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The combination of recent emerging technologies such as network function virtualization (NFV) and network programmability (SDN) gave birth to the Network Slicing revolution. 5G networks consist of multi-tenant infrastructures capable of offering leased network “slices” to new customers (e.g., vertical industries) enabling a new telecom business model: Slice-as-a-Service (SlaaS). In this paper, we aim i) to study the slicing admission control problem by means of a multi-queuing system for heterogeneous tenant requests, ii) to derive its statistical behavior model, and iii) to provide a utility-based admission control optimization. Our results analyze the capability of the proposed SlaaS system to be approximately Markovian and evaluate its performance as compared to legacy solutions.