The advent of Satellite as a Service (SaaS) platforms has empowered satellite service providers (SPs) to rent portions of satellite capacity from infrastructure providers (IPs) to cater to the diverse demands of their users across multiple satellite services. To effectively manage costs and maintain a high Quality of Experience (QoE) for numerous concurrent connections, SPs should secure flexible capacity from IPs. However, the irregular and unpredictable nature of traffic demands from various applications complicates the capacity-renting framework. This study presents a dynamic capacity allocation framework that efficiently handles diverse traffic flows with varying arrival rates, aiming to minimize rental costs while meeting blocking probability and QoE requirements. Utilizing the 𝑀 𝑡 /𝑀 𝑡 /1 queuing model and a continuous-time Markov chain, the technical designs are framed as a statistical optimization problem. In this context, the system waiting-queue lengths are estimated using the transient probabilities of Kolmogorov equations. Subsequently, cumulative distribution functions are employed to re-formulate this stochastic optimization problem into a convex form, which can be tackled through the Lagrangian duality method.Through extensive simulations and numerical assessments, we illustrate our method's efficacy, with the proposed algorithm outperforming benchmarks by reducing costs by up to 9.85% and 3.1%.