Effects of delay and links between relays on the min-cut capacity in a wireless relay network

We study the effect of delay on the average capacity (min-cut capacity) of wireless relay networks. The nodes in the network are considered to be connected via Rayleigh flat fading channels. And we define the delay as the number of independent channel uses (number of different channel realizations) and study the effect of it on the average capacity of the network. For certain types of networks closed-form expressions of the capacity as a function of the number of channel uses (delay) are derived. One type that we consider is a network where there is one source, one destination, and multiple relays where all the relays are connected to each other. We arrive at an interesting result that the average capacity of this network and the same network but in which the relays are not connected to each other are not very different in terms of the average capacity. We further study this problem and give some upper bounds on the ratio of the capacities of these two networks.