Recently, it has been established on multiple experimental data sets that human contact processes exhibit heavy-tailed inter-event distributions. This characteristic makes it difficult to transport data with a finite transfer time in a network of mobile devices, relying on opportunistic contacts only. Using various experimental data sets, we analyze how different types of communication infrastructure impact the feasibility of data transfers among mobile devices. The first striking result is that the heavy tailed nature of the contact processes persists after infrastructure is introduced. We establish experimentally that infrastructure improves significantly multiple opportunistic contact properties, relevant to opportunistic forwarding algorithms. We discuss how infrastructure can be used to design simpler and more efficient (in terms of delay and number of hops) opportunistic forwarding algorithms. In addition to this, for the first time in a study like this, the communication pattern of nodes is taken into account in the analysis. We also show that node pairs that have a real-life history of communication have contact properties that are better for opportunistic message forwarding to each other than what other node pairs have.