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A subjective Bayesian approach to the theory of queues. I: Modeling. (English) Zbl 0651.60098

Summary: This is the first of an expository two-part paper which outlines a point of view different from that currently used in queueing theory. In both parts, the focus is on concepts. Here we adopt a personal probability point of view to all sources of uncertainty in the theory of queues and explore the consequences of our approach by comparing our results to those that are currently available. For ease of exposition, we confine attention to the M/M/1/\(\infty\) and the M/M/1/K queues.
In Part I we outline the general strategy and focus on model development. In Part II, see the following entry, we address the problem of inference in queues within the subjective Bayesian paradigm and introduce a use of Shannon’s measure of information for assessing the amount of information conveyed by the various types of data from queues.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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