Point and interval estimation of decomposition error in discrete-time open tandem queues

We analyze the approximation quality of the discrete-time decomposition approach, compared to simulation, and with respect to the expected value and the 95th-percentile of waiting time. For both performance measures, we use OLS regression models to compute point estimates, and quantile regression models to compute interval estimates of decomposition error. The ANOVA reveal major influencing factors on decomposition error while the regression models are demonstrated to provide accurate forecasts and precise confidence intervals for decomposition error.     

The M/G/1 FIFO Queue with Several Customer Classes

In this note we present short derivations of the joint queue length distribution in the M/G/1 queue with several classes of customers and FIFO service discipline.     

M/G/1非空竭服务休假排队系统的平衡条件分析

讨论了一般非空竭服务M/G/1型休假排队系统的嵌入更新过程常返的条件,为稳态队长与等待时间的随机分解奠定理论基础.并且在独立休假策略下进一步简化Fuhrman与Cooper(1985)休假排队系统的随机分解的条件,并得到完整的随机分解结构.     

具有可利用服务员的M/G/1排队模型

本文考虑了具有可利用服务员的M／G／1有有限容量的排队模型．当工作量超过k(k是常数或者随机变量),可利用服务员参与工作,一直到工作量少于或等于k．可利用服务员的速率依赖于目前工作量．应用Level-crossing方法,获得了工作量的平稳分布．应用Kolmogorov向后微分方程方法,构造更新方程以获得忙期的Laplace变换．     

空竭服务Geom/G/1休假模型

本文用嵌入Markov链的方法证明了Geom／G／1的边界状态变体模型的随机分解定理，同时又证明两种具体模型的结果．     

A consistent diffusion approximation for finite-capacity multiserver queues

A diffusion approximation is developed for general multiserver queues with finite waiting spaces, which are typical models of manufacturing systems as well as computer and communication systems. The model is the standard GI/G/s/s + r queue with s identical servers in parallel, r extra waiting spaces, and the first-come, first-served discipline. The main focus is on the steady-state distribution of the number of customers in the system. The process of the number of customers is approximated by a time-homogeneous diffusion process on a closed interval in the nonnegative real line. A conservation law plus some heuristics standing on solid theoretical ground generate approximation formulas for the steady-state distribution and other congestion measures. These formulas are consistent with the exact results for the M/G/s/s and M/M/s/s + r queues. The accuracy of approximations for principal congestion measures are numerically examined for some particular cases.     

Review of Some Functionals of Compound Poisson Processes and Related Stopping Times

The paper reviews recent results of D. Perry, W. Stadje and S. Zacks, on functionals of stopping times and the associated compound Poisson process with lower and upper linear boundaries. In particular, formulae of these functionals are explicitly developed for the total expected discounted cost of discarded service in an M/G/1 queue with restricted accessibility; for the expected total discounted waiting cost in an M/G/1 restricted queue; for the shortage, holding and clearing costs in an inventory system with continuous input; for the risk in sequential estimation and for the transform of the busy period when the upper boundary is random.      

Queueing and Fluid Analysis of Partial Message Discarding Policy

We consider a stream of packets that arrive at a queue with a finite buffer. A group of consecutive packets constitutes a frame. We assume that when an arriving packet finds the queue full, not only is the packet lost but also the future packets that belong to the same frame will be rejected. The first part of the paper deals with a detailed packet level queueing model; we obtain exact expressions for the stationary queue length distribution and the goodput ratio (i.e. the fraction of arriving frames that experience no losses). The second part deals with a fluid model and the fluid analysis leads to simple closed form expressions for the stationary workload process and the fluid goodput ratio.     

Moment inequalities for the discrete-time bulk service queue

For the discrete-time bulk service queueing model, the mean and variance of the steady-state queue length can be expressed in terms of moments of the arrival distribution and series of the zeros of a characteristic equation. In this paper we investigate the behaviour of these series. In particular, we derive bounds on the series, from which bounds on the mean and variance of the queue length follow. We pay considerable attention to the case in which the arrivals follow a Poisson distribution. For this case, additional properties of the series are proved leading to even sharper bounds. The Poisson case serves as a pilot study for a broader range of distributions.     

Performance analysis of discrete-time queue GI/G/1 with negative arrivals

In this paper, we consider a discrete-time GI/G/1 queueing model with negative arrivals. By deriving the probability generating function of actual service time of ordinary customers, we reduced the analysis to an equivalent discrete-time GI/G/1 queueing model without negative arrival, and obtained the probability generating function of buffer contents and random customer delay.