  Multi-connectivity facilitates higher throughput, shorter delay, and lower
outage probability for a user in a wireless network. Considering these
promises, a rationale policy for a network operator would be to implement
multi-connectivity for all of its users. In this paper, we investigate whether
the promises of multi-connectivity also hold in such a setting where all users
of a network are connected through multiple links. In particular, we consider a
network where every user connects to its k closest base stations. Using a
framework of stochastic geometry and probability theory, we obtain analytic
expressions for per-user throughput and outage probability of $k$-connectivity
networks under several failure models. In contrast to the conclusions of
previous research, our analysis shows that per-user throughput decreases with
increasing k. However, multi-connected networks are more resilient against
failures than single connected networks as reflected with lower outage
probability and lead to higher fairness among the users. Consequently, we
conclude that rather than implementing multi-connectivity for all users, a
network operator should consider it for its users who would benefit from
additional links the most, e.g., cell edge users.
