Limiting Theorems for Markov Chains and Their Application to Queues with State-Dependent Arrival Patterns

摘要

The purpose of the report is twofold: to provide results for the ergodic theory of Markov chains and to analyze queuing systems with state-dependent arrival rates, employing results from the first part. The ergodic theory is developed in two directions. The first extends and supplements the work of Pakes. It is noted that the motivation for both classes of results arose from problems involving particular imbedded Markov chains in the theory of queues. In the second part of the dissertation, theorems from the first part are used to classify the imbedded chain arising from a GI/M/s queuing system whose interarrival times are dependent upon the state of the system at arrival epochs. The notion of state-dependent arrival patterns is extended to include state-dependent batch sizes. (Author)