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.

  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.