| In queueing theory, the choice between one "fast" and multiple "slow" servers (where the aggregate service rate is the same for both systems) is considered a classic textbook problem for M/M/c queueing systems. This question has never been investigated for polled queueing systems. This dissertation solves the one fast/many slow servers problem for selected polled queueing models.; The inspiration for this problem comes from a wireless token ring network, where one could choose to use frequency division multiplexing to vary the number of transmission channels. Using this method allows for an efficient use of the transmission channel as well as improvements in certain performance measures. Additionally, although not a focus of this dissertation, manufacturing applications for these types of systems certainly exist.; This dissertation focuses on the time a customer spends waiting in the system. Although we are somewhat interested in average wait tunes, our primary interest is in the waiting time probability distribution. In other words, the primary question is, what is the probability that some arbitrary customer will complete service prior to sonic time cutoff?; Three primary approaches to this problem are used, and the first two each use numerical methods for their analysis. First, the model is simplified to two queues with either one or two servers (where both systems have the same aggregate service rate). Second, the restriction on the number of queues and servers is removed, and a server vacation approach is taken. Lastly, simulation results are presented for models that are too complicated to fit into the structure of the other approaches.; We find conditions on system parameters such that splitting the service capacity results in improved probabilities of service completion by some time cutoff. As expected, this is often at the cost of some small increase in the system waiting time averages. |
