  Proactive tile-based virtual reality video streaming computes and delivers
the predicted tiles to be requested before playback. All existing works
overlook the important fact that computing and communication (CC) tasks for a
segment may squeeze the time for the tasks for the next segment, which will
cause less and less available time for the latter segments. In this paper, we
jointly optimize the durations for CC tasks to maximize the completion rate of
CC tasks under the task duration-squeezing-aware constraint. To ensure the
latter segments remain enough time for the tasks, the CC tasks for a segment
are not allowed to squeeze the time for computing and delivering the subsequent
segment. We find the closed-form optimal solution, from which we find a
minimum-resource-limited, an unconditional and a conditional resource-tradeoff
regions, which are determined by the total time for proactive CC tasks and the
playback duration of a segment. Owing to the duration-squeezing-prohibited
constraints, the increase of the configured resources may not be always useful
for improving the completion rate of CC tasks. Numerical results validate the
impact of the duration-squeezing-prohibited constraints and illustrate the
three regions.
