A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times

International audienc

Enhancing Integrated Communication Network Service Using a Queueing Model

This paper describes a strategy for efficiently constructing the demand servicing process of an Integrated Communication Network (ICN). Performance analysis, service problems, and relief action of ICNs are provided. End-to-end statistical performance parameters are first used to measure network compliance over a given fixed period. If any of the performance objectives are not satisfied, a servicing function determines the corrective action required to maintain service quality. The advantage of this network model is its efficiency and flexibility in handling a variety of services and applications. Enhanced network service and ICN traffic problems are solved using adaptive queuing models

Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved

Optimal Supply & Demand Balance In Service Environments

We study service environments that can be modeled as stochastic finite-capacity double-ended queues, where supply and demand arrive in independent Poisson processes to be instantly paired-off. In the case where throughput (output rate) is not a significant metric of system performance (as typically studied in the literature), we derive analytical results to gain managerial insights. We find that the operational decision on optimal supply/demand balance and the strategic decision on how to achieve that optimal balance can be decoupled and stratified. With the purpose of providing a managerial guide, we identify conditions for when to manipulate demand rather than supply, and vice versa. For the first time in the literature, we study throughput considerations in this context, and we analytically characterize the optimal strategy. Specifically, we show that it is optimal to manipulate either demand, or supply (and not both), and that the optimal system balance and the strategy on how to achieve it are strongly tied. Our findings can shed light on the managerial decision making process in these environments, and they can be used to revisit any governing strategies dictating management of demand (or supply) as a first course of action

Queuing Models To Balance Systems With Excess Supply

Many manufacturing and service activities can be modeled using queuing theory. The optimization of the long-run solution to imbalances between supply and demand is very important to established businesses. This paper presents a family of queuing models that minimize the expected total cost incurred when restoring equilibrium to a stochastic system that has become unstable due to changes in the environmental parameters affecting its behavior. Analytical expressions for the expected total cost in terms of a policy parameter are derived from which numerically-savvy users can obtain the policy that minimizes the expected total cost. To determine the model parameters that most affect the optimal policy and to facilitate the determination of near-optimal policies, exact solutions were found for a large number of scenarios and then used to fit a regression model. The resulting regression equation can be used by practitioners to find policy parameters that approximately minimize the expected total cost due to imbalances in supply and demand

A Markovian Queueing System for Modeling a Smart Green Base Station

International audienceWe investigate a model to assess the performance of a base station (BS) fully powered by renewable energy sources. The BS is modeled as a three-queue system where two of them are coupled. One represents accumulated energy, the second is the data queue and the third one serves as a reserve energy queue. This smart BS is able to dynamically adjust its coverage area (thereby controlling the traffic intensity) and to generate signals to the reserve energy queue that trigger the movement of energy units to the main energy buffer. Given the randomness of renewable energy supply and the internal traffic intensity control, our queueing model is operated in a finite state random environment. Using the matrix analytic formalism we construct a five-dimensional Markovian model to study the performance of the BS. The stationary distribution of the system state is obtained and key performance metrics are calculated. A small numerical example illustrates the model and a simplified product-form approximation is proposed

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included