The M/M/1 queue with gated random order of service

We analyse an M / M /1 queueing model with gated random order of service discipline. In this service discipline there is a waiting room, in which arriving customers are collected, and a service queue. Each time the service queue becomes empty, all customers in the waiting room are instantaneously put in random order in the service queue. We find the joint stationary distribution of the number of customers in the waiting room and the service queue. Furthermore, we obtain the bivariate Laplace–Stieltjes transform of the joint distribution of the sojourn times of a customer in the waiting room and the service queue.     

爱尔朗排队模型在配送中心车辆调度中的应用研究

利用随机过程和排队论的相关知识,通过对爱尔朗排队模型进行性能分析以及参数求解,给出其在配送中心中的具体应用,并通过实例求解。通过求解系统空闲的概率、系统平均队长、排队等候平均队长、车辆在配送中心中的逗留时间、平均排队时间,比较单路排队和多路排队的区别,以此判断配送中心的车辆调度系统建设是否合理。     

Might randomization in queue discipline be useful when waiting cost is a concave function of waiting time?

This paper suggests that introducing randomization in queue discipline might be welfare enhancing in certain queues for which the cost of waiting is a concave function of waiting time. Concavity can make increased variability in waiting times good not bad for aggregate customer welfare. Such concavity may occur if the costs of waiting asymptotically approach some maximum or if the customer incurs a fixed cost if there is any wait at all. As examples, cost might asymptotically approach a maximum for patients seeking organ transplants who will not live beyond a certain threshold time, and fixed costs could pertain for knowledge workers seeking a piece of information that is required to proceed with their current task, so any delay creates a “set up charge” associated with switching tasks.     

Further results for the double ended queue

Summary For the double ended queue involving taxis and customers at a taxi-stand (Kashyap, 1965 a; b) the probabilities that (i) only taxis are waiting and (ii) only customers are waiting have been investigated by the use of Laplace transform. The L.T.s of the mean queue lengths of taxis and of customers are also obtained. The arrivals of taxis and customers are taken as general and Poisson respectively. The supplementary variable technique (Syski, 1960) has been used.     

Waiting time probabilities in the M/G/1 + M queue

We consider an M/G/1 queueing system where the customers may leave the queue if their services do not commence before an exponentially distributed random time. The (conditional) offered waiting time distribution is approximated by a gamma distribution via matching the first and second moments of the actual waiting time. A simulation study is conducted to assess the accuracy of the approximation and it reveals that the approximation performs satisfactorily under general conditions on service time distributions.     

带后续队列长度通告的呼叫中心性能分析

从排队心理学的角度考虑了队列长度对顾客等待耐心的影响,设计了一个带队列信息通告机制的M／M／N模型。等待的顾客可以像有形排队一样获知目前排队的人数及其所处的队列位置,并以此决定继续等待或者放弃。使用仿真方法对该机制下的呼叫中心性能进行了分析,并与Erlang—A模型和Erlang—C模型进行了比较。     

Queues with batch poisson arrivals and hyper-exponential service time distribution

Summary We consider in this paper the transient behaviour of the queuing system in which (i) the input, following a Poisson distribution, is in batches of variable numbers; (ii) queue discipline is ‘first come first served’, it being assumed that the batches are pre-ordered for service purposes; and (iii) service time distribution is hyper-exponential withn branches. The Laplace transform of the system size distribution is determined by applying the method of generating functions, introduced in queuing theory byBailey [1]. However, assuming steady state conditions to obtain, the problem is completely solved and it is shown that by suitably defining the traffic intensity factor,ϱ, the value,p ₀, of the probability of no delay, remains the same in this case of batch arrivals also as in the case of single arrivals. The Laplace transform of the waiting time distribution is also calculated in steady state case from which the mean waiting time may be calculated. Some of the known results are derived as particular cases.     

Strategic behavior and social outcomes in a bottleneck queue: experimental evidence

We theoretically and experimentally study the differential incentive effects of three well known queue disciplines in a strategic environment in which a bottleneck facility opens and impatient players decide when to arrive. For a class of three-player games, we derive equilibrium arrivals under the first-in-first-out (FIFO), last-in-first-out (LIFO), and service-in-random-order (SIRO) queue disciplines and compare these predictions to outcomes from a laboratory experiment. In line with our theoretical predictions, we find that people arrive with greater dispersion when participating under the LIFO discipline, whereas they tend to arrive immediately under FIFO and SIRO. As a consequence, shorter waiting times are obtained under LIFO as compared to FIFO and SIRO. However, while our theoretical predictions admit higher welfare under LIFO, this is not recovered experimentally as the queue disciplines provide similar welfare outcomes.     

Finite project life and uncertainty effects on investment

This paper revisits the important result of the real options approach to investment under uncertainty, which states that increased uncertainty raises the value of waiting and thus decelerates investment. Typically in this literature projects are assumed to be perpetual. However, in today's economy firms face a fast-changing technology environment, implying that investment projects are usually considered to have a finite life. The present paper studies investment projects with finite project life, and we find that, in contrast with the existing theory, investments may be accelerated by increased uncertainty. It is shown that this particularly happens at low levels of uncertainty and when project life is short.     

基于排队论的银行客户服务系统问题研究

阐述中国金融业现状和银行业面临的竞争,分析了排队论及其三个组成部分、性能指标和模型。利用排队论来分析银行服务系统的等待问题,并从运筹学和经济学的角度来优化系统,使其效益达到最高。     

A Path Construction for the Virtual Waiting Time of an M/G/1 Queue

Consider the M/G/1 queue, the finite dam M/G/1 with capacity T, and the impatient customer M/G/1 model, where customers become lost customers if their waiting time exceeds τ. In this note we prove that for all three models and each xe(0, r) the distribution of the number of downcrossings of the virtual waiting time process with level x during a busy cycle is identical. This implies the weaker statement that on [0, T) the distribution functions of the steady state distributions of the amount of unprocessed work (virtual waiting time) are proportional. A number of applications is given.     

Back to the roots of the M/D/s queue and the works of Erlang, Crommelin and Pollaczek

A.K. Erlang introduced the M/D/ s queue in 1917, while F. Pollaczek and C.D. Crommelin formalized the theory using complex analysis and transforms. Let D ( s , λ ) denote the stationary probability of experiencing no waiting time in the M/D/ s queue with arrival rate λ and service requirement 1. We use D ( s , λ ) as a vehicle to give an overview of some of the results we obtained over the last years, including explicit characterizations of the roots, the derivation of infinite series from expressions in terms of roots using Fourier sampling and heavy-traffic limits obtained from square-root staffing. We propose to call D ( s , λ ) the Erlang D formula, for which several new results are presented and compared with the results of Pollaczek.     

基于排队论的港口泊位服务系统优化仿真研究

为尽可能提高泊位系统的服务质量,以满足港口吞吐量增长的需求和减少船方在港停留时间,阐述港口泊位系统的特点及其影响因素,借助系统模拟、排队论方法构造泊位服务系统模拟模型和分析泊位服务水平,对比泊位服务系统在新的泊位配置下的服务质量,以指导港口的实际生产。     

Queueing with reneging

Summary In this paper we consider a queue in which a person, having joined, may decide to leave and give up service if it appears that the time consumed will exceed some maximum which he has available. Specifically, three problems are treated: a) How to make a rational (sequential) decision while waiting in the queue, b) the probable effect of this decision, and c) the behavior of a queue in which all persons are employing such a procedure.

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Zusammenfassung Dieser Bericht behandelt eine “Schlange”, in der ein sich dieser “Schlange” angeschlossener Mensch entschlie?t, seinen Platz und die Bedienung aufzugeben wenn es ihm scheint, da? die notwendige Zeit ein ihm zur Verfügung stehendes Maximum überschreiten wird. Insbesondere werden drei Probleme diskutiert: a) Wie man eine rationale (sequentielle) Entscheidung trifft, w?hrend man in einer “Schlange” wartet, b) der wahrscheinliche Effekt einer solchen Entscheidung, c) das Benehmen einer “Schlange”, in dem alle Menschen ein solches Verfahren gebrauchen würden.

     

自然策化安全系统构架危岩体的预警

仅仅立足于预警,是一个被动措施,换句话说仅仅等待滑坡的发生,而人类的期望是最好不要发生这类事件。为此,人类必须立足于主动的地位,积极采取必要而正确的措施避免滑坡的发生,这类措施在多数场合主要是科学地布置好地表排水系统,合理布局林、地、田,而不是挡土墙等大规模工程。     

基于排队论的医院急诊模型

本文用排队论的方法对医院急诊室排队系统进行分析,确定了该系统的的排队模型。给出了统计平衡条件的排队系统的主要指标。讨论了该排队系统的最优化,并进行了实例分析。     

自助银行排队系统分析

利用排队法对自助银行的排队系统进行分析,确定排队模型。给出了统计平衡条件下的主要指标。讨论了系统费用最优化,并进行实例分析。     

Scientific planning of urban cordon sanitaire for desired queuing time

The outbreak of the COVID-19 pandemic disrupted ofur normal life. Many cities enforced a cordon sanitaire as a countermeasure to protect densely inhabited areas. Travelers can only cross the cordon after being checked. To minimize the waiting time in the queue, this paper proposes a method to determine the scientific planning of urban cordon sanitaire for desired queuing time, which is a significant problem that has not been explored. A novel two-stage optimization model is proposed where the first stage is the transportation system equilibrium problem to predict traffic inflow, and the second stage is the queuing network design problem to determine the allocation of test stations. This method aims to minimize the total health infrastructure investment for the desired maximum queuing time. Note that queuing theory is used to represent the queuing phenomenon at each urban entrance. A heuristic algorithm is designed to solve the proposed model where the Method of Successive Averages (MSA) is adopted for the first stage, and the Genetic Algorithm (GA) with elite strategy is adopted for the second stage. An experimental study with sensitivity analysis is conducted to demonstrate the effectiveness of the proposed methods. The results show that the methods can find a good heuristic optimal solution. This research is helpful for policymakers to determine the optimal investment and planning of cordon sanitaire for disease prevention and control, as well as other criminal activities such as drunk driving, terrorists, and smuggling.     

A queueing problem with arrival and service in batches of variable size

This paper studies the transient behaviour of a single-channel queueing problem wherein (i) the input, following aPoisson distribution, is in batches of variable size (ii) the queue discipline is first-come-first-served; it being assumed that the batches are pre-ordered for service purposes (iii) the output, following a general distribution, is in batches of variable size. TheLaplace transform of the probability generating function of the waiting line size is obtained and the corresponding results are derived when the service time distribution is (i) hyper-exponential with m branches (ii) phase-type and (iii) exponential. Finally, some particular cases are discussed.     

高等院校建设项目多视角立体审计模式探讨

建设项目的实施是一个系统工程,也是动态过程,对项目的建设实施有效的审计监督,是合理控制工程造价,提高投资效益的有效途径。本文通过高等院校建设项目审计现状的调研,对建设项目实施的全过程进行分析,针对影响项目投资的相关因素和关键环节,提出对项目建设实施一体化管理,多节点控制,多视角审计的新模式,与同行探讨。