# Rational arrival process

In queueing theory, a discipline within the mathematical theory of probability, a **rational arrival process** (**RAP**) is a mathematical model for the time between job arrivals to a system. It extends the concept of a Markov arrival process, allowing for dependent matrix-exponential distributed inter-arrival times.^{[1]}

The processes were first characterised by Asmussen and Bladt^{[2]} and are referred to as rational arrival processes because the inter-arrival times have a rational Laplace–Stieltjes transform.

## Software

## References

- ↑ Bladt, M.; Neuts, M. F. (2003). "Matrix‐Exponential Distributions: Calculus and Interpretations via Flows".
*Stochastic Models*.**19**: 113. doi:10.1081/STM-120018141. - ↑ Asmussen, S. R.; Bladt, M. (1999). "Point processes with finite-dimensional conditional probabilities".
*Stochastic Processes and their Applications*.**82**: 127. doi:10.1016/S0304-4149(99)00006-X. - ↑ Pérez, J. F.; Van Velthoven, J.; Van Houdt, B. (2008). "Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods".
*Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools*(PDF). doi:10.4108/ICST.VALUETOOLS2008.4368. ISBN 978-963-9799-31-8.

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