Life Expectancy of Transient Microchaotic Behaviour

The application of digital control may lead to so-called transient chaotic behaviour. In the present paper, we analyse a simple model of a digitally controlled mechanical system, which may create such vibrations. As a consequence of the digital effects, i.e., the sampling and the round-off error, the behaviour of this system can be described by a one-dimensional piecewise linear map. The lifetime of chaotic transients is usually characterized by the so-called escape rate. In the literature, the reciprocal of the escape rate is considered to be the expected duration of the transient chaotic phenomenon. We claim that this approach is not always fruitful, and present a different way of calculating the mean lifetime in the case of one-dimensional piecewise linear maps. Our method might also be used to solve diffusion problems in one-dimensional models of periodic arrays.     

Tail Behaviour of the Area Under the Queue Length Process of the Single Server Queue with Regularly Varying Service Times

This paper considers a stable GI∨GI∨1 queue with a regularly varying service time distribution. We derive the tail behaviour of the integral of the queue length process Q(t) over one busy period. We show that the occurrence of a large integral is related to the occurrence of a large maximum of the queueing process over the busy period and we exploit asymptotic results for this variable. We also prove a central limit theorem for ∫₀^t Q(s) ds.AMS subject classification: 60K25, 90B22.     

Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review

The first paper to introduce the concept of a cyclic queue appeared in the Operational Research Quarterly in 1954. The paper dealt with the 'flow' of aircraft engines from operation to maintenance to available for operation. In 1958, the first paper analyzing the cyclic queue model appeared in the same journal. This paper was application of queue theory to underground coal mining. In 1965 it was shown that stochastic queue networks can be treated analytically in the same manner as cyclic queues with a small adjustment in the auxiliary parameters. Since then cyclic queue models have been applied not only to the problems mentioned above but also to many other production and service industry problems: computer design and control, ship operations, production processes, communications flow, ingot movements in a steel mill, to name but a few. In order for this to be possible, extension and advances in theory have been required and these have come from many nations and many fields of endeavour. This paper traces the development of the theory of cyclic queues and queue networks from 1954 to the present.     

A Finite Buffer Fluid Queue Driven by a Markovian Queue

We consider a finite buffer fluid queue receiving its input from the output of a Markovian queue with finite or infinite waiting room. The input flow into the fluid queue is thus characterized by a Markov modulated input rate process and we derive, for a wide class of such input processes, a procedure for the computation of the stationary buffer content of the fluid queue and the stationary overflow probability. This approach leads to a numerically stable algorithm for which the precision of the result can be specified in advance.     

Influence of the Homogenization on the Transient Behaviour of Size Distributed Polycrystals

The deformation in polycrystals is often heterogenous, e.g. due to grain size dependent hardening. In a semi-analytical representative volume element (RVE), a log-normal distributed grain size is assumed together with a grain size dependent local plastic behavior. The numerical results are well approximated by a simple analytical expression. The effect of the homogenization comparison stiffness on the transient behaviour is explained using a simplified localization equation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient Behaviour of an M/M/1/N queue

For a simple queue with finite waiting space the difference equations satisfied by the Laplace transforms of the state probabilities at finite time are solved and the state probabilities have been obtained. The method economizes in algebra and the simple closed form of the state probabilities is used to obtain important parameters.     

The Index of a Cyclic Quartic Field

Let K be a cyclic quartic field. Let i(K) denote the index of K. It is known that i(K){1, 2, 3, 4, 6, 12}. In Part 1 of this paper we show that i(K) assumes all of these values and we give necessary and sufficient conditions for each to occur. In Part 2 an asymptotic formula is given for the number of cyclic quartic fields with discriminant x and i(K)=i for each i{1, 2, 3, 4, 6, 12}.Received May 6, 2002; in revised form December 24, 2002 Published online June 23, 2003     

The Index of a Cyclic Quartic Field

Let K be a cyclic quartic field. Let i(K) denote the index of K. It is known that i(K){1, 2, 3, 4, 6, 12}. In Part 1 of this paper we show that i(K) assumes all of these values and we give necessary and sufficient conditions for each to occur. In Part 2 an asymptotic formula is given for the number of cyclic quartic fields with discriminant x and i(K)=i for each i{1, 2, 3, 4, 6, 12}.     

离散时间优先队列的尾部渐近性分析

本文研究在离散情形下,两类不同优先权的顾客进入服务系统的情况.稳态概率可以用矩阵形式表示出来.用矩阵分析法,联合稳态概率在一定条件下几何衰减.     

The Setting and Optimization of Quick Queue

Considering that customer arrival is a peak and post-peak period, we establish a fluid model of queuing behavior. In order to reduce the sum of waiting time of customers, we study the method of the setting and optimization of quick queue in a random service system. Under the premise of the total number of service equipment, we construct two queuing models, with one including only common queues and the other including both common and quick queues and propose the formulas for calculating the sum of the waiting time of the two models. In the two cases of peak and post-peak periods, we analyze the effect of quick queue on service system performance. And we present the method for calculating the number of quick queues that gives the best overall system performance. Taking the quick queue setting and optimization of the supermarket service system as an example, we verify the validity of the proposed method, which indicates the reference value of the method to the management practice.     

Embedding of a Cyclic Extension into a Cyclic Extension

A necessary and sufficient condition of the existence of a cyclic Galois extension of degree containing a given quadratic extension is found. Bibliography: 1 title.     

The Lattice of Cyclic Flats of a Matroid

A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats of a matroid form a lattice under inclusion. We study these lattices and explore matroids from the perspective of cyclic flats. In particular, we show that every lattice is isomorphic to the lattice of cyclic flats of a matroid. We give a necessary and sufficient condition for a lattice of sets and a function to be the lattice of cyclic flats of a matroid and the restriction of the corresponding rank function to . We apply this perspective to give an alternative view of the free product of matroids and we show how to compute the Tutte polynomial of the free product in terms of the Tutte polynomials of the constituent matroids. We define cyclic width and show that this concept gives rise to minor-closed, dual-closed classes of matroids, two of which contain only transversal matroids. Received May 29, 2005     

The Single Server Queue with Mixing Dependencies

Methodology and Computing in Applied Probability - We study a single server queue, where a certain type of dependence is introduced between the service times, or between the inter-arrival times, or...     

The Primitive Idempotents of a Cyclic Group Algebra

Explicit expressions are obtained for the 2n + 1 primitive idempotents in FG, the semisimple group algebra of the cyclic group G of order pⁿ (p an odd prime, n ≥ 1) over the finite field F of prime power order q, when q has order φ(pⁿ)/2 modulo pⁿ.AMS Mathematical Subject Classification (2000): 20C05, 94B05, 12E20, 16S34.     

Optimal Decisions in a Time Priority Queue

We show how the position of a limit order (LO) in the queue influences the decision of whether to cancel the order or let it rest. Using ultra-high-frequency data from the Nasdaq exchange, we perform empirical analysis on various LO book events and propose novel ways for modelling some of these events, including cancellation of LOs in various positions and size of market orders. Based on our empirical findings, we develop a queuing model that captures stylized facts on the data. This model includes a distinct feature which allows for a potentially random effect due to the agent’s impulse control. We apply the queuing model in an algorithmic trading setting by considering an agent maximizing her expected utility through placing and cancelling of LOs. The agent’s optimal strategy is presented after calibrating the model to real data. A simulation study shows that for the same level of standard deviation of terminal wealth, the optimal strategy has a 2.5% higher mean compared to a strategy which ignores the effect of position, or an 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting an LO during adverse conditions and obtaining a good queue position before conditions become favourable.     

Transient and Stationary Distributions for the GI/G/k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution

In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator–geometric stationary distribution. Thus it is shown that matrix–analytical methods can be extended to provide a modeling tool even for the general multi-server queue.     

The MMCPP/GE/c Queue

We obtain the queue length probability distribution at equilibrium for a multi-server, single queue with generalised exponential (GE) service time distribution and a Markov modulated compound Poisson arrival process (MMCPP) – i.e., a Poisson point process with bulk arrivals having geometrically distributed batch size whose parameters are modulated by a Markovian arrival phase process. This arrival process has been considered appropriate in ATM networks and the GE service times provide greater flexibility than the more conventionally assumed exponential distribution. The result is exact and is derived, for both infinite and finite capacity queues, using the method of spectral expansion applied to the two dimensional (queue length by phase of the arrival process) Markov process that describes the dynamics of the system. The Laplace transform of the interdeparture time probability density function is then obtained. The analysis therefore could provide the basis of a building block for modelling networks of switching nodes in terms of their internal arrival processes, which may be both correlated and bursty.     

离散时间优先队列的尾部渐近性分析（英文）

本文研究在离散情形下,两类不同优先权的顾客进入服务系统的情况.稳态概率可以用矩阵形式表示出来.用矩阵分析法,联合稳态概率在一定条件下几何衰减.     

Analysis of a Multiserver Queue with Setup Times

This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length. AMS subject classification: 90B22, 60K25     

The Analysis of a General Input Queue with N Policy and Exponential Vacations

This paper studies a single removable server in a G/M/1 queueing system with finite capacity where the server applies an N policy and takes multiple vacations when the system is empty. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distributions of the number of customers in the system. The method is illustrated analytically for exponential and deterministic interarrival time distributions. We establish the distributions of the number of customers in the queue at pre-arrival epochs and at arbitrary epochs, as well as the distributions of the waiting time and the busy period.