On a dual queueing system with preemptive priority service discipline

In this paper, we use matrix–analytic methods to construct a novel queueing model called the dual queue. The dual queue has the additional feature of a priority scheme to assist in congestion control. Detailed structure of the infinitesimal generator matrix is derived and used in the solution process. Using a computational algorithm, which utilises a combination of iterative and elementary matrix techniques, the steady state solution is obtained for all queues with a finite buffer. Finally, we present numerical examples to illustrate the algorithm.     

Waiting time analysis for a tandem queue with correlated service

The effect on overall waiting time including service is investigated when there is positive correlation between the first and second stage service times in a two stage tandem system. The importance of understage waiting (or “buffer”) space is underlined. The analysis is an application of the authors' work reported in [1].     

Waiting time distributions in the accumulating priority queue

We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right.     

Waiting time and queue length analysis of Markov-modulated fluid priority queues

Queueing Systems - This paper considers a multi-type fluid queue with priority service. The input fluid rates are modulated by a Markov chain, which is common for all fluid types. The service rate...     

A preemptive repeat priority queue with resampling: Performance analysis

In this paper, we analyze a discrete-time preemptive repeat priority queue with resampling. High-priority packets have preemptive repeat priority, and interrupted low-priority packets are subjected to independent retransmission attempts. Both classes contain packets with generally distributed transmission times. We show that the use of generating functions is beneficial for analyzing the system contents and packet delay of both classes. The influence of the priority scheduling on the performance measures is illustrated by some numerical examples. This work has been supported by the Interuniversity Attraction Poles Programme–Belgian Science Policy.     

对一类等待空间有限的抢占优先权排队的分析

讨论M/M/1抢占优先权排队模型, 且假设低优先权顾客的等待空间有限. 该模型可以用有限位相拟生灭过程来描述. 由矩阵解析方法, 对该拟生灭过程进行了分析, 并得到排队模型平稳队长的计算公式, 最后还用数值 结果说明了方法的有效性.     

Performance analysis of a GI-Geo-1 buffer with a preemptive resume priority scheduling discipline

In this paper, we analyze a discrete-time GI-Geo-1 preemptive resume priority queue. We consider two classes of packets which have to be served, where one class has preemptive resume priority over the other. We show that the use of generating functions is beneficial for analyzing the system contents and packet delay of both classes. Moments and (approximate) tail probabilities of system contents and packet delay are calculated. The influence of the priority scheduling is shown by some numerical examples.     

Exact tail asymptotics for a discrete-time preemptive priority queue

In this paper, we consider a discrete-time preemptive priority queue with different service completion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers’ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuoustime model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.     

Optimal threshold policies in a two-class preemptive priority queue with admission and termination control

We consider a two-class 1 preemptive priority queue in which there are two essential, on-line decisions that have to be taken. The first is the decision to either accept or reject new type-1 or type-2 jobs. The second is the decision to abort jobs, i.e., to remove any type-1 or type-2 jobs from the system. We show that there exist optimal threshold policies for these two types of, decisions.     

Strong approximations for a Kumar-Seidman network under a priority service discipline

In this paper,we derive the strong approximations for a four-class two station multi-class queuing network（Kumar-Seidman network） under a priority service discipline.Within a group,jobs are served in the order of arrival,that is,a first-in-first-out disciple,and among groups,jobs are served under a pre-emptiveresume priority disciple.We show that if the input data（i.e.,the arrival and service processe） satisfy an approximation（such as the functional law-of-iterated logarithm approximation or the strong approximation）,the output data（the departure processes） and the performance measures（such as the queue length,the work load and the sojourn time process） satisfy a similar approximation.     

On the fluid approximation for a multiclass queue under non-preemptive SBP service discipline

A multi-class single server queue under non-preemptive static buffer priority (SBP) service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.     

Asymptotics of waiting time distributions in the accumulating priority queue

Queueing Systems - We analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by...     

Delay analysis of discrete-time priority queue with structured inputs

This paper investigates a discrete-time priority queue with multi-class customers. Applying a delay-cycle analysis, we explicitly derive the probability generating function of the waiting time for an individual class in a geometric batch input queue under preemptive-resume and head-of-the-line priority rules. The conservation law and waiting time characterization for a general class of discrete-time queues are also presented. The results in this paper cover several previous results as special cases.     

A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers

In this paper we consider an unreliable single server retrial queue accepting two types of customers, with negative arrivals, preemptive resume priorities and vacations. A distinguishing feature of the model is that the rates of the Poisson arrival process depends on the server state. For this model we investigate the stability conditions and the joint queue length distribution in steady state. We also prove that our model satisfies the stochastic decomposition property. Transient, as well as steady state solutions for reliability measures are obtained. Finally, numerical results demonstrate the typical features of the model under consideration.     

Time-dependent analysis of a queue with batch arrivals andn levels of nonpreemptive priority

A queueing system with batch arrivals andn classes of customers with nonpreemptive priorities between them is considered. Each batch arrives according to the Poisson distribution and contains customers of all classes while the service times follow arbitrary distributions with different probability density functions for each class. For such a model the system states probabilities both in the transient and in the steady state are analysed and also expressions for the Laplace transforms of the busy period densities for each class and for the general busy period are obtained.