Stable optimal design of an optical packet ring with tunable transmitters and fixed receivers

Optical packet switching is known to leverage the statistical multiplexing in optical networks, but in turn it may cause stability issues at the input queues containing packets waiting for transmission. Stability issues need to be addressed by a proper scheduling of the packet transmissions and dimensioning of the network. This paper aims to address the problem of dimensioning an optical packet switched ring with stability guarantees. In such a ring, the stability issues occur because a single tunable transmitter can insert the locally generated packets on different wavelengths. The necessary and sufficient stability conditions derived for a class of scheduling policy are identified, linearized and included in the mixed linear programming formulation that models the dimensioning problem. Optimal results show that neglecting the stability conditions may lead to more than 50% of the design to be unstable. To guarantee stability in such design, a 20% increase of the network cost may be required mainly for the additional wavelengths.