A Complete and Simple Solution to a Discrete-Time Finite-Capacity BMAP/D/c Queue

We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.

Stationary Characteristics of the Single-Server Queue System with Losses and Immediate Service Quality Control

Semi-Markovian model of operation of a single-server queue system with losses and immediate service quality control has been built. In case of unsatisfactory request service quality, its re-servicing is carried out. Re-servicing is executed till it is regarded satisfactory. Time between request income, and request service time are assumed to be random values with distribution functions of general kind. An explicit form of the system stationary characteristics has been defined.

SINGLE SERVER QUEUES WITH A BATCH MARKOVIAN ARRIVAL PROCESS AND BULK RENEWAL OR NON-RENEWAL SERVICE

We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent of each other as well as the arrival process. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Next we obtain queue-length distributions at various other epochs such as, pre-arrival, arbitrary and pre-service using relations with post-departure epoch. Later we also obtain the system-length distributions at post-departure and arbitrary epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue-lengths and mean waiting times have been obtained Total expected cost function per trait time is also derived to determine the locally optimal values of a and b. Secondly, we perform similar analysis for the corresponding infinite-buffer single server queue where arrivals occur according to a BMAP and service process in this case follows a non-renewal one, namely, Markovian service process （MSP）.

区块链共识窗口下Web服务兼容性评价方法

针对传统的服务计算框架下,web服务的性能评价缺乏时效性且缺乏服务兼容性能评价方法的问题,提出了一种基于马尔科夫链和共识时间窗口的兼容性能评价方法。首先,提出增强型面向服务架构计算框架,利用区块链共识算法产生时间较为固定的特点,将时间分隔成长度固定的时间窗口,从而产生服务性能的“时效性”。其次,提出服务兼容性能评价方法,利用当前时段服务池调用记录,计算出能够预测服务下一时段服务兼容性的参数“连接值”。最后,选取4种共识算法BitCoin PoW、PPCoin DPoS、Fabric PBFT以及PBFT+DPoS,对这4种共识算法产生的时间窗口下服务池的离散程度、连接值的分布、兼容性能评价效果进行了对比。结果表明,笔者提出的计算模型,可以准确地区分服务池内服务的兼容属性,区分度随区块链共识算法改变,效果排名依次是PoW,PBFT,DPoS,PBFT+DPoS。

非泊松工件流CSPS系统的Q学习算法适用性仿真研究

研究工件非泊松到达情况下,传送带给料加工站(CSPS)系统无法建立成半马尔可夫决策过程(SMDP)模型时, Q学习算法的适用性问题.首先,以马尔可夫调制泊松过程(MMPP)和半马尔可夫调制泊松过程(SMMPP)来模拟非泊松工件流,并在相同的平均到达率下,仿真评估其Q学习算法性能,并分别与泊松工件流情况下的Q学习算法性能进行比较:其次,在非泊松工件流情况下,观测以实时统计平均到达率作为工件标准泊松到达率的理论优化情况:最后讨论在MMPP和SMMPP叠加混合非泊松工件流情况下CSPS系统的Q学习算法性能.实验表明,在工件非泊松到达情况下Q学习算法依然能学到较好的控制策略,从而说明了CSPS系统中Q学习算法的适用性.

基于离差指数和马尔可夫拟合模型的在线性能分析方法

针对粗监控粒度和突发性负载的情况下传统的基于平均服务时间的排队模型的性能分析不准确的问题，提出了一种适用于粗监控粒度的在线性能分析方法。该方法采用基于请求数目离差指数（IDC）的马尔可夫拟合技术，利用IDC描述服务时间过程的突发性，在马尔可夫拟合模型的基础上构建有效的排队网络。试验结果表明，与传统的采用均值分析（MVA）方法求解的排队模型相比，该方法更准确。以性能参数响应时间和吞吐量为例．相对误差分别平均降低了6．38％和6．27％，最大可降低11．45％和15．06％。

A Stochastic Inventory System with Postponed Demands and Infinite Pool in Discrete-Time Setup

In this article,we consider a discrete-time inventory model in which demands arrive according to a discrete Markovian arrival process.The inventory is replenished according to an es;ST policy,and the lead time is assumed to follow a discrete phase-type distribution.The demands that occur during stock-out periods either enter a pool which has an infinite capacity or leave the system with a predefined probability.The demands in the pool are selected one by one,if the on-hand inventory level is above s t 1;and the interval time between any two successive selections is assumed to have a discrete phase-type distribution.The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady-state case.We derive the system performance measures under steady state and using these measures,the total expected cost rate of the system is calculated.The impacts of arrival rate on the performance measures are graphically illustrated.Finally,we study the impact of cost on the optimal values of the total expected cost rate,inventory level and the reorder point.

具有负顾客到达和RCH移除策略的GI/D—MSP/1/N离散时间排队系统

综合运用补充变量方法和基于条件概率矩阵迭代的嵌入Markov链方法研究了具有负顾客到达和RCH移除策略的离散时间GI/D—MSP/1/N排队系统.获得了稳态情形下正顾客到达前夕,任意时隙分点以及外部观测时刻的三种队长分布.并进一步讨论了可入系统正顾客的等待时间分布.最后通过几个特殊情形下的数值算例验证了计算方法理论分析的正确性.

The MAP/PH/N Retrial Queue in a Random Environment

We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.