An investigation and historical overview of the G/M and M/G queueing processes

We present a historical and theoretical overview of the more complicated and less used G/M and M/G queueing processes, which allow for non-specific arrival and service time distributions. Such a model provides a more general setting for model fitting of real data for which the Markov property may not hold.Department of Statistics and SARChI at the University of Pretoriahttp://www.sastat.org.za/journal.htmam201

On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form

Bulk-arrival queues with single servers that provide bulk service are widespread in the real world, e.g., elevators in buildings, people-movers in amusement parks, air-cargo delivery planes, and automated guided vehicles. Much of the literature on this topic focusses on the development of the theory for waiting time and number in such queues. We develop the theory for the number stranded, i.e., the number of customers left behind after each service, in queues of the M/G/1 form, where there is single server, the arrival process is Poisson, the service is of a bulk nature, and the service time is a random variable. For the homogenous Poisson case, in our model the service time can have any given distribution. For the non-homogenous Poisson arrivals, due to a technicality, we assume that the service time is a discrete random variable. Our analysis is not only useful for performance analysis of bulk queues but also in designing server capacity when the aim is to reduce the frequency of stranding. Past attempts in the literature to study this problem have been hindered by the use of Laplace transforms, which pose severe numerical difficulties. Our approach is based on using a discrete-time Markov chain, which bypasses the need for Laplace transforms and is numerically tractable. We perform an extensive numerical analysis of our models to demonstrate their usefulness. To the best of our knowledge, this is the first attempt in the literature to study this problem in a comprehensive manner providing numerical solutions.Queueing Bulk queues Downside risk

Performance analysis of time-dependent queueing systems: survey and classification

Many queueing systems are subject to time-dependent changes in system parameters, such as the arrival rate or number of servers. Examples include time-dependent call volumes and agents at inbound call centers, time-varying air traffic at airports, time-dependent truck arrival rates at seaports, and cyclic message volumes in computer systems.There are several approaches for the performance analysis of queueing systems with deterministic parameter changes over time. In this survey, we develop a classification scheme that groups these approaches according to their underlying key ideas into (i) numerical and analytical solutions,(ii)approaches based on models with piecewise constant parameters, and (iii) approaches based on mod-ified system characteristics. Additionally, we identify links between the different approaches and provide a survey of applications that are categorized into service, road and air traffic, and IT systems

Development of a model for the attention of settlement in a bank branchEvent: Office Unicentro Bank Caja Social

132 Páginas.Este proyecto de investigación busca desarrollar un modelo que permita analizar las diversas variables que inciden en la determinación de la utilización de recursos humanos para la realización de transacciones financieras en una oficina bancaria del Banco Caja Social. Se hace un análisis de la demanda transaccional y se construye una herramienta de pronóstico que es la base para la determinar la cantidad de personal FTE (full time equivalent) requeridos para atender de manera coherente con la estrategia de servicio definida por la entidad a los clientes dicho requerimiento. Se utilizan herramientas estadísticas de pronóstico, programación lineal para la optimización de recursos, y modelos de simulación de operaciones que generen elementos objetivos para la toma de decisiones

Analysis of buffer allocations in time-dependent and stochastic flow lines

This thesis reviews and classifies the literature on the Buffer Allocation Problem under steady-state conditions and on performance evaluation approaches for queueing systems with time-dependent parameters. Subsequently, new performance evaluation approaches are developed. Finally, a local search algorithm for the derivation of time-dependent buffer allocations is proposed. The algorithm is based on numerically observed monotonicity properties of the system performance in the time-dependent buffer allocations. Numerical examples illustrate that time-dependent buffer allocations represent an adequate way of minimizing the average WIP in the flow line while achieving a desired service level