STOCHASTIC MODELING AND PERFORMANCE PREDICTION OF QUEUEING SYSTEMS WITH SERVICE INTERRUPTION

Abstract

The service interruptions are unavoidable phenomenon in day-to-day queueing situations of routine life as well as in industrial organizations. The interruptions in queueing systems, whether intentional or unintentional, have a substantial effect on the system's performance and smooth functioning. This thesis investigates the service interruption characteristics of the queueing systems in order to predict the performance indices and minimize the delay in service. The objective of the present study is to investigate the stochastic models for queueing systems with service interruptions. The service interruptions in queueing systems may take place due to maintenance purposes, power saving mode, to permit the server a regular pause due to technical reasons, etc. On the other hand, a variety of interruptions in the service systems might occur due to server failure, machine breakdown, power outage, catastrophes/disaster failure and other similar circumstances. The service interruptions can lead to several consequences, such as delay in service, cost enhancement, customers’ impatience behavior that results in balking and/or reneging, etc. Therefore, it is important to address the issue of service interruption in the queueing models developed for performance prediction and cost optimization. Sometimes, after the completion of the service, the customers may rejoin the system if unsatisfied with the service received; this phenomenon is known as feedback. The customer’s feedback can significantly affect the total revenue and reputation of the service facility. The current thesis aims at examining various queueing systems which are subject to service interruptions due to some reasons, including server vacation, disaster failure, unreliable server, hardware/software failure, switching failure, etc. By considering several realistic features such as impatient customers and feedback phenomenon, some queueing models with service interruption are investigated via analytical methods, namely continued fraction (CF), probability generating function (PGF), confluent hypergeometric functions (CHF) and numerical techniques viz. matrix analytic method (MAM) and Runge-Kutta IV order method, etc. In order to determine the optimal design parameters and minimum cost associated with the queueing system, particle swarm optimization (PSO) and direct search approach (DSA) are used. The hybrid soft computing technique, namely adaptive neuro-fuzzy inference system (ANFIS), is used to explore the feasibility of developing an AI-based controller for complex systems. The investigations focusing on the stochastic modeling and performance analysis of queueing models with service interruptions are organized systematically into ten chapters. Chapters 2-9 and Chapter 10 are concerned with the performance analysis of transient Markovian queueing system with different types of service interruptions and M/M/1 fluid queue with disaster failure, respectively. Chapter 1 is devoted to the motivation, basic concepts, and related methodological aspects of the queueing models with service interruptions, relevant literature survey, and outlines of the research works compiled in the thesis. Chapter 2 presents a transient Markovian queueing model that incorporates disaster failure, balking, feedback, and reneging. The study utilizes probability generating function (PGF) and continued fraction (CF) approaches to provide an analytical formula for the queue size distribution. The numerical results are obtained for the key performance metrics of the system. Chapter 3 examines a Markovian queueing model with disaster failure and working vacation. PGF and CF techniques are used to derive the transient probabilities for the system states. The numerical simulation is carried out to investigate the sensitivity of the system parameters for various performance metrics. Chapter 4 focuses on a state-dependent Markovian queueing system with the provision of choice between complete vacation (CV) and working vacation (WV). The time-dependent analytical results are obtained by employing the PGF and CF methods. Numerical simulation results are provided to predict the system performance and the total cost of the system. Chapter 5 extends the Markovian queueing model discussed in Chapter 4 by incorporating the realistic feature of customers' impatience behavior. The transient queue size distribution is established via PGF and CF methods. The numerical results are obtained to offer insights into the sensitivity of the parameters on the system performance indices. The cost function is also established to provide the minimum cost corresponding to the optimal system parameters. Chapter 6 explores the bi-level vacation policy for a Markovian queueing system with the provision of reneged customers. The transient analytical solution is derived to investigate the performance metrics. In order to find the optimal service parameters, a heuristic method, namely the direct search approach, is used to minimize the total cost function. Chapter 7 deals with the performance prediction of a software-embedded fault-tolerant machining system (FTMS) that incorporates the switching failure, reneging, and mixed standbys. Runge-Kutta IV order method is employed to establish the transient system size distribution and other queueing and reliability metrics. The total cost function is framed, and direct search approach (DSA) is employed to calculate the optimum cost. Chapter 8 deals with the software-embedded FTMS that incorporates the switching failure and vacationing server. The model utilizes the matrix analytic method (MAM) to obtain the transient solutions. Various other performance measures are established by evaluating the transient probabilities of the system states. The total cost associated with the model is minimized by using the meta-heuristic approach, namely particle swarm optimization (PSO). Chapter 9 examines a fault-tolerant machining system (FTMS) by incorporating the realistic concepts of server vacation, working breakdown, vacation breakdowns, and reboots. The MAM is used to formulate the transient distribution of the system size. Several queueing and reliability indices are derived to assess the quality and performance of the FTMS. Moreover, the particle swarm optimization and direct search approach are used to optimize the cost-effective ratio. Chapter 10 examines the M/M/1 system approximated as fluid queue that incorporates disaster, imperfect coverage, and reboot. The analytical techniques of PGF and CF are used to establish the stationary buffer content distribution. The numerical results are provided to depict the effect of system parameters on the buffer content. Furthermore, the numerical results obtained are validated through computational outcomes gathered via the adaptive neuro-fuzzy inference system (ANFIS) approach. The thesis is concluded by highlighting the noble features of the study and outlining the potential future research scope. The analysis, optimization and numerical simulation carried out in the thesis have significant managerial implications and offer valuable insights to the system designers and decision makers of the queueing systems regarding upgrading the performance and overall profitability. At the end of the thesis, the relevant references are listed in alphabetical order.