On the Quantum Entanglement of Random Walks and Queueing Systems

It is well established that there exist strong connections between random walks (RWs) in the nonnegative quarter plane and queueing systems arising in many fields. This includes the study of adaptive threshold-based load balancing in concert with affinity scheduling to address fundamental trade-offs in parallel systems between keeping the workload balanced and scheduling tasks where they run most efficiently. Other examples include studies of scheduling parallel jobs on parallel systems under spacesharing and timesharing policies, as well as studies of asymptotic capacity and performance scalability in wireless and linear loss networks. Given these strong connections, we focus herein on methodological solutions of a representative general class of RWs in the nonnegative quarter plane that are skip-free to the left and right, particularly solution methods based on quantum computing.