Optimal control of parallel server systems with many servers in heavy traffic

We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the many-server heavy traffic regime for parallel server systems when the service times are only server pool dependent and exponentially distributed. J.G. Dai’s research supported in part by National Science Foundation grants CMMI-0727400 and CNS-0718701, and by an IBM Faculty Award.     

Two fluid approximations for multi-server queues with abandonments

Insight is provided into a previously developed M/M/s/r+M(n) approximation for the M/GI/s/r+GI queueing model by establishing fluid and diffusion limits for the approximating model. Fluid approximations for the two models are compared in the many-server efficiency-driven (overloaded) regime. The two fluid approximations do not coincide, but they are close.     

Bayesian Analysis of Abandonment in Call Center Operations

In this paper, we consider the modeling and the inference of abandonment behavior in call centers. We present several time to event modeling strategies, develop Bayesian inference for posterior and predictive analyses, and discuss implications on call center staffing. Different family of distributions, piecewise time to abandonment models, and mixture models are introduced, and their posterior analysis with censored abandonment data is carried out using Markov chain Monte Carlo methods. We illustrate the implementation of the proposed models using real call center data, present additional insights that can be obtained from the Bayesian analysis, and discuss implications for different customer profiles. Copyright © 2012 John Wiley & Sons, Ltd.     

深水套管切割力学模型

针对深水套管切割力学模型单一、切割泵冲选择困难等问题, 利用长杆铣削模型, 建立了深水套管切割力学模型, 计算出钻柱切割扭矩和切割允许的最大泵冲, 得出了切割扭矩占井口驱动扭矩的比例与作业水深之间的关系, 对深水弃井作业中套管割断判断指标的形成具有指导意义. 结合南海某两口井套管切割的现场数据, 验证了模型的正确性, 其计算结果可以为深水弃井作业中合理的泵冲参数选择提供理论参考, 为深水弃井作业提供技术保证, 进一步提高切割效率, 具有很好的应用价值.     

An entry-exit model involving construction and abandonment periods

We analyze, using the optimal stopping theory, the entry-exit decision on a project, which takes time to be constructed and abandoned. We obtain the closed-form expressions of optimal start time of entry, optimal start time of exit, and the maximal expected present value of the project. In addition, we examine the effects of construction and abandonment periods on the optimal start times of entry and exit.     

Strong approximations for Markovian service networks

Inspired by service systems such as telephone call centers, we develop limit theorems for a large class of stochastic service network models. They are a special family of nonstationary Markov processes where parameters like arrival and service rates, routing topologies for the network, and the number of servers at a given node are all functions of time as well as the current state of the system. Included in our modeling framework are networks of M _t /M _t /n _t queues with abandonment and retrials. The asymptotic limiting regime that we explore for these networks has a natural interpretation of scaling up the number of servers in response to a similar scaling up of the arrival rate for the customers. The individual service rates, however, are not scaled. We employ the theory of strong approximations to obtain functional strong laws of large numbers and functional central limit theorems for these networks. This gives us a tractable set of network fluid and diffusion approximations. A common theme for service network models with features like many servers, priorities, or abandonment is “non-smooth” state dependence that has not been covered systematically by previous work. We prove our central limit theorems in the presence of this non-smoothness by using a new notion of derivative. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the probability of abandonment in queues with limited sojourn and waiting times

Consider the Geo/Geo/1 queue with impatient customers and let X reflect the patience distribution. We show that systems with a smaller patience distribution X in the convex-ordering sense give rise to fewer abandonments (due to impatience), irrespective of whether customers become patient when entering the service facility.