On the queueing problem of correlated arrivals with many servers in a finite waiting space

This paper provides an analysis of the steady state behaviour of a discrete time, first come first served limited space queueing problem with many serers. The arrival probabilities at two consecutive time-marks are correlated, whereas the departure probabilities, though depending on the queue length, are assumed to be statistically independent. Probability generating functions for the queue length for the various cases have also been listed. A few particular cases have also been derived. Mean queue lengths are also found out.     

A queueing problem with batch arrivals and correlated departures

Summary This paper considers the steady state behaviour of a queueing system in which (i) the input following the Hypergeometric Distribution is in batches of variable size (ii) queue discipline is first come first served it being assumed that the batches are preordered for service purposes and (ii) the service at two consecutive time marks is correlated. Probability generating functions for the various cases have been obtained and the mean queue lengths derived.     

Solution of a transient state,limited space queueing problem with arrival and departure rates depending on queue length

Summary This paper provides an analysis of a transient state, single channel, limited space queueing problem. The queue discipline is first come first served. The arrival and departure rates depend on queue length. Ample use of Generating Functions andLaplace transforms have been made. A few particular and important cases along with steady state solutions have also been derived.     

Time dependent solution of a queueing problem with correlated batch arrivals and general service time distribution

This paper considers the transient behaviour of queueing problem in which (i) the arrivals occur in batches of variable size (ii) the arrival and no arrival of a batch at two consecutive transition marks are correlated (iii) the service time distribution for each, unit is general with probability density functionD(x). TheLaplace transform of various probability generating functions of queue length are obtained and some particular cases are derived therefrom.     

Queueing problems with arrivals in general stresm and phase type service

This paper deals with the steady state behaviour of a discrete time, single channel, first-come-first-served queueing problem wherein the service phases at two consecutive time-marks are correlated but the arrivals occur in General Stream. Probability Generating functions for the number of phases are obtained under two different models each with assumption that the service phases at two consecutive time marks are (i) correlated and (ii) uncorrelated. For each case the mean queue lengths when the number of phases demanded by an arriving unit is one, are derived. Some particular cases are discussed.     

Waiting-time probabilities in the M/G/1 retrial queue

This paper deals with the difficult problem of calculating the waiting-time probabilities in the M / G /1 queue with retrials. The waiting-time distribution is approximated by a gamma distribution by matching the first two moments. Numerical results indicate that this approximation performs satisfactory for practical purposes.     

Queues with service speed adaptations

In this paper, we consider various queueing models in which the server can work at two different service speeds. The speed of the server depends on either the number of customers or the workload. Our main interest is in the model in which service speed adaptations can take place only at the arrival instants of an external Poisson observer. Using insightful probabilistic arguments, we give the structure of the steady‐state queue length and workload distributions in the various models. In addition, in case the service speed can only be adapted right after departure instants based on the number of customers, we provide explicit and intuitively appealing expressions for the steady‐state distribution of the number of customers present.     

On certain type of Queues in series

Summary This paper studies the steady-state behaviour of a queueing system consisting of three servers S₁, S₂ and S₃ . Two types of units each requiring two phases of service arrive and form two queues Q₁ and Q₂ in-front of the two servers S₁ and S₂, respectively, which attend to their first phase of service in order of arrival. On completion of the first phase the units discharged from these servers from a single queue Q₃ in-front of S₃ for the phase 2 service. The various stochastic processes namely, the interrarrival times and the service times, have been assumed to be distributed exponentially. We derive for this queueing process an expression for the mean queue length and some particular cases thereof.     

Prediction of the next hypercalcemia free period: application of random effect models with selection on first event

The length of repeated hypercalcemia free periods of patients with bone metastasis of breast cancer with at least one hypercalcemic event was modelled according to a generalized linear mixed model formulated in terms of transition probabilities and according to a latent variable model. In the former case the periods were assumed to be lognormally distributed with two variance components (patients and residue). In the latter case the conditional intensity given a patient was assumed to be the intensity of the Weibull distribution, while the random patient effect (frailty) was assumed to be drawn from a gamma distribution. In both cases the selection of only patients with at least one hypercalcemic event was taken into consideration. In both models the variance of the patient effect turned out to be negligible. For the second and later periods the Weibull appeared to fit better than the lognormal model. For the first period there was almost no information available.     

基于权值的自动化立体仓库中共享站台的调度策略研究

针对某厂成品高架库的输送线路结构和实际情况,对其中的共享站台,提出了一种依据排队队列的优先级别、队列的列长、前一服务任务的队列类型以及前方的堵塞状况等四个因素来综合确定队列权值的调度策略。     

A queueing problem with correlated arrivals and correlated phase-type service zur theorie des rangtests

Summary This paper studies the steady-state behaviour of a discrete-time, single-channel, first-come-first-served queueing problem wherein (i) the arrivals at two consecutive time-marks are correlated (ii) the service is accomplished in phases and (iii) the completion of phases at two consecutive time-marks are correlated. The probability generating function (p.g.f.) of the number of phases waiting and in service is obtained. Further, the p.g.f. of queue length is obtained for the case when each unit demands only one phase of service, and the mean queue length is derived therefrom. Finally, the p.g.f. and the mean queue length are discussed for the special cases, (i) r=0,R≠0, (ii) r≠0,R=0, (iii) r=0,R=0, (iv) r≠0,R=−I, (v) r=0,R=−I, (vi) r=−I,R≠0, (vii) r=−I,R=0, (viii) r=I,R≠0, (ix) r=I,R=0, (x) r≠0,R=I, (xi) r=0,R=I, where r andR are the respective coefficients of correlation between arrivals and completion of phases at two consecutive time-marks.     

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.     

Congestion in a city with a central bottleneck

We consider dynamic congestion in an urban setting where trip origins are spatially distributed. All travelers must pass through a downtown bottleneck in order to reach their destination in the CBD. Each traveler chooses departure time to maximize general concave scheduling utility. We find that, at equilibrium, travelers sort according to their distance to the destination; the queue is always unimodal regardless of the spatial distribution of trip origins. We construct a welfare maximizing tolling regime, which eliminates congestion. All travelers located beyond a critical distance from the CBD gain from tolling, even when toll revenues are not redistributed, while nearby travelers lose. We discuss our results in the context of acceptability of tolling policies.     

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。     

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。     

ALGORITHMIC METHODS FOR SINGLE SERVER SYSTEMS WITH REPEATED ATTEMPTS

In many practical situations customers applying for service and finding the server busy will not join a queue, but make a new attempt to enter service after some time. In this paper we study single server systems with repeated attempts both for infinite-source input and finite-source input where the service times are general and the reattempt times are exponential. Numerically stable recursion schemes are derived by which the time-average and customer-average steady-state probabilities can be effectively computed.     

Explaining differences in labour market transitions between panel and life-course data in West-Germany

Panel and life-course data are ideally suited to unravelling labour market dynamics, but their designs differ, with potential consequences for the estimated relationships. To gauge the extent to which these two data designs produce dissimilar transition rates and the causation thereof, we use the German Life History Study and the German Socio-Economic Panel. Life-course data in particular suffer from recall effects due to memory bias causing understated transition probabilities. Panel data suffer from seam effects due to spurious transitions between statuses recalled in activity calendars that generate heaps at particular time points and cause overstated transition probabilities. We combine the two datasets and estimate multilevel (multistate) discrete-time models for event history data to model transitions between labour market states taking these factors into account. Though we find much lower transition rates in the life-course study, confirming the results of Solga (Qual Quant 35:291–309, 2001) in this Journal for East-Germany, part of the difference can be explained by short spells recall bias. The estimated models on exit, re-entry and job mobility on the combined datasets show indeed a negative retrospective design effect. Another specification that includes the length of the recall period shows no significant decrease in the transition probabilities with increasing length, suggesting that the negative design effect is due to other design differences.     

Solving endogenous regime switching models

This paper solves rational expectations models in which structural parameters switch across multiple regimes according to state-dependent (endogenous) transition probabilities. Assuming small shocks and smooth transition probabilities, we apply a perturbation approach. We first provide for conditions under which a unique bounded equilibrium exists. We then compute first- and second-order approximations. In a new-Keynesian model with monetary policy switching, we document new effects of monetary policy switching when transition probabilities depend on inflation.     

On a certain type of priority queueing problem

This paper studies the transient behaviour of a queueing problem in which two type of units form queuesQ ₁ andQ ₂ before a single server. The units ofQ ₁ are considered first for service. As soon as there are no units ofQ ₁ in the system, a batch ofm units fromQ ₂ or the whole queue length shifts toQ ₁ and are served. Probability generating functions for the queue lengths for the two cases have been obtained.     

A mechanism for reducing small-business customer waiting-line dissatisfaction

This paper presents a technique whereby a small business (i.e. a one-cash register operation) can reduce customer waiting-line time dissatisfaction in the purchase stage of the consumer decision process. When the queue length reaches or exceeds critical value N^*, another employee is temporarily transferred to the role of ‘server assistant’ to increase the effective service rate; when the queue length eventually decreases to a second critical value N_*, the server assistant returns to primary duties. An optimal customer-reneging decision model is utilized to model the reneging character of the queue. Simulation experiments confirm key hypotheses concerning the behaviour of the queue and compare the effectiveness of a computed (N^*, N_*) policy with that of alternatives.