Workload Process,Waiting Times,and Sojourn Times in a Discrete Time MMAP[K]/SM[K]/1/FCFS Queue

Abstract

In this paper, we study the total workload process and waiting times in a queueing system with multiple types of customers and a first-come-first-served service discipline. An M/G/1 type Markov chain, which is closely related to the total workload in the queueing system, is constructed. A method is developed for computing the steady state distribution of that Markov chain. Using that steady state distribution, the distributions of total workload, batch waiting times, and waiting times of individual types of customers are obtained. Compared to the GI/M/1 and QBD approaches for waiting times and sojourn times in discrete time queues, the dimension of the matrix blocks involved in the M/G/1 approach can be significantly smaller.     

A Markov regime‐switching model for crude‐oil markets: Comparison of composite likelihood and full likelihood

We use the two‐state Markov regime‐switching model to explain the behaviour of the WTI crude‐oil spot prices from January 1986 to February 2012. We investigated the use of methods based on the composite likelihood and the full likelihood. We found that the composite‐likelihood approach can better capture the general structural changes in world oil prices. The two‐state Markov regime‐switching model based on the composite‐likelihood approach closely depicts the cycles of the two postulated states: fall and rise. These two states persist for on average 8 and 15 months, which matches the observed cycles during the period. According to the fitted model, drops in oil prices are more volatile than rises. We believe that this information can be useful for financial officers working in related areas. The model based on the full‐likelihood approach was less satisfactory. We attribute its failure to the fact that the two‐state Markov regime‐switching model is too rigid and overly simplistic. In comparison, the composite likelihood requires only that the model correctly specifies the joint distribution of two adjacent price changes. Thus, model violations in other areas do not invalidate the results. The Canadian Journal of Statistics 41: 353–367; 2013 © 2013 Statistical Society of Canada     

Robust location estimation with missing data

In a missing data setting, we have a sample in which a vector of explanatory variables ${\bf x}_i$ is observed for every subject i, while scalar responses $y_i$ are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L‐functionals and M‐functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived. The proofs of the theorems are presented in Supplementary Material available online. The Canadian Journal of Statistics 41: 111–132; 2013 © 2012 Statistical Society of Canada     

Bounded influence estimation for regression and scale

Bednarski and Müller [Optimal bounded influence regression and scale M-estimators in the context of experimental design, Statistics 35 (2001), pp. 349–369] introduced a class of bounded influence M estimates for the simultaneous estimation of regression and scale in the linear model with normal errors by solving the corresponding normal location and scale problem at each design point. This limits the proposal to regressor distributions with finite support. Based on their approach, we propose a slightly extended class of M estimates that is not restricted to finite support and is numerically easier to handle. Moreover, we employ the even more general class of asymptotically linear (AL) estimators which, in addition, is not restricted to normal errors. The superiority of AL estimates is demonstrated by numerical comparisons of the maximum asymptotic mean-squared error over infinitesimal contamination neighbourhoods.     

论洛杉矶文学先锋创作：詹姆斯·凯恩和 霍勒斯·麦科伊

凯恩和麦科伊被称作洛杉矶文学开拓先锋,他们的创作存在许多相似之处。首先,他们有着相似的城市经历。其次,他们作品中的主人公都没有归属感,都是无根之人。 他们背离自己的生命之源土地,被蛊惑来到这片精神贫瘠之地寻找希望和梦想。在这片梦幻的空间,人类基本的关系遭受了巨大的冲击以致最终崩溃。这两位作家赋予洛杉矶一种 全新的文学身份。     

第五次跨国并购浪潮的特点及动因分析

第五次跨国并购浪潮呈现出并购金额巨大、增长速度迅猛、发达国家在并购出售额和购买额中居主导地位、以水平及善意并购方式为主要特点。推动其形成和发展的动因,既有经济全球化、新科技革命发展等宏观原因,也有谋求经营协同、财务协同、获取并购战略价值、操纵市场等微观原因。面对此浪潮,我国应积极更新观念,加强立法,改善环境;以顺应并利用跨国并购为我国经济结构调整和经济发展服务。     

INSIGHTS ON SERVICE SYSTEM DESIGN FROM A NORMAL APPROXIMATION TO ERLANG'S DELAY FORMULA

We show how a simple normal approximation to Erlang's delay formula can be used to analyze capacity and staffing problems in service systems that can be modeled as M/M/s queues. The numbers of servers, s, needed in an M/M/s queueing system to assure a probability of delay of, at most, p can be well approximated by s ≅ p + z_***I-p+, where z_1-p, is the (1 - p)th percentile of the standard normal distribution and ρ, the presented load on the system, is the ratio of Λ, the customer arrival rate, to μ, the service rate. We examine the accuracy of this approximation over a set of parameters typical of service operations ranging from police patrol, through telemarketing to automatic teller machines, and we demonstrate that it tends to slightly underestimate the number of servers actually needed to hit the delay probability target—adding one server to the number suggested by the above formula typically gives the exact result. More importantly, the structure of the approximation promotes operational insight by explicitly linking the number of servers with server utilization and the customer service level. Using a scenario based on an actual teleservicing operation, we show how operations managers and designers can quickly obtain insights about the trade-offs between system size, system utilization and customer service. We argue that this little used approach deserves a prominent role in the operations analyst's and operations manager's toolbags.     

The influence of tax authorities on the employment of tax practitioners: Empirical evidence from a survey and interview study

Tax practitioners play a crucial role in the degree of taxpayers’ compliance – a role that has increased as tax systems worldwide have become more complex. However, little is known about tax authorities’ impact on taxpayers’ decisions to employ tax practitioners. Based on earlier research on motivations to employ a tax practitioner and the extended slippery slope framework of tax compliance, we conducted two studies which provide some answers. A survey study – comprising a representative sample of 500 Austrian self-employed taxpayers – revealed that financial gain is not the most important reason to employ a tax practitioner but instead the motivation to avoid problems with the tax authorities. Related to that, we also find that taxpayers’ perception of tax authorities wielding coercive power motivates them to employ tax practitioners. In the interview study with 33 self-employed taxpayers and 30 tax auditors, taxpayers indicated that they sought to avoid contact with tax officers by employing tax practitioners. This finding was supported by tax officers who reported preferring interaction with tax practitioners over direct contact with taxpayers. The two studies point to the complex relationship between taxpayers, tax authorities and tax practitioners, and allow the drawing of theoretical and practical implications.