On Quantum Algorithms for Random Walks in the Nonnegative Quarter Plane

It is well known that strong connections exist between random walks (RWs) in the nonnegative quarter plane and the mathematical performance modeling, analysis and optimization of computer systems and communication networks. Examples include adaptive threshold-based load balancing in concert with affinity scheduling, scheduling parallel jobs on parallel computer systems, and asymptotic scalabilty in wireless and linear loss networks. Motivated by such strong connections, we focus herein on obtaining the stationary distribution of a representative general class of RWs in the nonnegative quarter plane that are skip free to the left and right, with a particular focus on efficient solution methods based on quantum computing.