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.     

The M/M\1 queue in a heavy-tailed random environment

We consider an M / M /1 queue with the special feature that the speed of the server alternates between two constant values s_L and s_H > s_L . The high-speed periods are exponentially distributed, and the low-speed periods have a regularly varying distribution. We obtain explicit asymptotics for the tail of the workload distribution. The two cases in which the offered traffic load is smaller respectively larger than the low service speed are shown to result in completely different asymptotics.     

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.     

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.     

The M/G/∞ Queueing Model for Optimistic Concurrency Control

The M / G /∞ queue with Optimistic Concurrency Control (OCC) is a model for a special form of parallel transaction processing in a real-time database. Transactions arrive according to a Poisson process and require some generally distributed execution time. One of the differences with ordinary multi- and infinite-server queueing models is that under OCC the successful completion of one transaction may immediately cause the failure of one or more of the other transactions. This happens if the completing transaction has overwritten a data-item that is in use by another transaction in progress. As soon as this failure is detected the failed transaction is restarted. So the total service time of a transaction consists of its final successful run and the time spent on unsuccessful runs.
In this study we develop an approximation for the distribution of the total service time, and test the approximation against simulation. Although in practice the number of servers is never unlimited, this study provides valuable insight in the asymptotics with respect to the number of servers. The approximation clearly demonstrates the very limited performance gain from an increase of the number of servers.     

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.     

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.     

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.     

Recent sojourn time results for multilevel processor-sharing scheduling disciplines

Multilevel Processor-Sharing (MLPS) disciplines refer to a family of age-based scheduling disciplines introduced decades ago. A time-discretized version of an MLPS discipline is applied in the scheduler of the traditional UNIX operating system. In recent years, MLPS disciplines have been used to study the way that packet level scheduling mechanisms impact the performance perceived at the flow level in the Internet. Inspired by this latter application, many new sojourn time results have been discovered for these disciplines in the context of the M/G/1 queue. The aim of this paper was to give a consistent overview of these new results. In addition, it points out some intriguing open problems for further research.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

Upper and lower bounds on infinite time ruin probabilities in case of constraints on claim size distributions

Probabilities of ruin (or non-ruin) are solutions of differential or integro-differential equations. Solving these kinds of equations analytically and/or numerically causes a lot of mathematical difficulties. In addition there exists a practical problem of determining, estimating or guessing the distribution of the risk. A realistic way to deal with this problem consists in deriving upper and lower bounds for the ruin probability in case of incomplete information on the distribution F. The present contribution is inspired by and generalises a result of G. Taylor who uses the concept of ordering of risks to order ruin probabilities. We show how some of the results obtained by F. De Vylder for deriving sharp bounds on the stop-loss premium in case of incomplete information can be applied to the evaluation of practical bounds on infinite time ruin probabilities.     

On a generalised stirling distribution

In this note we consider a generalisation of theStirling noumber of the second kind. The distribution of the sum ofn independent zero-truncated Poisson variables, which can be expressed in terms of such a gneralised number, may be called horizontally generalised Stirling distribution of the second kind. A recurrence relation for the probability function of this distribution, which will be useful for tabulation purposes, is given. The distribution function is obtained in terms of a linear combination of incomplete gamma functions.     

基于双层规划模型的冷链物流网络多目标优化

针对冷链物流时效性强这一特性,应用软时间窗反映客户满意度,并结合T.T.T理论换算货损成本。在考虑满足客户时间窗的条件下,寻找配送中心建设及操作成本、车辆成本、惩罚成本及货损成本所构成的总成本最小时的最优配送方案,建立冷链物流配送选址及路径优化的双层规划模型,并将改进的遗传算法运用到该模型中,借助Matlab软件对具体实例进行求解,得到最优结果,为冷链物流网络多目标优化问题提供理论依据。     

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。     

数据分布诊断对排队模型优化影响——基于兰州市某油库排队问题数据

对甘肃省兰州市某油库真实排队数据进行分布诊断,发现用M/G／C/∞排队模型计算出来的平均队长和平均等待时间比M／M／C／∞排队模型减少了一半．应根据数据分布诊断结果科学选择排队模型。     

A consistent nonparametric test for nonlinear causality—Specification in time series regression

Since the pioneering work by Granger (1969), many authors have proposed tests of causality between economic time series. Most of them are concerned only with “linear causality in mean”, or if a series linearly affects the (conditional) mean of the other series. It is no doubt of primary interest, but dependence between series may be nonlinear, and/or not only through the conditional mean. Indeed conditional heteroskedastic models are widely studied recently. The purpose of this paper is to propose a nonparametric test for possibly nonlinear causality. Taking into account that dependence in higher order moments are becoming an important issue especially in financial time series, we also consider a test for causality up to the Kth conditional moment. Statistically, we can also view this test as a nonparametric omitted variable test in time series regression. A desirable property of the test is that it has nontrivial power against T^1/2-local alternatives, where T is the sample size. Also, we can form a test statistic accordingly if we have some knowledge on the alternative hypothesis. Furthermore, we show that the test statistic includes most of the omitted variable test statistics as special cases asymptotically. The null asymptotic distribution is not normal, but we can easily calculate the critical regions by simulation. Monte Carlo experiments show that the proposed test has good size and power properties.     

Multivariate t and beta distributions associated with the multivariate F distribution

Relationships between F, skew t and beta distributions in the univariate case are in this paper extended in a natural way to the multivariate case. The result is two new distributions: a multivariate t/skew t distribution (on ℜ^m) and a multivariate beta distribution (on (0,1)^m). A special case of the former distribution is a new multivariate symmetric t distribution. The new distributions have a natural relationship to the standard multivariate F distribution (on (ℜ⁺)^m) and many of their properties run in parallel. We look at: joint distributions, mathematically and graphically; marginal and conditional distributions; moments; correlations; local dependence; and some limiting cases. Received: March 2001     

Logistics optimization through a social approach for food distribution

The management of supply chains is becoming more important in economic and social environments. Currently, the social sustainability is a factor that must be considered to design governmental strategies and policies. The objective of this research paper was to show, with a case study an approach to optimize distribution and delivery logistics of food in a social assistance program of school breakfast using mathematical models that include transportation distance, optimal locations, and vehicle routing through different clusters. By using qualitative variables like poverty levels, food insecurity and social exclusion, different clustering methods are proposed with the purpose of identifying the common characteristics in the studied population; and at the same time, reducing the distribution complexity. The results show an efficient approach to design a supply chain that includes economic and social factors. The new model developed in this paper can be used to plan social assistance governmental programs, to identify the specific needs and characteristics of the beneficiaries, minimizing the total cost of the distribution network logistics when delivering food for school meals.     

Approximating the distribution of Greenwood's statistic

Statistics based on uniform spacings are often used in goodness-of-fit problems. In this paper special attention is paid to the distribution of Greenwood's statistic. Although its asymptotic distribution is normal, the normal approximation is extremely bad, even for large sample sizes. It is shown that the Edge-worth expansion yields a considerably better approximation for the distribution of this statistic. Furthermore, an overview is given of the higher order asympto-tics for the sum of functions of uniform spacings, of which Greenwood's statistic is a special case.     

供应链视角下餐饮O2O模式的配送路径优化

O2O最后一公里配送往往需要综合考虑时间和成本的关系,研究平台对订单的分配和路径优化对提升O2O供应链的整体效率和产业链升级具有十分重要的意义。从餐饮商家和O2O平台两个主要参与者出发对物流配送系统进行研究,提出了适合于O2O餐饮供应链的配送网络,并考虑道路阻塞、最大里程数等约束,搭建了上层模型最短时间、下层模型最低成本的双层规划模型,进而通过NSGA-Ⅱ算法求得可行解,最后验证了算法的可行性,为进一步研究O2O配送提供了新的解决思路。