FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE

By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.

On the M/G/1 queueing system with multiclass customers and fixed feedback

The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributions, and feedback numbers. The joint probabifity generation function of queue size of each class and the Laplace-Stieltjes transform of the total sojourn time of a customer in each class are presented, which extended the results obtained by Choi B D. The mean queue size of each class and mean total sojourn time of a customer in each class are obtained with this result. The results can be used in computer and communication networks for their performance analysis.

Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N,D)-Policy Control

Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.

m1A/m5C/m6A/m7G调控基因预测胃癌预后及免疫关联性

目的基于m1A/m5C/m6A/m7G甲基化调控基因建立胃癌预后风险预测模型,并分析该模型与免疫的关联性。方法通过癌症基因组图谱(TCGA)-胃癌数据集筛选表达具有显著差异的m1A/m5C/m6A/m7G调控基因,通过单基因Cox回归分析和LASSO算法构建预后风险评分(risk score,RS)模型,使用Kaplan-Meier(K-M)统计进行RS模型验证,并应用细胞系进行RT-qPCR验证。利用单因素、多因素Cox回归分析建立nomogram模型。使用CIBERSORT算法和estimate包进行免疫关联性分析。结果建立了基于八个甲基化调控基因的预后RS模型,将胃癌患者分为高风险和低风险。这八个基因在胃癌细胞系中高表达(P<0.05)。在TCGA-胃癌训练集和GSE62254-验证集中,患者总生存率(OS)与分组状态之间存在显著相关性(P<0.001)。nomogram生存模型预测的1年(C-index=0.703)、3年(C-index=0.729)和5年(C-index=0.734)生存率与实际生存率的一致性较好。免疫关联性分析表明,与低风险患者组相比,高风险患者组免疫评分和免疫检查点相关基因的表达较高(P<0.05)。结论基于m1A/m5C/m6A/m7G调控基因的预后RS模型可预测胃癌预后并指导个体免疫治疗决策。

SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution,but not on the interarrival distribution.We shall also give explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）.

具有随机检修-策略M/G/1系统队长的瞬态与稳态分析

研究一个具有随机检修<p,Y>-策略的M/G/1排队系统,当系统变空时,以概率p(0≤p≤1)对系统进行检修,且检修时间是具有任意分布的随机变量。首先,分析了队长的嵌入马尔可夫链,得到了其稳态分布的概率母函数。其次,讨论了在任意时刻t队长的瞬态分布,得到了队长的瞬态分布关于时间t的拉普拉斯变换表达式。在队长瞬态分析的基础上,应用洛必达法则,通过直接计算获得了在任意时刻队长的稳态分布的递推式,给出了稳态队长的随机分解结构。最后,建立了系统的费用模型,并通过数值实例得到了使系统费用最少的最优检修策略。

有Bernoulli检修与顾客进入控制策略的M/G/1可修排队的可靠性

本文研究一个具有Bernoulli检修与顾客进入控制策略的M/G/1可修排队模型,其中服务台在服务顾客期间可能发生故障.Bernoulli检修与顾客进入控制策略是指每当系统变空时依概率p(0≤p≤1)进入检修,或者依概率(1−p)不进入检修而是等待下一个顾客进入系统后直接开始服务,而且在系统的检修期内至多允许N个顾客进入.运用更新过程理论、全概率分解技术与拉普拉斯变换工具,我们对系统的一些可靠性指标进行了讨论,例如时刻t服务台处于故障状态的概率、在(0,t]内服务台的平均失效次数等等.最后通过数值计算研究了一些系统参数对系统可靠性指标的影响.

A NEW AND DIRECT METHOD OF ANALYSIS THE DEPARTURE PROCESSES OF SINGLE SERVER QUEUEING SYSTEMS

In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.

SOME NEW RESULTS ON WAITING TIME AND BUSY TIME IN M/G/1 QUEUE

This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.

The M^X/M/1 Queue with Multiple Working Vacation

We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtained, from which we obtain the stochastic decomposition structure of system length which indicates the relationship with that of the MX/M/1 queue without vacation. Some performance indices are derived by using the PGF of the stationary system length distribution. It is important that we obtain the Laplace Stieltjes transform (LST) of the stationary waiting time distribution. Further, we obtain the mean system length and the mean waiting time. Finally, numerical results for some special cases are presented to show the effects of system parameters.

A New Vector Markov Process for M/G/1 Queue

In this paper, by considering the stochastic proces s of the busy period and the idle period, and introducing the unfinished work as a supplementary variable, a new vector Markov process was presented to study th e M/G/1 queue again. Through establishing and solving the density evolution equa tions, the busy-period distribution, and the stationary distributions of waitin g time and queue length were obtained. In addition, the stability condition of th is queue system was given by means of an imbedded renewal process.

The M//M//1 Queue with Controlled Multiple Working Vacations

In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and enter regular busy period with probability 1 p (if there are customers in the queue) or continue the vacation with probability p. For this model, we drive the analytic expression of the stationary queue length and demonstrate stochastic decomposition structures of the stationary queue length and waiting time, also we obtain the additional queue length and the additional delay of this model. The results we got agree with the corresponding results for working vacation model with or without vacation interruption if we set p = 0 or p = 1, respectively.

A Residual Time Based Scheduling: Performance Modeling in M/G/C Queueing Applications

It is well known, in queueing theory, that the system performance is greatly influenced by scheduling policy. No universal optimum scheduling strategy exists in systems where individual customer service demands are not known a priori. However, if the distribution of job times is known, then the residual time (expected time remaining for a job), based on the service it has already received, can be calculated. Our particular research contribution is in exploring the use of this function to enhance system performance by increasing the probability that a job will meet its deadline. In a detailed discrete event simulation, we have tested many different distributions with a wide range of C2 and shapes, as well as for single and dual processor system. Results of four distributions are reported here. We compare with RR and FCFS, and find that in all distributions studied our algorithm performs best. In the study of the use of two slow servers versus one fast server, we have discovered that they provide comparable performance, and in a few cases the double server system does better.

一类具有两个服务阶段、反馈的M/G/1重试排队系统

研究了一个具有两个服务阶段带反馈的M/G/1重试排队系统.在假定重试区域中只有队首的顾客允许重试的情况下,重试时间分布具有一般分布时,证明了系统存在稳态的充分必要条件.利用向量马氏过程的方法求得了稳态时系统队长和重试区域中队长分布、顾客的平均等待时间、重试期间服务台处于空闲的概率、重试区域为空的概率.并指出所讨论的重试排队在把系统中服务台空闲的时间看作休假的情况下也满足随机分解的性质.

推广的(t，T)策略下M/G/1排队系统队长分布的递推解及最优策略

本文考虑当系统变空后的延迟关闭时间为一般概率分布的(t,T)策略下的M/G/1/排队系统。通过引进"服务员忙期"和使用全概率分解技术,首次研究了系统在任意时刻队长的瞬态性质,导出了队长瞬态分布的L变换的递推表达式和稳态分布的递推表达式,进一步得出了系统稳态队长的随机分解结果。最后,建立系统的费用结构模型,讨论了系统变空后的最优关闭时间,并给出了具体数值计算例子。

优先权的N策略M/G/1排队在通信网中的应用

分析通信网中带有两个优先权的N策略M/G/1排队系统的性能,利用补充变量法对此排队系统的状态转移方程进行分析,获得了带有两个优先权的N策略M/G/1排队系统的队长分布母函数及通信网缓冲器中的平均队长,并对两个优先权排队进一步讨论。

基于M/G/1/K排队理论的IEEE 802.15.4网络吞吐量分析

针对IEEE 802.15.4时隙载波侦听多址接入与碰撞避免(CSMA/CA)算法,利用二维Markov链分析方法提出了一个网络分析模型。该模型特别考虑了IEEE 802.15.4协议的休眠模式以及退避窗口先于退避阶数(NB)达到最大值的情况。在此基础上,结合M/G/1/K排队理论推导得到了吞吐量的表达式,进而分析了网络在非饱和状态下数据包到达率对吞吐量的影响,利用模拟平台NS2进行了仿真。实验结果显示理论分析结果与仿真结果可以较好地拟合,并能准确描述网络吞吐量的变化,验证了分析模型的有效性。

附有选择性服务与无等待能力的M/G/1排队系统稳定性分析

研究附有选择性服务与无等待能力的M/G/1排队系统。通过对描述其系统行为的偏微分方程组的规范化,将其转化为Banach空间中抽象的Cauchy问题。然后,利用强连续有界线性算子半群理论,证明了系统的非负稳定解恰是系统算子的0本征值对应的非负本征向量。同时通过研究系统算子的谱特征,证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱,进而得到系统的渐近稳定性,特别在范数意义下系统的动态解收敛到稳态解。

具有固定反馈次数的M/G/1排队系统排队长度分析

将具有固定反馈次数的M/G/1排队模型扩充到一般情况,即每位顾客总共接受m次服务,每次服务时间的分布函数各不相同,将第i次接受服务的顾客视为Ci类顾客.给出了在平稳状态时排队系统中各类顾客排队长度的联合概率生成函数,同时提供了一种计算各类顾客平均排队长度的方法.结果可广泛应用于各种通信和计算机网络,为它们的性能建模分析提供强有力的数学分析工具.