Rational arrival process explained

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

• Q-MAM a MATLAB toolbox which can solve queueing systems with RAP arrivals.^[3]

Notes and References

1. 10.1081/STM-120018141. Matrix‐Exponential Distributions: Calculus and Interpretations via Flows. Stochastic Models. 19. 113. 2003. Bladt . M. . Neuts . M. F. .
2. 10.1016/S0304-4149(99)00006-X. Point processes with finite-dimensional conditional probabilities. Stochastic Processes and their Applications. 82. 127. 1999. Asmussen . S. R. . Bladt . M. . free.
3. Book: 10.4108/ICST.VALUETOOLS2008.4368. Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods. Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools. 2008. Pérez . J. F. . Van Velthoven . J. . Van Houdt . B. . 978-963-9799-31-8.