Rational arrival process

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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.


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


  1. ^ Bladt, M.; Neuts, M. F. (2003). "Matrix‐Exponential Distributions: Calculus and Interpretations via Flows". Stochastic Models. 19: 113. doi:10.1081/STM-120018141. 
  2. ^ 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. 
  3. ^ 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). ISBN 978-963-9799-31-8. doi:10.4108/ICST.VALUETOOLS2008.4368.