite Buffer and Poisson Flow

A retrial single-server queueing system with finite buffer is considered. The primary incoming flow is Poissonian. If the buffer is overflown, a call entering the system becomes a repeat call and joins the group of repeat calls referred to as an orbit. The maximum number of calls that can simultaneously be contained in the orbit is limited. A call from the orbit makes new attempts to enter the system until a vacancy occurs. Time between repeat attempts for each call is an exponentially distributed random variable. At the initial moment of service, a type of a call is defined: with probability a _i it becomes a call of type i and its service time in this case has distribution function B _i (x), i = . For this system, the stationary joint distribution of queues in the buffer and orbit is found. Numerical examples are given.     

一类Fork－Join排队系统的分析

本文研究了一类具有有限排队空间且其到达率和服务率均依赖于状态的Ｆｏｒｋ－Ｊｏｉｎ排队系统，给出了稳态概率和任务等待时间各阶矩的计算方法，并用仿真检验算法的正确性．     

一类Fork-Join排队系统的分析

本文研究了一类具有有限排队空间且其到达率和服务率均依赖于状态的Ｆｏｒｋ－Ｊｏｉｎ排队系统，给出了稳态概率和任务等待时间各阶矩的计算方法，并用仿真检验算法的正确性。     

On a Retrial Single-Server Queueing System with Finite Buffer and Multivariate Poisson Flow

We consider a single-server queueing system with a finite buffer, K input Poisson flows of intensities _i , and distribution functions B _i (x) of service times for calls of the ith type, . If the buffer is overflowed, an arriving call is sent to the orbit and becomes a repeat call. In a random time, which has exponential distribution, the call makes an attempt to reenter the buffer or server, if the latter is free. The maximum number of calls in the orbit is limited; if the orbit is overflowed, an arriving call is lost. We find the relation between steady-state distributions of this system and a system with one Poisson flow of intensity where type i of a call is chosen with probability _i / at the beginning of its service. A numerical example is given.     

Control of a Heterogeneous Two-Server Exponential Queueing System

A dynamic control policy known as "threshold queueing" is defined for scheduling customers from a Poisson source on a set of two exponential servers with dissimilar service rates. The slower server is invoked in response to instantaneous system loading as measured by the length of the queue of waiting customers. In a threshold queueing policy, a specific queue length is identified as a "threshold," beyond which the slower server is invoked. The slower server remains busy until it completes service on a customer and the queue length is less than its invocation threshold. Markov chain analysis is employed to analyze the performance of the threshold queueing policy and to develop optimality criteria. It is shown that probabilistic control is sub-optimal to minimize the mean number of customers in the system. An approximation to the optimum policy is analyzed which is computationally simple and suffices for most operational applications.     

Determining Stationary Characteristics of Two-Channel Queueing Systems with Erlangian Distribution of Service Time

The author proposes a method to study M/E₂/2/m and M/E₂/2/∞ queueing systems: standard systems and systems with the threshold and hysteretic strategies of random dropping of customers in order to control the input flow. Recurrence relations are obtained to compute the stationary distribution of the number of customers in the system and stationary characteristics. The constructed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools.     

Robust Feedback Control of a Single Server Queueing System

This paper extends previous work of Ball et al. [BDKY] to control of a model of a simple queueing server. There are n queues of customers to be served by a single server who can service only one queue at a time. Each queue is subject to an unknown arrival rate, called a “disturbance” in accord with standard usage from H _∞ theory. An H _∞-type performance criterion is formulated. The resulting control problem has several novel features distinguishing it from the standard smooth case already studied in the control literature: the presence of constraining dynamics on the boundary of the state space to ensure the physical property that queue lengths remain nonnegative, and jump discontinuities in any nonconstant state-feedback law caused by the finiteness of the admissible control set (choice of queue to be served). We arrive at the solution to the appropriate Hamilton–Jacobi equation via an analogue of the stable invariant manifold for the associated Hamiltonian flow (as was done by van der Schaft for the smooth case) and relate this solution to the (lower) value of a restricted differential game, similar to that formulated by Soravia for problems without constraining dynamics. An additional example is included which shows that the projection dynamics used to maintain nonnegativity of the state variables must be handled carefully in more general models involving interactions among the different queues. Primary motivation comes from the application to traffic signal control. Other application areas, such as manufacturing systems and computer networks, are mentioned. Date received: August 14, 1998. Date revised: May 17, 1999.     

On the Invariance of Ant Colony Optimization

Ant colony optimization (ACO) is a promising metaheuristic and a great amount of research has been devoted to its empirical and theoretical analysis. Recently, with the introduction of the hypercube framework, Blum and Dorigo have explicitly raised the issue of the invariance of ACO algorithms to transformation of units. They state (Blum and Dorigo, 2004) that the performance of ACO depends on the scale of the problem instance under analysis. In this paper, we show that the ACO internal state - commonly referred to as the pheromone - indeed depends on the scale of the problem at hand. Nonetheless, we formally prove that this does not affect the sequence of solutions produced by the three most widely adopted algorithms belonging to the ACO family: ant system, MAX-MIN ant system, and ant colony system. For these algorithms, the sequence of solutions does not depend on the scale of the problem instance under analysis. Moreover, we introduce three new ACO algorithms, the internal state of which is independent of the scale of the problem instance considered. These algorithms are obtained as minor variations of ant system, MAX-MIN ant system, and ant colony system. We formally show that these algorithms are functionally equivalent to their original counterparts. That is, for any given instance, these algorithms produce the same sequence of solutions as the original ones.     

Study of a Controllable Queueing System with Unreliable Heterogeneous Servers

We consider a two-channel Markov queueing system with unreliable heterogeneous servers and a common queue. The claims are distributed among the servers with a threshold control policy. According to this policy, a server with the smaller average usage cost must be busy if the system itself is not empty, and the other server is used if the number of customers in the queue exceeds a certain threshold. We analyze the system in stationary mode. We present a method for computing the probabilities of system states and expressions for average performance and reliability characteristics. For the problem of minimizing average losses per unit of time, we obtain a heuristic formula that approximately computes the optimal threshold policy and proposes a method for computing the stationary distribution of the claim waiting time in the system.     

基于Java的排队系统仿真研究

在概述排队系统的基础上,分析了常见排队系统的数学特性,构建了新的事件驱动的仿真算法,应用Java对M/M/c,M/M/c/N, G/G/c/∞/K,G/G/c/N/K等排队系统进行仿真。最后对仿真结果进行了评估,发现基于Java用新算法仿真排队系统有速度快、精度高、应用面广等优点。     

自相似排队系统的蒙特卡罗仿真研究

自相似性是网络通信量的普遍性质并且对网络性能有很大的影响。论文利用蒙特卡罗方法研究了自相似排队系统的性能问题。研究表明长程相关和短程相关对于排队系统性能具有非常不同的影响,尤其是在缓存较大的情况下。同时,还发现通信量中长程相关发生作用的尺度与通信量以及排队系统本身的参数都有关,这对于实际的网络设计具有较强的参考意义。     

On Minimax Interpolation of Stationary Sequences

Cybernetics and Systems Analysis - The problem of the optimal linear estimation of functionals that depend on the unknown values of the stochastic stationary sequence of observations of a sequence...     

具有不耐烦用户VOD单播系统的排队分析研究

本文运用排队论的方法对视频服务系统单播情形下的部分指标进行了定性分析,分析了系统服务状态,以用户等待平均数和系统吞吐量为主要考察对象,给出了用户等待平均数与系统服务强度及用户耐心程度的关系,阐述了系统吞吐量受服务强度及用户耐心程度的影响.仿真结果表明,这也是一种节省资源、提高视频服务水平的有效途径.     

Queueing Analysis of a Reordering Issue

In this paper an M/G/∞queue is considered that receives a stream of numbered tasks. Results are derived concerning the probabilistic properties of the reordering done by the queue.