  Owing to severe path loss and unreliable transmission over a long distance at
higher frequency bands, we investigate the problem of path selection and rate
allocation for multi-hop self-backhaul millimeter wave (mmWave) networks.
Enabling multi-hop mmWave transmissions raises a potential issue of increased
latency, and thus, in this work we aim at addressing the fundamental questions:
how to select the best multi-hop paths and how to allocate rates over these
paths subject to latency constraints? In this regard, we propose a new system
design, which exploits multiple antenna diversity, mmWave bandwidth, and
traffic splitting techniques to improve the downlink transmission. The studied
problem is cast as a network utility maximization, subject to an upper delay
bound constraint, network stability, and network dynamics. By leveraging
stochastic optimization, the problem is decoupled into: path selection and rate
allocation sub-problems, whereby a framework which selects the best paths is
proposed using reinforcement learning techniques. Moreover, the rate allocation
is a nonconvex program, which is converted into a convex one by using the
successive convex approximation method. Via mathematical analysis, we provide a
comprehensive performance analysis and convergence proofs for the proposed
solution. Numerical results show that our approach ensures reliable
communication with a guaranteed probability of up to $99.9999\%$, and reduces
latency by $50.64\%$ and $92.9\%$ as compared to baseline models. Furthermore,
the results showcase the key trade-off between latency and network arrival
rate.
