无阻塞概率下的排队效率分析

排队在日常生活当中屡见不鲜,为了使顾客排队等待的时间尽可能减少,除了合理安排工作人员的服务质量及服务设备外,还应该考虑如何安排排队更有效。本文在通讯系统排队问题分析的基础上,在假设阻塞概率趋近于零的情况下,比较了不同排队方式下的效率,得出结论：排成一个大队要优于排成几个小队。     

Investigation of almost deterministic queueing systems

Two almost deterministic queuing models are investigated. The influence of small stochastic disturbances on deterministic queuing systems under high loading is estimated. The queuing system G|G|1|∞ with group service is investigated in the case where the group size n tends to infinity. A theorem about the tendency of a stationary probability of a group queue to go to zero if n→∞ is formulated and proved. An application of the group-service model to the construction of an insurance system with a small insurance percent, a small initial capital, and a small ruin probability is considered. This construction is based on the cooperative effect of unification of independent and identically distributed insurance systems. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I.     

Tables for M/G/c queuing systems with phase-type service

Currently much research is done on the development of simple approximations for complex queuing systems. This practically important research is usually hampered by the fact that no exact results are available for a thorough testing of the approximations. In this paper we give for several M/G/c queuing systems with phase-type service the exact values for both the delay probability and the first two moments of the queuing time. These tables considerably extend the widely used Hillier-Lo tables which only consider Erlangian service and small values for the number of servers. The aim of the publication of our tables is to supply much needed test material to the research community and in this way to contribute to further progress in the research on queuing approximations. We present the result of the testing of several existing approximations. Also, the tables provide the practitioner with numerical results useful to design queuing systems.     

The Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime

The paper gives a formula for the probability that a randomlychosen elliptic curve over a finite field has a prime numberof points. Two heuristic arguments in support of the formulaare given as well as experimental evidence. The paper also givesa formula for the probability that a randomly chosen ellipticcurve over a finite field has kq points where k is a small numberand q is a prime.     

The probability of generating a soluble subgroup of a finite group

It is proved that for finite groups G, the probability thattwo randomly chosen elements of G generate a soluble subgrouptends to zero as the index of the largest soluble normal subgroupof G tends to infinity.     

The probability of generating a nilpotent subgroup of a finite group

It is proved that for finite groups G the probability that tworandomly chosen elements of G generate a nilpotent subgrouptends to 0 as the index of the Fitting subgroup of G tends toinfinity.     

Realization probability in multi-class closed queuing networks

Perturbation analysis results of single-class queuing networks are extended to the multi-class case. The realization probability is defined and used to calculate the limiting value of the sample derivative of the system throughout with respect to mean service times a multi-class closed queuing network with exponentially distributed service times. A necessary condition for this value to be an asymptotically unbiased estimate of the derivative of the steady-state throughout is given.     

基于概率论的移动营业厅用户排队问题研究

用概率论知识研究移动营业厅排队问题,通过建立移动营业厅静态排队模型,引进新的客户满意度指标,分析比较了最优排序和随机排序的指标值.     

带有优先权、不耐烦顾客及负顾客的$M_1,M_2/G_1,G_2/1$可修重试排队系统

研究了带有优先权,不耐烦顾客及负顾客的M1,M2/G1,G2/1可修重试排队系统.假设两类顾客的优先级不同且各自的到达过程分别服从独立的泊松过程.有优先权的顾客到达系统时如服务器忙,则以概率H1排队等候服务,以概率1-H1离开系统;而没有优先权的顾客只能一定的概率进入Orbit中进行重试,直到重试成功.此外,假设有服从Poisson过程的负顾客到达:当负顾客到达系统时,若发现服务台忙,将带走正在接受服务的顾客并使机器处于修理状态;若服务台空闲或已经处于失效状态,则负顾客立即消失,对系统没有任何影响.应用补充变量及母函数法给出了该模型的系统指标稳态解的拉氏变换表达式,并得到了此模型主要的排队指标及可靠性指标.     

The discrete-time queue with autoregressive inputs revisited

In this paper, we present an exact queuing analysis of a discrete-time queue whose arrival process is correlated and consists of a discrete autoregressive model of order 1 (DAR(1)). The functional equation describing this DAR(1)/D/1 queuing model, originally derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41), is manipulated and transformed into a mathematical tractable form. By using simple analytical transform techniques, we show how our proposed approach allows us to derive an equivalent (yet simpler) expression for the steady-state probability generating function (pgf) of the queue length, as originally derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41). From this pgf, we characterize the distribution of the packet delay. New numerical results related to packet loss ratio and mean delay of the DAR(1)/D/1 queue are also presented. The proposed approach outlines an alternate solution technique and a general framework under which more complex time-series based queuing models can be analyzed. AMS Subject Classifications 60K25     

Self-Similarity and Probability: Parameters Describing the Geometry of Cantor Sets

A deterministic self-similar Cantor set F defines a naturalprobability space, the elements of which are neighbourhoodsof various sizes of all points in F. Considering random variableson this probability space, some porosity and density parametersare explicitly calculated. 1991 Mathematics Subject Classification28A80, 60D05.     

Mathematical problems in the theory of shared-processor systems

This article considers new approaches in queuing theory associated with mathematical modelling and analysis of contemporary computer systems and networks using shared processors. Emphasis is placed on results concerning exact determination of probability distributions for such characteristics as sojourn times and waiting times. Various methods of analyzing shared-processor systems are considered, their characteristics analyzed, and special attention is devoted to the broad class of M ¦GI¦1 queuing disciplines that result in Poisson throughput. Several limit theorems for heavyload conditions are described.Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 29, pp. 3–82, 1990.The author would like to thank M. Ya. Kelbert for helpful comments.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

A characterization of finite soluble groups

Let G be a finite soluble group of order m and let w(x₁, ...,x_n) be a group word. Then the probability that w(g₁, ..., g_n)= 1 (where (g₁, ..., g_n) is a random n-tuple in G) is at leastp^–(m–t), where p is the largest prime divisor ofm and t is the number of distinct primes dividing m. This contrastswith the case of a non-soluble group G, for which Abérthas shown that the corresponding probability can take arbitrarilysmall positive values as n .     

Analysis of a busy period queuing system with balking,reneging and motivating

Queuing model is widely applied in production, inventory and service industries. It is fundamental to improve the performance of queuing model by characterizing the practical queuing characteristics. In this paper, we consider impatient behaviors of customers who possibly balk and renege in a multi-server busy period queuing system, and study strategic behavior of the service provider who attempts to improve service rate when the system is busy. The piecewise curves with threshold structure are used to construct the dynamic inputting probability, dynamic service degree and dynamic reneging rate, and they are introduced to model the balking, motivating and reneging behaviors of the busy queue. The steady-state probabilities and the performance measures of the proposed model are derived. Finally, an empirical example is given to show the effectiveness of the proposed model by comparing it with the queuing model in literature.     

A global Riesz decomposition theorem on trees without positive potentials

We study the potential theory of trees with nearest-neighbortransition probability that yields a recurrent random walk andshow that, although such trees have no positive potentials,many of the standard results of potential theory can be transferredto this setting. We accomplish this by defining a non-negativefunction H, harmonic outside the root e and vanishing only ate, and a substitute notion of potential which we call H-potential.We define the flux of a superharmonic function outside a finiteset of vertices, give some simple formulas for calculating theflux and derive a global Riesz decomposition theorem for superharmonicfunctions with a harmonic minorant outside a finite set. Wediscuss the connection of the H-potentials with other notionsof potentials for recurrent Markov chains in the literature.     

制造企业成品出入库两级排队协同服务模型

优化企业成品出入库协同服务水平、平衡工作负荷,从而提高企业仓储服务效率、降低物流成本,是现代制造企业亟待解决的一个重要的管理细节问题。针对这个问题,本研究以仓储入库和出库两个排队过程为研究对象,建立出入库等待时间溢出情景下的两级排队协同服务模型,分析了在排队等待时间控制目标下,出入库员工优化配置方案。该模型引入溢出和串联两个协同服务机制,分三种情景即前方与后方服务台都有空闲,前方繁忙与后方空闲,前方空闲(或繁忙)与后方繁忙,建立了各情景下的系统状态转移方程,求解系统状态的概率,并进而推算出反映系统表现的各项指标,如员工使用率,队列长度,等待时间,以及等待时间超过溢出界值的概率。用制造企业成品出入库管理案例进行验证分析,对企业目前采用的M/M/S出入库排队系统与两级排队协同服务系统进行了数值计算对比。结果表明后者能有效提升出入库服务效率,减少出入库排队系统平均等待时间,降低由于入库和出库两个服务过程效率不均衡而产生的企业内部物流成本,是提升企业内部物流协同管理水平的一个重要方法。其应用可以服务于仓储出入库协同管理的信息化与自动化水平的提高。     

Invariant measures for real analytic expanding maps

Let X be a compact connected subset of ^d with non-empty interior,and T:X X a real analytic full branch expanding map with countablymany branches. Elements of a thermodynamic formalism for suchsystems are developed, including criteria for compactness oftransfer operators acting on spaces of bounded holomorphic functions.In particular, a new sufficient condition for the existenceof a T-invariant probability measure equivalent to Lebesguemeasure is obtained.     

Upper tails for intersection local times of random walks in supercritical dimensions

We determine the precise asymptotics of the logarithmic uppertail probability of the total intersection local time of p independentrandom walks in ^d under the assumption p(d–2) > d.Our approach allows a direct treatment of the infinite timehorizon.     

Eine bemerkung zur existenz unendllcli vieler ”leorpunkte“ in bedienungssystemen liiit liiienillm-li vleleii bedienungsgeräten

In this paper a queuing system G/GI/ ∞ with stationary input is considered. It is given a necessary and sufficient condition for existing with the probability 1 of an infinite number of moments of calls, in which the system is empty.