SOME LADDER PROCESSES IN CONTINUOUS TIME WITH APPLICATIONS TO QUEUES

Ladder processes are constructed for a basic stochastic process in continuous time with discrete state space. These processes are used to obtain limit theorems for the supremum and infimum functionals defined on this basic process. Application of these results to queues with Poisson arrivals and gen...

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Bibliographic Details
Main Author: Worthington,Frank M
Format: Report
Language:English
Subjects:
DISTRIBUTION FUNCTIONS
LADDER PROCESSES
LIMIT THEOREM
MATHEMATICAL MODELS
Operations Research
PROBABILITY
QUEUEING THEORY
RANDOM VARIABLES
RENEWAL THEORY
REPLACEMENT THEORY
SEQUENCES(MATHEMATICS)
STATISTICAL PROCESSES
STOCHASTIC PROCESSES
THEOREMS
THESES
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Summary:Ladder processes are constructed for a basic stochastic process in continuous time with discrete state space. These processes are used to obtain limit theorems for the supremum and infimum functionals defined on this basic process. Application of these results to queues with Poisson arrivals and general Erlangian type service time density are then discussed in the case where no steady state exists, that is, where the traffic intensity is greater than or equal to one. (Author) See also Technical Report 29, AD-659 318.