Canonical Form of Order-2 Non-stationary Markov Arrival Processes

Canonical forms of Markovian distributions and processes provide an efficient way of describing these structures by eliminating the redundancy of general representations. Canonical forms of order 2 stationary Markov arrival processes (MAPs) have already been established for both continuous and discrete time. In this paper we present canonical form of continuous time non-stationary MAPs of order 2. We also investigate the relation of the order 2 stationary Markov arrival processes and rational arrival processes. It turns out that the irreducibility of the underlying Markov chain has important qualitative consequences.