Optimal Service Allocation For Multi-Hop Network With Intermittent Connectivity

A network of queues is partitioned into K tandem, disjoint sets of parallel queues. A queue that belongs to set k is randomly connected to the queues in set k+1 with probability p. Time is slotted into fixed size transmission frames. A scheduler selects one packet per hop (set) per transmission frame to be forwarded to the next hop. Exogeneous arrivals may be inserted into set 1 queues only. This setup can be used to model a wireless relay network (WRN), where set 1 represents the subscriber stations (SS), while the other sets represent multi-hop relay stations (RS). In this paper, we investigate an optimal dynamic packet scheduling algorithm for this network. We define the optimal policy as the dynamic packet scheduling policy that minimizes, in a stochastic ordering sense, the process of cost function of the queue sizes in all hops. We consider a system with symmetrical connectivity and arrival distributions across the queues in each of the K sets. We prove that a policy that tries to balance the lengths of all queues in each of the K sets of queues in the system at every transmission frame is optimal. For the proof, we use coupling arguments. We also provide a low-complexity implementation algorithm and we prove that it will result in an optimal policy.