2015-09-01
Efficient Content Delivery in the Presence of Impatient Jobs
Publication
Publication
Presented at the
International Teletraffic Congress, Gent
We consider a content delivery problem in which
jobs are processed in batches and may abandon before their
service has been initiated. We model the problem as a Markovian
single-server queue and analyze two different settings: (1) the
system is cleared as soon as the server is activated, i.e., service
rate mu = infinity, and (2) the service speed is exponentially distributed
with rate mu < infinity. The objective is to determine the optimal
clearing strategy that minimizes the average cost incurred by
holding jobs in the queue, having jobs renege, and performing setups.
This last cost is incurred upon activation of the server in the
case mu = infinity, and per unit of time the server is active otherwise.
Our first contribution is to prove that policies of threshold type
are optimal in both frameworks. In order to do so we have
used the Smoothed Rate Truncation method which overcomes the
problem arising from unbounded transition rates. For our second
contribution, we derive the steady-state job-length distribution
under threshold policies. The latter yields a characterization of
the optimal threshold strategy, which can be easily implemented.
Finally, we present numerical results for our solution across a
wide range of parameters. We show that the performance of nonoptimal
threshold policies can be very poor, which highlights the
importance of computing the optimal threshold.
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IEEE Explore | |
S. Wittevrongel , M.C. Meo , C. Rosenberg | |
doi.org/10.1109/ITC.2015.16 | |
International Teletraffic Congress | |
Organisation | Stochastics |
Larrañaga, M., Boxma, O., Núñez Queija, R., & Squillante, M. (2015). Efficient Content Delivery in the Presence of Impatient Jobs. In S. Wittevrongel, M. C. Meo, & C. Rosenberg (Eds.), Proceedings of International Teletraffic Congress 2015 (ITC 27). IEEE Explore. doi:10.1109/ITC.2015.16 |