  In this paper, we present a delay-optimal packet scheduler for processing the
M2M uplink traffic at the M2M application server (AS). Due to the
delay-heterogeneity in uplink traffic, we classify it broadly into
delay-tolerant and delay-sensitive traffic. We then map the diverse delay
requirements of each class to sigmoidal functions of packet delay and formulate
a utility-maximization problem that results in a proportionally fair
delay-optimal scheduler. We note that solving this optimization problem is
equivalent to solving for the optimal fraction of time each class is served
with (preemptive) priority such that it maximizes the system utility. Using
Monte-Carlo simulations for the queuing process at AS, we verify the
correctness of the analytical result for optimal scheduler and show that it
outperforms other state-of-the-art packet schedulers such as weighted round
robin, max-weight scheduler, fair scheduler and priority scheduling. We also
note that at higher traffic arrival rate, the proposed scheduler results in a
near-minimal delay variance for the delay-sensitive traffic which is highly
desirable. This comes at the expense of somewhat higher delay variance for
delay-tolerant traffic which is usually acceptable due to its delay-tolerant
nature.
