Uniform Limit Theorems for Synchronous Processes with Applications to Queues
STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH
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In the present paper we investigate conditions under which the Cesaro averaged functionals. We show that to obtain uniform convergence requires placing further conditions on the Positive Recurrence Process PRS. This is in sharp contrast to both classical regenerative processes and discrete time Harris recurrent Markov chains where renewal theory can be applied where such uniform convergence holds without any further conditions. For continuous time positive Harris recurrent Markov processes where renewal theory can not be applied we show that these further conditions are in fact automatically satisfied. In this context, applications to queueing models are given. Synchronous process, Cesaro convergence, Limit theorems, Point processes.
- Operations Research