  The emergence of bandwidth-intensive latency-critical traffic in 5G Networks,
such as Virtual Reality, has motivated interest in wireless resource allocation
problems for flows with hard-deadlines. Attempting to solve this problem brings
about two challenges: (i) The flow arrival and the channel state are not known
to the Base Station (BS) apriori, thus, the allocation decisions need to be
made online. (ii) Wireless resource allocation algorithms that attempt to
maximize a reward will likely be unfair, causing unacceptable service for some
users. We model the problem as an online convex optimization problem. We
propose a primal-dual Deadline-Oblivious (DO) algorithm, and show it is
approximately 3.6-competitive. Furthermore, we show via simulations that our
algorithm tracks the prescient offline solution very closely, significantly
outperforming several existing algorithms. In the second part, we impose a
stochastic constraint on the allocation, requiring a guarantee that each user
achieves a certain timely throughput (amount of traffic delivered within the
deadline over a period of time). We propose the Long-term Fair Deadline
Oblivious (LFDO) algorithm for that setup. We combine the Lyapunov framework
with analysis of online algorithms, to show that LFDO retains the
high-performance of DO, while satisfying the long-term stochastic constraints.
