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.     

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.     

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.     

基于排队论的集成电路出货检验研究

通过应用排队论（M/M/s）,对某集成电路生产线出货检验工作进行研究,分析和评价产品在出货检验站点排队与滞留状况及其原因,为节约产品排队时间,提高出货检验站点的质量、效率,以及平衡产品排队时间与出货检验站点效率之间的关系提供一种较有效的管理决策手段。     

A Simple Proof of the Equivalence of the Limiting Distributions of the Continuous-Time and the Embedded Process of the Queue Size in the M/G/1 Queue*

This paper presents an extremely simple proof of the known remarkable fact that for the M/G/1 queue the continuous-time process describing the number of customers in the system has the same limiting distribution as the embedded process describing the number of customers in the system just after service completion epochs.     

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。     

Condorcet efficiency of positional voting rules with single-peaked preferences

Consider a three-alternative election with n voters and assume that preferences are single-peaked. LetC(λ,n) be the Condorcet efficiency of the rule that assigns 1,λ and 0 points (respectively) to each first, second and third place vote. An exact representation is obtained forC(λ,∞). This relation shows that Borda rule (λ=1/2) is not the most efficient rule. In addition to this result, exact closed form relations are provided forC(0,n),C(1/2,n) andC(1,n). All these relations are obtained by assuming that every admissible configuration of preferences is equally likely to occur. This research was supported in part by the Swedish Insitute     

On the generalized Poisson distribution

We use Euler's difference lemma to prove that, for θ > 0 and 0 ≤λ < 1, the function P _n defined on the non-negative integers by
P _n (θ, λ) = [θ(θ + n λ) ^{n −1}/ n !]e^{− n λ−θ}
defines a probability distribution, known as the Generalized Poisson Distribution.     

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.     

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.     

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.     

研发投资、舞弊风险与审计费用

以2007—2018年中国A股市场研发投资额大于零的非金融类上市公司为研究对象,实证研究研发投资强度对财务舞弊风险和审计费用的影响以及CPA审计治理效果。研究结果表明：研发投资强度与财务舞弊风险和审计费用均正相关,并且财务舞弊风险在研发投资强度对审计费用的影响中存在部分中介效应。使用工具变量法进行内生性分析发现,研发投资强度在前三种度量方式（研发投入额÷总资产、研发投入额÷净资产、研发投入额÷公司员工数）下具有很强的外生性,而在第四种度量方式（研发投入额÷营业收入）下是内生的。对审计治理效果进行分析发现,虽然高审计收费保证了CPA较高的执业努力程度,但与审计合谋正相关的异常审计费用的存在使得CPA审计治理效果并不佳,并且对研发投资强度大的客户、财务舞弊风险高的客户和高新技术企业收取更高的异常审计费用通常与更高的审计合谋倾向有关。     

Efficiency evaluation of China's high-tech industry with a multi-activity network data envelopment analysis approach

This paper employs a Russell multi-activity network DEA model and divides the overall innovation process into the upstream Research and Development (R&D) process and the downstream commercialization process to appraise the innovation performance of China's high-tech industries from 2009 to 2013. This model can deal with the problems of intermediates, shared inputs and slack-based measure in a unified framework, and the result can provide policy makers with process-specific information on how to improve the innovation performance of China's high-tech industries. The main findings are presented as follows. First, the overall efficiency of China's high-tech industries still remains at a low level, which has its roots mainly in commercialization inefficiencies other than R&D inefficiencies. Second, for most provinces, their R&D efficiencies do not match up with their commercialization efficiencies. Finally, the innovative activities of China's high-tech industries should be driven by the market demand -oriented for the improvement of innovation efficiency.     

中国行业层面研究与试验发展资本存量核算

研究目标：测算中国八大行业门类研究与试验发展（Research and Development,R&D）资本存量。研究方法：基于SNA2008的GDP核算框架,厘清R&D支出的资本化核算框架;再利用美国BEA方法测算R&D资本存量。研究发现：1990~2015年,中国R&D资本存量不到美国R&D资本存量的1/4;然而,自1994年后,中国R&D资本存量年均增长率达24.79%,而美国仅为4.86%,中美两国R&D资本存量差距呈逐渐缩小趋势;制造业R&D资本存量占全国R&D资本存量的比例呈上升趋势,从1990年的17.41%增长到2015年的68.08%,这与中国加快制造业转型升级的事实相符。研究创新：给出完整的R&D支出资本化核算过程,首次测算中国八大行业门类的R&D资本存量。研究价值：为分析技术进步对经济增长的影响提供了行业层面R&D投资和资本存量数据序列。     

Learning from R&D outsourcing vs. learning by R&D outsourcing

We analyze how research and development (R&D) outsourcing influences product innovation. We propose a separation between learning from R&D outsourcing, whereby the firm improves its ability to innovate by using outsourced R&D directly in new products, from learning by R&D outsourcing, whereby the firm indirectly uses outsourced R&D by integrating it with internal R&D to create new products. Building on the knowledge-based view, we argue that learning from R&D outsourcing is likely to have an inverse U-shaped relationship with product innovation, because the initial benefits of using outsourced component R&D knowledge to innovate products is eventually outweighed by the hollowing out of the firm's ability to innovate. In contrast, we propose that learning by R&D outsourcing is likely to have a U-shaped relationship with product innovation, because the initial challenges of integrating internal and external R&D are eventually overcome, resulting in more innovations. Finally, we distinguish between domestic and foreign R&D outsourcing and propose a liability of foreignness in R&D outsourcing as it has a lower impact on new products than domestic R&D outsourcing. The empirical analysis shows that outsourced R&D has an inverted U-shaped relationship with the number of new products, while the interaction between outsourced R&D and internal R&D has a U-shaped relationship with the number of new products. It also shows that domestic outsourced R&D has a higher positive impact on the number of new products than foreign outsourced R&D.     

The impact of cluster connectedness on firm innovation: R&D effort and outcomes in the textile industry

Recent research into the clustering effect on firms has moved away from a simplistic view to a more complex approach. More realistic and complex causal relationships are now considered when analysing these territorial networks. Specifically, this paper attempts to analyse how cluster connectedness moderates the relationship of a firm's innovation effort and the results obtained from this effort. We want to question the commonly accepted direct and positive impact of R&D effort, and moreover, we suggest the existence of a saturation effect and that the level of cluster's inter-connectedness in the cluster moderates this effect. We have developed our empirical study focusing on the Spanish textile industrial cluster. This is a complex manufacturing industry that uses relatively low-technology manufacturing and R&D. Our findings suggest that the degree to which a firm is involved with, or connected to, other firms in the cluster can moderate the effect of the R&D effort on its innovation results. More generally, we aim to contribute to the discussion on the degree to which firms should be involved in the cluster network in order to operate efficiently and gain the maximum competitive advantages. Our findings have implications both in recent cluster and network literature as well for institutional policy.     

Statistics for the contact process

A d -dimensional contact process is a simplified model for the spread of an infection on the lattice Z ^d . At any given time t ≥ 0 , certain sites x ∈ Z ^d are infected while the remaining once are healthy. Infected sites recover at constant rate 1, while healthy sites are infected at a rate proportional to the number of infected neighboring sites. The model is parametrized by the proportionality constant λ. If λ is sufficiently small, infection dies out (subcritical process), whereas if λ is sufficiently large infection tends to be permanent (supercritical process).
In this paper we study the estimation problem for the parameter λ of the supercritical contact process starting with a single infected site at the origin. Based on an observation of this process at a single time t , we obtain an estimator for the parameter λ which is consistent and asymptotically normal as t →∞     

How to optimize the allocation of research resources? An empirical study based on output and substitution elasticities of universities in Chinese provincial level

Although significant progress has been made in China's basic research in recent years, there remains a wide gap between research in China and that from developed countries. How to optimize the allocative efficiency of research resources is of great importance for increasing research output. In this paper, using the fixed effect stochastic frontier model based on the translog production function, we estimate output and substitution elasticities of research and development (R&D) inputs at universities in China's provincial level during 2009–2016. We find that the R&D technical efficiency of China's universities, after a rapid growth, has tended to become relatively stable. Improvements of internationalization degree and exogenous R&D capabilities are conducive to promoting R&D technical efficiency, whereas expenditures from government grants inhibit the promotion of R&D technical efficiency; the effects of R&D capital deepening and internet penetration are not evident. The output elasticity of R&D capital is much higher than that of R&D personnel, suggesting that R&D capital is the main driving force of research output. The substitution elasticity between R&D capital and personnel has experienced a change from substitution to complementary since 2014. To realize sustained growth of research output, we should increase R&D input with positive output elasticity or reduce R&D input with negative output elasticity, making the necessary trade-offs according to the substitution relationship between the two R&D inputs.     

Forecasting in cointegrated systems

We consider the implications for forecast accuracy of imposing unit roots and cointegrating restrictions in linear systems of I(1) variables in levels, differences, and cointegrated combinations. Asymptotic formulae are obtained for multi-step forecast error variances for each representation. Alternative measures of forecast accuracy are discussed. Finite sample behaviour in a bivariate model is studied by Monte Carlo using control variables. We also analyse the interaction between unit roots and cointegrating restrictions and intercepts in the DGP. Some of the issues are illustrated with an empirical example of forecasting the demand for M1 in the UK.     

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。