Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Input Process

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_200324

The stochastic point process representing some aspect of customers actually entering a queueing system (or nodal part of one) or some aspect of the state of the node at the instant of input, with points representing the instants of entrance. For example, in finite capacity queues, and (Xa, Ta) process has the Xa process as a sequence of 1s and 0s representing whether the queue is full or not at an arrival and the Ta process represents the times of arrivals. The subset of the Ta process for which Xa = 0 represents the set of arrival epochs at which a customer actually enters the node, while the Ta for which Xa = 1 represents the set of arrival times at which customers do not gain access to the node but overflow.

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© Springer Science+Business Media New York 2013