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Problem Definition: We determine the jointly optimal service capacity and retrial intervals between unsuccessful service attempts for a major provider of cloud computing services. Allocating sufficient capacity to cloud services is a challenging task because demand is time-varying. Thus, most firms have been expanding their capacity with little regard to the consequences associated with idle resources, such as excessive energy consumption and excess costs. Academic/Practical Relevance: We model the system as a multi-station queueing network where the arrival rate of jobs is time-varying and the servers represent CPU cores. Jobs are infinitely impatient and those that are not immediately serviced may retry several times before permanently abandoning the system. We introduce an offered load approximation that allows us to construct a recursive representation of the offered load function which describes the fluid dynamics of the system. Methodology: We develop a calculus-of-variation approach to minimize the total functional variation of the constructed offered load function. We show that an optimal policy can be efficiently obtained and prove that it is similar to maximizing the penalized system throughput. Results: Using a data set of cloud computing requests over a representative 24-hour period from a typical service of our partner organization, we show that our optimal policy results in a 10% reduction in capacity. We also demonstrate that small changes to their service-level agreements may elicit additional savings. Managerial Implications: Our model can help reduce idle capacity and has implications for managing more sustainable and environmentally friendly cloud computing services. It may also help to explain why so much global cloud capacity is typically idle. That is, in order to satisfy service level agreements encouraging retrial jobs to be processed during off-peak periods while also ensuring that they have short wait times, providers must provision large amounts of capacity. |
