  We consider a horizontal traffic queue (HTQ) on a periodic road segment,
where vehicles arrive according to a spatio-temporal Poisson process, and
depart after traveling a distance that is sampled independently and identically
from a spatial distribution. When inside the queue, the speed of a vehicle is
proportional to a power $m >0$ of the distance to the vehicle in front. The
service rate of HTQ is equal to the sum of the speeds of the vehicles, and has
a complex dependency on the state (vehicle locations) of the system. We show
that the service-rate increases (resp., decreases) in between arrivals and
departures for $m<1$ (resp., $m>1$) case. For a given initial condition, we
define the throughput of such a queue as the largest arrival rate under which
the queue length remains bounded. We extend the busy period calculations for
M/G/1 queue to our setting, including for non-empty initial condition. These
calculations are used to prove that the throughput for $m=1$ case is equal to
the inverse of the time required to travel average total distance by a solitary
vehicle in the system, and also to derive a probabilistic upper bound on the
queue length over a finite time horizon for the $m>1$ case. Finally, we study
throughput under a release control policy, where the additional expected
waiting time caused by the control policy is interpreted as the magnitude of
the perturbation to the arrival process. We derive a lower bound on throughput
for a given combination of maximum allowable perturbation, for $m<1$ and $m>1$
cases. In particular, if the allowable perturbation is sufficiently large, then
this lower bound grows unbounded as $m \to 0^+$. Illustrative simulation
results are also presented.
