Broadband integrated services digital network(B-ISDN) provides multimedia services with different characteristics requiring various quality of services. For the analysis of the system with multimedia services, we need to investigate feedback queueing systems with multi-class customers, and we need to know probabilistic characteristics of the multimedia traffics such as video traffics in B-ISDN.
In the first part (chapter 2 -- chapter 4) of this dissertation, we deal with feedback queues with multi-class customers. It is very complicate to model this system as Markov process, because we need to know not only the number of customers in each class but also information on what type of customer is in order. For analysis of feedback queues with multi-class customers we give a new approach in which a relation between joint queue size at beginning epochs of the ith service and the i+1st service of arbitrary customer is derived.
In chapter 2, we consider an M/G/1 queueing system where each customer visits the queue a fixed number of times before departure. We obtain the joint probability generating function of the numbers of class-j-customers(customer on its jth visit to the queue) and also obtain the Laplace Stieltjes transform of the total response time of a customer.
In chapter 3, we consider an M/G/1 queueing system with Bernoulli feedback policy and multi-class customers. We assume that different classes of customers have different arrival rates, service time distributions and feedback parameters. We obtain the joint probability generating function of queue size of each class and also obtain the Laplace-Stieltjes transform of the total response time of a customer in each class. This has been an open problem.
In chapter 4, we consider an M/G/1 queueing system with multiple types of feedback, FCFS policy and gated vacations where the first service attempt of new customer is either successful (and then the customer leaves the system) or unsuccessful (and then the ...