Control charts for traffic intensity monitoring of Markovian multiserver queues

Abstract

A number of recent research studies have applied queueing theory as an approximate modeling tool to mathematically describe industrial systems, which include manufacturing, distribution, and service, for instance. Among the main observable characteristics in queues, the number of users in the system can be controlled to keep waiting times as minimal as possible. The design of efficient control charts is an attempt to monitor and control such systems. Control charts are proposed to monitor infinite queues with Markovian arrivals, exponential service times, and s identical parallel servers. The proposed charts monitor traffic intensities, which are the ratio between the arrival rate and the service rate, estimated through the number of users in the queueing system at random epochs. The effectiveness and efficiency of the proposed approaches in terms of the average run lengths are established by a comprehensive set of Monte Carlo simulations. KEYWORDS attribute control charts, average run length, Markovian queues, quality control wileyonlinelibrary.com/journal/qre [Colour figure can be viewed at wileyonlinelibrary.com] [Colour figure can be viewed at wileyonlinelibrary.com] Frederico R. B. Cruz holds a bachelor's degree in electrical engineering (1988) as well as a master's degree (1991) and a doctorate (1997) in computer science from the Universidade Federal de Minas Gerais, where he is a full professor in the Department of Statistics and conducts research in operations research.Roberto C. Quinino has a PhD in production engineering from the Universidade de São Paulo (1998). He is currently a full professor at the Universidade Federal de Minas Gerais. He develops research on quality control and marketing engineering with an emphasis on stochastic modeling applications acting on the following subjects: Taguchi online, Markov chains, misclassification, optimization, control chart planning, regression analysis, planning of experiments, and conjoint analysis. He supervises undergraduate, specialization, master's, and doctoral students. He has published papers in several international journals.

The Dynamic Adjusting Model of Traffic Queuing Time—A Monte Carlo Simulation Study

“…In addition, the Monte Carlo methods are generally easily parallelizable, with some techniques being ideal for use. The (model/methodological) novelty of its application in traffic queueing compares with its previous applications [9][10][11][12][13][14][15][16] as follows. Based on the traffic flow pattern in single intersection, the authors employ the Monte Carlo method in combination with MATLAB to simulate, which is proved to be more effective than the conventional control methods [9].…”

“…Li et al [15] apply the Monte Carlo simulation to develop their new traffic noise prediction approach. Cruz et al [16] develop the control chart to monitor traffic intensity and further utilize the Monte Carlo simulation to verify their resulting outcomes.…”