On the level crossing of multi-dimensional delayed renewal processes. (English) Zbl 0896.60056

Summary: The paper studies the behavior of an \((l+3)\)-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the “crossing level” and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.


60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K05 Renewal theory
60K25 Queueing theory (aspects of probability theory)
60G25 Prediction theory (aspects of stochastic processes)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
91B28 Finance etc. (MSC2000)
91B26 Auctions, bargaining, bidding and selling, and other market models
90B22 Queues and service in operations research
Full Text: DOI EuDML