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We study the design of caching policies in applications such as serverless computing where there is not a fixed size cache to be filled, but rather there is a cost associated with the time an item stays in the cache. We present a model for such caching policies which captures the trade-off between this cost and the cost of cache misses. We characterize optimal caching policies in general and apply this characterization by deriving a closed form for Hawkes processes. Since optimal policies for Hawkes processes depend on the history of arrivals, we also develop history-independent policies which achieve near-optimal average performance. We evaluate the performances of the optimal policy and approximate polices using simulations and a data trace of Azure Functions, Microsoft's FaaS (Function as a Service) platform for serverless computing. 

In the context of subscription-based services, many technologies improve over time, and service providers can provide increasingly powerful service upgrades to their customers but at a launching cost and the expense of the sales of existing products. We propose a model of technology upgrades and characterize the optimal pricing and timing of technology introductions for a service provider who price-discriminates among customers based on their upgrade experience in the face of customers who are averse to switching to improved offerings. We first characterize optimal discriminatory pricing for the infinite horizon pricing problem with fixed introduction times. We reduce the optimal pricing problem to a tractable optimization problem and propose an efficient algorithm for solving it. Our algorithm computes optimal discriminatory prices within a fraction of a second even for large problem instances. We then show that periodic introduction times, combined with optimal pricing, enjoy optimality guarantees. In particular, we first show that, as long as the introduction intervals are constrained to be nonincreasing, it is optimal to have periodic introductions after an initial warm-up phase. When allowing general introduction intervals, we show that periodic introduction intervals after some time are optimal in a more restricted sense. Numerical experiments suggest that it is generally optimal to have periodic introductions after an initial warm-up phase. Finally, we focus on a setting in which the firm does not price-discriminate based on customers’ experience. We show both analytically and numerically that in the nondiscriminatory setting, a simple policy of Myerson (i.e., myopic) pricing and periodic introductions enjoys good performance guarantees. Funding: This material is based upon work supported by INSEAD and University Pierre et Marie Curie [Grant ELICIT], as well as by the National Science Foundation [Grant 2110707]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2364 .