101. Efficient Content Delivery in the Presence of Impatient Jobs
- Author
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Larrañaga, M., Boxma, Onno, Núñez Queija, Rudesindo, Squillante, Mark, Wittevrongel, S., Meo, M.C., Rosenberg, C., Stochastics (KDV, FNWI), Stochastics, Stochastic Operations Research, and Eurandom
- Subjects
Service (business) ,Exponential distribution ,Computer science ,batch processing ,Abandonment (legal) ,Distributed computing ,Markov process ,020206 networking & telecommunications ,Content delivery ,02 engineering and technology ,Optimal control ,01 natural sciences ,abandonment ,010104 statistics & probability ,symbols.namesake ,optimal control ,content delivery ,0202 electrical engineering, electronic engineering, information engineering ,Batch processing ,symbols ,0101 mathematics ,threshold policies ,Queue - Abstract
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.
- Published
- 2015