PERFORMANCE ANALYSIS AND OPTIMAL CONTROL STRATEGIES FOR STATE DEPENDENT QUEUEING SYSTEM

Abstract

The performance modeling of Markovian and non-Markovian queueing models plays a vital role in design of real time queueing systems. The application of such models can be seen at many places including telecommunication system, computer networks, industrial and production system, etc. The state-dependent queueing models are of practical use and robust in depicting many real life congestion scenarios. These queues deal with the many realistic situations such as queues with discouragement, time sharing system, machine repair problems, etc. Optimal control of parameters of the queueing system is the key concern as far as the organizer as well customer’s point of view. The arriving customers decide before joining the system whether to join or not to join the system based on their prior assessment of the queue length. So far as the controlling of the arrivals in the finite capacity system is concerned, admission control F-policy is quite useful to control the congestion of the customers/jobs and it can be helpful in reducing the lost customers/jobs in particular when the system capacity is full. The admission control F-policy mainly restricts the customers/jobs from an entry in the queueing system when the system capacity is exhausted and further admission of customers/jobs is allowed when enough customers/jobs are served so that the number of customers/jobs in the system drops to a threshold level 'F ' . The admission control F-policy can be employed to resolve the issue of controlling of the arrivals in the queueing system so as to avoid the loss of revenue and inconvenience to the customers. In the present thesis, we investigate state dependent queueing models applicable to several queueing scenarios. The noble features of the investigation done are design of the control policies for some Markov and non-Markov queueing models by incorporating several features such as admission control F-policy, balking, reneging, feedback, unreliable server, retrial orbit, vacation, etc. In order to study the concerned queueing models, various system metrics such as number of customers in the system and in the queue, throughput, customer’s loss, long run probabilities and reliability indices have been obtained using the relevant analytical/numerical techniques. The cost optimization and evaluation of optimal control parameters of the concerned queueing models, have been done using various methods such as quasi-Newton method, genetic algorithm, Harmony search algorithm, etc. The soft computing approaches namely fuzzy logic, neuro fuzzy technique, parametric non-linear programing are also employed for the prediction of performance indices of the concerned queueing models. ii The main focus of our investigation in the present thesis is to the state dependent queueing models along with optimal control strategies. The work done on the optimal strategies and evaluation of performance indices of state dependent queueing models is organized into eight chapters. Some state-dependent queueing models have been developed by incorporating customer’s joining strategies, admission control policy, double orbit, etc. The numerical results based on sensitivity analysis are also performed to validate the results derived for the concerned queueing model. The investigations done in the thesis are divided into eight chapters which are described as follows. Chapter 1 is devoted for an overview and the motivation of the relevant topics alongwith preliminary concepts used for the concerned queueing models. The brief description of the methodologies used and the literature survey of relevant topics have been highlighted. Chapter 2 is concerned with an unreliable retrial queueing model under the admission control F-policy by incorporating the startup time and threshold policy. The adaptive neuro fuzzy inference system (ANFIS) technique is implemented to compare the numerical results obtained by Gauss- Seidel method. Chapter 3 presents the single server state-dependent model with general retrial attempts under admission control F-policy. The minimum cost of the system corresponding to optimal threshold parameter and optimal service rate is also determined using direct search method and quasi-Newton method. Chapter 4 deals with the multi-server finite queueing model with customer’s balking behaviour. The concepts of admission control of customers based on F-policy and one additional server are incorporated to shorten the queue length formed by the customers in the rush hour. The system cost is minimized using direct search method and quasi- Newton method to obtain the admission control parameter. Chapter 5 contains various results for the single server finite capacity queueing model with discouragement and general retrial times while the system operates under admission control Fpolicy. The soft computing based artificial neuro fuzzy inference system (ANFIS) method is applied to validate the results obtained by analytical method. Cost analysis is also done using genetic algorithm (GA) and quasi-Newton method by evaluating the optimal control parameters. Chapter 6 deals with the finite population models with general distributed retrial time under admission control F-policy. The fuzzy cost analysis for the finite population model is done by considering the cost elements as trapezoidal fuzzy numbers. Furthermore, the signed distance method is used to defuzzify the cost function. To determine the optimal control parameter and minimum cost of the system, genetic algorithm (GA) is also applied. Chapter 7 presents finite iii crisp and fuzzy population model for the multi-component machining system with general repair, standby support and server vacation. The cost analysis is done using Harmony search algorithm to determine optimal control parameters. In Chapter 8, three infinite capacity double orbit retrial queueing models are studied. The first model is concerned with the customers’ joining strategy in a double orbit retrial queueing system with balking. This model is transformed into fuzzy environment to study the fuzzified indices using the parametric nonlinear programing (P-NLP). The cost optimization is also done to determine optimal service rates using GA. The second model deals with double orbit feedback model. In the third double orbit model, the single server is taken as unreliable. In order to validate the feasibility of use neuro- fuzzy controller, ANFIS technique is also implemented. The cost function is framed and used to obtain the optimal service rates using quasi-Newton method. At the end of the thesis, the concluding remarks and future scope have been outlined. The relevant references have been listed in the end of the thesis in alphabetical order.