Move-forward rules and f-SWAP rules applied to a communication problem

In a communication network, one might attempt to route calls from an origin to a destination through n paths that will be tried one by one, each having a success probability p_i ∈ (0,1), i = 1,2,. . . , n. The order of trying is controlled by a routing table. The number of attempts made is defined as the cost of the routing table. Move-forward self-organizing rules are applied to the routing table and comparisons of expected equilibrium costs are performed when p₂= p₃=⋯ = p_n. Stationary distributions for a subset of f-swap rules are obtained for general p _i's.