A Linear Programming Approach to Error Bounds for Random Walks in the   Quarter-plane
  We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities along the boundaries of the state space. A Markov reward approach is used to bound the approximation error. The main contribution of the work is the formulation of a linear program that provides the approximation error. 
Jasper Goseling, Richard J. Boucherie, Jan-Kees van Ommeren
math.PR