Queueing theory is one of the most important branches of modern probability theory which has many applications in computer science and communication networks.
The main purposes of this dissertation are to analyze threshold-based queueing systems and to apply these models to traffic controls in ATM networks such as the cell discarding(CD) scheme, the dynamic rate leaky bucket scheme and the queue-length- threshold(QLT) scheduling policy.
In Chapter 2, we analyze a queueing system MMPP/$G_1$, $G_2$/1/B with queue length dependent service times where arrivals follow a Markov-modulated Poisson process(MMPP). The service time of customers depends upon the queue length at service initiation epoch: if the queue length at service initiation epoch is less than or equal to a threshold L, the service time distribution of customer is $G_1$ ; otherwise, the service time distribution of customer is $G_2$. By using the embedded Markov chain method, we obtain the queue length distribution at departure epochs. Then, by using the supplementary variable method and the basic property of semi-Markov process, we obtain the queue length distribution at an arbitrary time. By this result, we obtain the loss probability and the mean waiting time. Our model has application to the cell discarding(CD) scheme operating at the output of a buffer for voice traffics in ATM networks. From numerical examples, we see that the loss probability and the mean waiting time for the CD scheme are improved considerably compared with those of the uncontrolled system without CD scheme.
In Chapter 3, we propose the leaky bucket scheme with threshold-based token generation intervals. The leaky bucket scheme is a promising method that regulates input traffics for preventive congestion control in ATM networks. In order to meet the constraint of loss probability for more bursty input traffics, it is known that the leaky bucket scheme with static token generation interval requires a larger data buffer and token ...