In this paper, we consider a half-duplex decode-and-forward multi-hop relay network. The model for the channel that we consider includes path loss, shadowing, and fast fading. For this system and channel model, we find the outage probability for the multi-hop relay communication strategy that allows a packet to follow any path through the relays in the network. Based on the outage probability and the rate that used in the network, we find the exact throughput of the system. From this understanding of the system throughput, we find the optimal operating rate and the optimal number of hops that maximize the throughput. We also consider a system in which the relays have buffers that allow them to delay transmission and transmit when the channel conditions are favorable. We compare the system throughput of this buffer-equipped multi-hop relay network with the conventional multihop relay network without buffers.