PERFORMANCE MODELING AND ANALYSIS OF STATE DEPENDENT MARKOVIAN QUEUES

Abstract

The performance modeling and analysis of state dependent Markovian queues play important role for the assessment and prediction of congestion scenarios and can be studied under several realistic assumptions. Queueing analysis with state dependent models, appeared in the queueing literature, rely on the state dependent arrival and departure rates which are independent of the server status. Inspired from the realistic congestion problems of today’s life, we have developed Markovian models by considering state dependent arrival rates and service rates based on the varying environment depending upon the server’s status. The state dependent queueing models have globally ubiquitous applications, such as in the management of industrial and production systems, communication and computer networks, banking and railways stations and many other daily life congestion situations. Depending on whether the server is available or not, the joining of the tasks/ customers may be affected. The optimal decision parameters are also required to ensure that the system is operating effectively at the optimal cost while maintaining the economic quality of service. In this present thesis, state dependent Markovian queues under realistic features like retrial, imaginary customers, vacation, impatient customers, server breakdown, customer’s feedback, etc. are developed to reduce the congestion at the possible optimum total cost. The upgradation of service and prediction of joining behavior of the customers have also taken into account. In order to develop Markovian queueing models, probability distribution function for the steady state and transient state are derived via analytical techniques such as linear difference method, probability generating function, continued fractions, recursive approach, etc. By using the analytical results, we are able to establish various key metrics such as expected queue length, expected waiting time, throughput and long run probabilities which are useful to predict the system behavior. To minimize the total cost of the system, numerical as well as metaheuristic optimization techniques like particle swarm optimization, steepest descent method, harmony search approach, golden search section, quasi-Newton method, etc. have been successfully implemented. The hybrid soft computing technique viz artificial neural fuzzy interference system (ANFIS) is also employed for the possible utilization and validation of the analytical results. The numerical simulation has been performed for the quantitative assessment of the performance metrics. The sensitivity analysis is also done to validate the analytical findings and examine the effects of variation in parameters.