Approximate solutions for heavily loaded Markov-modulated queues

The existing exact solutions for Markov-modulated queues are computationally intensive and prone to numerical problems when the number of states of the Markovian environment becomes large. To address this problem, a simple geometric approximation is proposed. It uses the dominant eigenvalue of the characteristic matrix polynomial, together with the associated left eigenvector. That approximation is shown to be asymptotically exact in heavy traffic. In other cases, its accuracy is examined numerically.