Routing in all optical networks is an important issue. Deflection routing provides a high throughput but suffers from unbounded transportation time. Convergence routing provides ending guarantee to packets entering the network. We focus on the Eulerian routing technique (convergence routing based on an Eulerian directed cycle), and several improvements which increase the throughput. In this paper, we show that these routing algorithms are very unstable when the traffic occurs by bursts. Thus an admission control is needed to maintain a high throughput.