VIRTUAL WAITING TIMES IN PRIORITY-M/G/1 QUEUES WITH VACARIONS

In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the six models analysed, the Laplace-Stieltjes transform of the virtual waiting time Wk(t) at time t of class k is derived by the method of collective marks. A sufficient condition for , where U has the standard normal distribution, is also given.

Stochastic Model for Multiple Classes and Subclasses Simple Documents Processing

The issue of document management has been raised for a long time, especially with the appearance of office automation in the 1980s, which led to dematerialization and Electronic Document Management (EDM). In the same period, workflow management has experienced significant development, but has become more focused on the industry. However, it seems to us that document workflows have not had the same interest for the scientific community. But nowadays, the emergence and supremacy of the Internet in electronic exchanges are leading to a massive dematerialization of documents;which requires a conceptual reconsideration of the organizational framework for the processing of said documents in both public and private administrations. This problem seems open to us and deserves the interest of the scientific community. Indeed, EDM has mainly focused on the storage (referencing) and circulation of documents (traceability). It paid little attention to the overall behavior of the system in processing documents. The purpose of our researches is to model document processing systems. In the previous works, we proposed a general model and its specialization in the case of small documents (any document processed by a single person at a time during its processing life cycle), which represent 70% of documents processed by administrations, according to our study. In this contribution, we extend the model for processing small documents to the case where they are managed in a system comprising document classes organized in subclasses;which is the case for most administrations. We have thus observed that this model is a Markovian ML×K/ML×K/1 queues network. We have analyzed the constraints of this model and deduced certain characteristics and metrics. In fine, the ultimate objective of our work is to design a document workflow management system, integrating a component of global behavior prediction.

Using a priority queuing approach to improve emergency department performance

Emergency department over-crowding has been a growing problem throughout the world.This paper presents a practical approach to estimate the waiting times for multi-class patients and apply the approach to reduce the waiting time for high priority patients.Patient flows with different levels of acuity are formulated based on the priority queue models.It derives explicit expressions of the wait time for the Markov queue and uses the concept of isomorphism to approximate the wait time in the general queue.Numerical results with simulation experiments are reported to display the accuracy of the approach.A case study from an emergency department indicates that the proposed approach can efficiently prioritize patient flows in decreasing waiting times.The queuing models have two features.First,the approximation applies to the general priority queues and reduces to the exact results of the Markov priority queue.Second,the models requires no iterative algorithm.