A generalization of the Erlang formula of traffic engineering

Calls arrive at a switch, where they are assigned to any one of the available idle outgoing links. A call is blocked if all the links are busy. A call assigned to an idle link may be immediately lost with a probability which depends on the link. For exponential holding times and an arbitrary arrival process we show that the conditional distribution of the time to reach the blocked state from any state, given the sequence of arrivals, is independent of the policy used to route the calls. Thus the law of overflow traffic is independent of the assignment policy. An explicit formula for the stationary probability that an arriving call sees the node blocked is given for Poisson arrivals. We also give a simple asymptotic formula in this case.Work on this paper was done while the author was at Bellcore and at Berkeley.     

Modeling a class of state-dependent routing in flexible manufacturing systems

We develop a closed queueing network model for flexible manufacturing systems (FMSs), where parts routing follows a probabilistic shortest-queue (PSQ) scheme, i.e. parts are routed to the shortest queue (or the most empty station) with the highest probability. We allow limited local buffer at each work station. We prove that with the PSQ routing, the Markovian queue-length process satisfies time reversibility and has a product-form equilibrium distribution. An algorithm is developed to compute the solutions to the model. The model can be used as a performance evaluation tool to study FMSs.     

Priority assignment: A conditioned sets approach

The author suggests how conditioned sets of fuzzy variables may be used to provide priority weights. A case is presented where the conditioned sets approach is contrasted with the prioritization information generated by the Eigenvalue Priority Assignment Model.     

Per Connection Performance Analysis of a Frame-Based TDMA/CDMA MAC Protocol Containing both Reservation and Contention Slots

A mixture of reservation plus contention data slots is now widely implemented in TDMA/ CDMA systems to make a system flexible enough to suit various kinds of packets but preserve the good nature of frame-based protocols. We conducted performance analysis for an arbitrary connection in such a system under the assumption of MMPP (Markov-modulated Poisson process) arrivals. Accessible slot locations of this connection in a frame are made general. Success probability in accessing a contention slot is also made general. We have obtained the system size distribution which can be used to evaluate the performance of various frame-based MAC protocols. The MMPP arrival pattern can be generalized to the BMAP (batch Markovian arrival process) family to further accommodate a broader set of traffic sources.Part of the work was performed when the authors were with Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan 106.This revised version was published online in June 2005 with corrected coverdate     

Product form stationary distributions for queueing networks with blocking and rerouting

In this paper we study Markovian queueing networks in which the service and the routing characteristics have a particular form which leads to a product form stationary distribution for the number of customers in the various queues of the network. We show that if certain transitions are prohibited due to blocking conditions, then the form of the stationary distribution is preserved under a certain rerouting protocol. Several examples are presented which illustrate the wide applicability of the model. This revised version was published online in June 2006 with corrections to the Cover Date.     

Equilibrium queueing strategies of two types of customers in a two-server queue

We consider a single queue with two identical servers and two types of customers. The high-type customer is more delay-sensitive but brings less workload to the system than the low-type customer. We obtain the equilibrium queueing strategy for each type of customers.     

Time-varying many-server finite-queues in tandem: Comparing blocking mechanisms via fluid models

This paper focuses on the mechanism of Blocking Before Service (BBS), in time-varying many-server queues in tandem. BBS arises in telecommunication networks, production lines and healthcare systems. We model a stochastic tandem network under BBS and develop its corresponding fluid limit, which includes reflection due to jobs lost. Comparing our fluid model against simulation shows that the model is accurate and effective. This gives rise to design/operational insights regarding network throughput, under both BBS and BAS (Blocking After Service).     

基于排队的两类顾客易逝品库存控制策略研究

本文采用排队理论在面向两类顾客需求的环境下讨论易逝品库存排队系统控制策略问题。首先刻画面向两类顾客服务且具有马尔科夫结构的易逝品库存系统排队模型,获得库存水平状态的稳态概率分布以及作为库存成本控制的系统稳态性能指标。接下来,构建库存控制成本函数及考虑服务水平约束的库存控制优化模型,设计了改进的遗传算法。最后,数值算例揭示出系统参数的敏感性和相应的管理启示。     

具有插队和止步行为的M/M/c 排队系统

研究了具有插队和止步行为的M/M/c排队系统. 将到达顾客分为常规顾客和插队顾客, 常规顾客在队尾排队等待服务, 插队顾客总是尽可能的靠近队首插队等待服务. 插队行为由到达顾客的插队概率和队列中等待顾客对插队行为的容忍来描述. 利用负指数分布的性质、Laplace-Stieltjes变换和全概率公式, 给出了处于等待队列位置n的顾客、任意一个常规顾客和任意一个插队顾客的等待时间的表达式. 在此基础上, 讨论了系统相关指标随系统参数的变化情况.     

带负顾客和非空竭服务随机休假的M~([x])/G/1可修排队系统

研究了带负顾客和非空竭服务随机休假的M~([X])/G/1可修排队系统.负顾客不仅仅移除一个正在接受服务的正顾客,而且还使得服务器损坏而立即进行修理.通过构造一个具有吸收态的马尔可夫链求得了系统稳态存在的充分必要条件.利用补充变量法求得了系统的排队指标和可靠性指标.最后我们还给出了一个数值实例.