A polling system with ‘Join the shortest - serve the longest’ policy

This paper studies a Markovian single-server non-symmetric two-queue polling system, operating simultaneously under a combination of two well-known queueing regimes: (i) ‘Join the Shortest Queue’ and (ii) ‘Serve the Longest Queue’. The system is defined as a two-dimensional continuous-time Markov chain, and analyzed via both probability generating functions approach and matrix geometric method. Although both queues are unbounded, by applying a non-conventional representation and without resorting to involved boundary-value problem analysis, we derive the joint steady-state probability distribution of the system's states, and consequently calculate its performance measures and derive its stability condition. Numerical results are presented, as well as a comparison with a corresponding M/G/1 queue.