On the single server retrial queue with priority subscribers and server breakdowns

The author concerned the reliability evaluation as well as queueing analysis of M1, M2/G1, G2/1 retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.     

A batch arrival retrial queue with starting failures,feedback and admission control

This paper is concerned with the analysis of a feedback M^[X]/G/1 retrial queue with starting failures and general retrial times. In a batch, each individual customer is subject to a control admission policy upon arrival. If the server is idle, one of the customers admitted to the system may start its service and the rest joins the retrial group, whereas all the admitted customers go to the retrial group when the server is unavailable upon arrival. An arriving customer (primary or retrial) must turn-on the server, which takes negligible time. If the server is started successfully (with a certain probability), the customer gets service immediately. Otherwise, the repair for the server commences immediately and the customer must leave for the orbit and make a retrial at a later time. It is assumed that the customers who find the server unavailable are queued in the orbit in accordance with an FCFS discipline and only the customer at the head of the queue is allowed for access to the server. The Markov chain underlying the considered queueing system is studied and the necessary and sufficient condition for the system to be stable is presented. Explicit formulae for the stationary distribution and some performance measures of the system in steady-state are obtained. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.     

A discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times

The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times. As soon as the orbit is empty, the server takes a vacation. However, the server is allowed to take a maximum number J of vacations, if the system remains empty after the end of a vacation. If there is at least one customer in the orbit at the end of a vacation, the server begins to serve the new arrivals or the arriving customers from the orbit. For this model, the authors focus on the steady-state analysis for the considered queueing system. Firstly, the authors obtain the generating functions of the number of customers in the orbit and in the system. Then, the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size. Besides, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided.     

重试,反馈M/M/s/k排队的呼叫中心性能分析

由于CTI(计算机电话集成)技术的发展,使呼叫中心得到广泛的应用.与呼叫中心实现技术的发展相比,对呼叫中心管理的研究显得有些滞后,而针对呼叫中心排队模型的研究,更是如此.针对呼叫中心服务系统中的重试和反馈问题,考虑一种带重试和反馈的M/M/s/k排队模型.将等待位置和服务台数推广到有限个.在模型求解过程中,尝试采用矩阵迭代的新方法,使求解过程简单明了.然后,采用逼近的方法给出模型的数值解,并得出反馈对系统的影响随系统负荷的增大而快速增大等结论.     

延迟多重休假MX/G/1排队系统的队长分布

考虑延迟多重休假的M^x／G／1排队，在假定延迟时间、休假时间和服务时间都是一般概率分布函数下，研究了队长的瞬态和稳态性质、通过引进“服务员忙期”，导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式，以及平稳队长的随机分解．     

带负顾客和不耐烦顾客的离散时间Geo/G/1重试排队

考虑了一个带负顾客和不耐烦顾客且重试时间为一般分布的离散时间Geo/G/1重试排队系统. 负顾客带走一个正在服务的顾客, 而对重试组中的顾客无影响.正顾客到达系统若遇服务器忙则可能进入重试组也可能离开系统.通过对此排队系统的嵌入马氏链进行分析, 得到了重试组队长和系统队长的概率母函数. 进而得到了一系列重要的排队指标. 此外, 还推导出了系统的稳态存在条件. 以及对无负顾客和不耐烦顾客时的特例进行了分析. 最后通过几个具体的数值实例演示了一些参数对系统关键性能指标的影响.     

具有多重休假和Min(N,V)-策略控制的Geo/G/1离散时间排队

考虑服务员具有多重休假和系统采用min(N,V)-策略控制的离散时间Geo/G/1排队系统,使用全概率分解技术和更新过程理论,研究了系统在任意时刻n+的瞬态队长分布和稳态队长分布,得到了瞬态队长分布的z-变换表达式和稳态队长分布的递推表达式.进一步,得到了系统在时刻点n,n~-和外部观察时刻点的稳态队长分布.特别地,本文直接获得了一些特殊离散时间排队系统相应的结果.最后,通过数值实例阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中的重要价值.     

负顾客及反馈的 Geo/Geo/1 多重工作休假排队系统的稳态队长分布

综合利用离散补充变量法、矩阵几何解及拟生灭链的方法研究了带有负顾客及伯 努利反馈的Geo/Geo/1多重工作休假排队系统. 首先运用离散补充变量方法得 到了此复杂系统的转移概率矩阵. 其次, 再利用矩阵几何解及拟生灭链的技术通 过解方程组获得了队长的稳态分布、平均队长及稳态队长的随机分解结果. 最后, 通过引入数值例子, 作出了系统的二维图形, 进而可以更直观地分析一些参数 对系统性能的影响.     

带启动时间的N-策略M/G/1排队系统的队长

从任意初始状态出发, 直接研究了系统队长的瞬态分布和稳态分布.通过引进的“服务员忙期", 使用全概率分解技术和拉普拉斯变换,导出了在任意时刻t队长的瞬态分布的拉普拉斯变换的表达式,进一步获得了有重要应用价值的稳态分布的具体的递推式子,以及稳态队长的随机分解结果. 特别地,还直接获得了一些特殊排队系统的更实用的稳态队长分布的递推表达式.     

具有有限等待空间的成批服务系统

应用有界线性算子半群理论证明一类成批服务系统的解的存在唯一性和非负性.     

考虑撤单率的电商配送服务能力自建与外包博弈模型与求解

针对在线冷静期内产生消费者撤单行为情况下电商配送服务能力的自建与外包决策问题,引入撤单率,从是否进行合作的角度给出了完全合作博弈、完全非合作博弈和不完全非合作三种合作强度的动态博弈模型,并将其中两种情形划分为三阶段动态博弈过程,采用逆向递归法求解这两种情形下各子博弈均衡解,得到了在线购买环境下电商配送服务能力自建与外包的最优解集.进一步地,在第三种情形下设计了成本分担、利润分配以及风险规避三种子博弈模型,以增强模型的灵活性.数值算例与分析表明电商配送服务能力博弈中,电商决策者能够有效实现撤单行为与成本变动影响下动态博弈的帕累托优化.     

A comparative study of the inventory system with service facility and postponed demands

In this article, we present a continuous review （s,S） inventory system with a service facility consisting of finite buffer （capacity N ） and a single server. The customers arrive according to a Poisson process. The individual customer＇s unit demand is satisfied after a random time of service, which is assumed to be exponential. When the inventory level drops to s＇an order for Q（= S-s） items is placed. The lead time of reorder is assumed to be exponential distribution. An arriving customer, who finds the buffer is full, enters into the pool of infinite size or leaves the system according to a Bernolli trial. At the time of service completion, if the buffer size drops to a preassigned level L （1 〈 L 〈 N） or below and the inventory level is above s, we select the customers from the pool according to two different policy ： in first policy, with probability p （0 〈 p 〈 1） we select the customer from the head of the pool and we place the customer at the end of the buffer; in the second policy, with p （0 〈 p 〈 1） the customer from the pool is transferred to the buffer for immediate service and after completion of his service we provide service to the customer who is in the buffer with probability one. If at a service completion epoch the buffer turns out to be empty, there is at least one customer in the pool and the inventory level is positive, then the one ahead of all waiting in the pool gets transferred to the buffer, and his service starts immediately. The joint probability distribution of the number of customers in the pool, number of customers in the buffer and the inventory level is obtained in the steady-state case. Various stationary system performance measures are computed and total expected cost rate is calculated. A comparative result of two models is illustrate numerically.     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS I： G/M（n）/1/K

In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M（n）/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate. In a subsequent companion paper, we study its dual system M（n）/G/1/K queue with statedependent vacations.     

网络外部性下的电信业务服务质量和定价的博弈分析

针对已有文献较孤立的关注网络外部性、多方参与以及服务质量对电信业务定价决策的影响这一不足, 从用户的效用出发, 推导出了网络外部性条件下的市场需求曲线, 进而建立了网络外部性、企业相对市场关系、服务质量与电信业务价格之间的统一分析框架, 考察了模型的均衡及其性质. 结果表明: 网络外部性和服务质量可以提高用户业务的支付费用并增加运营系统的利润. 当网络外部性较弱时, 参与企业双方同时决策意味着更优质的服务, 更低的业务支付, 更高的系统利润, 而序贯决策则意味着决策先行者拥有先动者优势. 当网络外部性较强时, 服务提供商先行决策可以带来更优质的服务, 更高的业务支付和系统利润, 但作为决策追随者的运营商可以利用优质服务改善价值获取, 获得后动者优势.     

易逝品随机生产库存模型动态定价、服务水平和生产控制策略

本文研究需求受价格和服务水平双重影响下的易逝品随机生产库存模型,探讨考虑外部随机扰动对库存变动影响下易逝品企业的最优联合动态定价、服务和生产策略,并基于随机最优控制理论,运用Hamilton-Jacobi-Bellman(HJB)方程对最优策略进行了求解.研究表明:最优动态价格、服务水平和生产速率是库存水平的线性反馈形式;外部随机扰动的大小对易逝品生产企业所获得的折现利润总期望会产生不同影响,在整个经营周期内外界不确定因素越大,易逝品生产企业所获得的折现利润总期望越小;价格敏感系数和服务敏感系数会影响易逝品企业生产、服务、价格策略.     

A perishable inventory system with service facilities, <Emphasis Type="Italic">MAP</Emphasis> arrivals and <Emphasis Type="Italic">PH</Emphasis> — Service times

We consider a continuous review perishable （s,S） inventory system with a service facility consisting of a waiting hall of finite capacity and a single server. We assume two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process （MAP）. An ordinary customer joins the queue and a negative customer instead of joining the queue removes one ordinary customer from the queue. The removal rule adopted in this paper is RCE （removal of a customer from the end）. The individual customer＇s unit demand is satisfied after a random time of service which is assumed to have a phase-type distribution. The life time of each item and the lead time of the reorders have been assumed to be independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained for the steady state case. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically.     

考虑交叉网络外部效应的多边配送平台增值服务投资与定价策略

针对考虑交叉网络外部效应的多边配送平台,本文讨论了该类平台增值服务投资与定价策略.首先构建了以平台利润最大化为目标的优化模型,然后求解得到最优增值服务投资和定价策略,最后通过数值分析探究了增值服务投资系数、边际增值服务投资成本、基础投资和交叉网络外部效应对最优定价策略、最优增值服务投资策略和平台最优利润的影响.研究表明:1)若增值服务投资系数较大,则平台应加大增值服务投资,同时提高交易费、广告费和配送费;2)若平台的基础投资较大,则平台应减少增值服务投资;3)若消费者对配送人员的网络外部性强度增加,则平台应提高广告费,加大增值服务投资,同时降低交易费和配送费,甚至对消费者进行补贴;4)若消费者对广告商的网络外部性强度增加,则平台应提高广告费和配送费,降低交易费,同时加大增值服务投资;5)若广告商对消费者的网络外部性强度增加,则平台应大幅度提高广告费和交易费,减少配送费,同时降低增值服务投资.该研究成果为多边配送平台的运营决策提供重要参考.     

A single-period inventory system with a general S-shaped utility and exponential demand

We discuss a single-period inventory system with a general S-shaped utility function and exponential demand.It is shown that there exists a state-dependent order-up-to policy to be optimal.Behaviors of optimal policy are illustrated by a numerical example.