## 4 Problem Formulation
### MILP Optimization Model  
The MILP formulation of the slice-aware DU/CU placement- and flow routing-optimization problem uses the variables defined in Table 2. \begin{table}
\begin{tabular}{l l} \hline \hline
**Sets** & \\ \hline \(\mathcal{V}\) & network nodes \\ \(\mathcal{V}^{\text{PP}}\) & PP nodes; \(\mathcal{V}^{\text{PP}}\subset\mathcal{V}\) \\ \(\mathcal{E}\) & network links \\ \(\mathcal{E}^{\text{S}}\) & output links of switches; \(\mathcal{E}^{\text{S}}\subset\mathcal{E}\) \\ \(\mathcal{C}\) & clusters of RUs \\ \(\mathcal{N}\) & types of network slices; \(\mathcal{N}=\{\text{eMBB},\text{URRLC}\}\) \\ \(\mathcal{S}\) & network slices \\ \(\mathcal{S}^{\text{EMBS}}\) & network slices of type eMBB; \(\mathcal{S}^{\text{CMBB}}\subset\mathcal{S}\) \\ \(\mathcal{S}^{\text{URLLC}}\) & network slices of type URLLC; \(\mathcal{S}^{\text{URLLC}}\subseteq\mathcal{S}\) \\ \(\mathcal{D}\) & traffic demands \\ \(\mathcal{D}(c)\) & demands associated with cluster \(c\in\mathcal{C}\); \(\mathcal{D}(c)\subseteq\mathcal{D}\) \\ \(\mathcal{D}(s)\) & demands belonging to network slice \(s\in\mathcal{S}\); \(\mathcal{D}(s)\subseteq\mathcal{D}\) \\ \(\mathcal{F}\) & types of traffic flows; \(\mathcal{F}=\{\text{FH},\text{MH}\}\) \\ \(\mathcal{H}(d,f,e)\) & demand-flow pairs of an equal/higher priority than flow \(f\) of demand \(d\), \\  & which cause buffering latencies of flow \(f\) in link \(e\in\mathcal{E}^{\text{S}}\) \\ \(\mathcal{L}(d,f,e)\) & demand–flow pairs of a lower priority than flow \(f\) of demand \(d\), \\  & which cause buffering latencies of flow \(f\) in link \(e\in\mathcal{E}^{\text{S}}\) \\ \(\mathcal{T}(d,f,e)\) & possible values of latency \(L(d,f,e)\) produced by lower priority flows \((d,f,e)\in\mathcal{L}(d,f,e)\) \\ \(\mathcal{L}(d,f,e,t)\) & demand–flow pairs producing latency \(\Gamma\in\mathcal{T}(d,f,e)\); \(\mathcal{L}(d,f,e,t)\subseteq\mathcal{L}(d,f,e)\) \\ \(\mathcal{P}\) & candidate routing paths \\ \(\mathcal{P}(d,f)\) & candidate paths for flow \(f\) of demand \(d\); \\ \(\mathcal{P}(d,f,v)\) & candidate paths for flow \(f\) of demand \(d\) terminated at PP node \(v\) \\ \(\mathcal{P}(d,f,e)\) & candidate paths for flow \(f\) of demand \(d\) going through link \(e\) \\ \(\mathcal{E}(p)\) & links belonging to path \(p\) \\ \hline
**Parameters** & \\ \hline \(H(e)\) & transmission capacity of link \(e\) \\ \(\mathcal{C}(p)\) & processing capacity of PP node \(v\) \\ \(H(d,f)\) & bit rate of flow \(f\) of demand \(d\) \\ \(g^{\text{DU}}\) & processing load of the DU of demand \(d\) \\ \(\rho^{\text{CU}}\) & processing load of the CU of demand \(d\) \\ \(L^{\text{P}}(e)\) & propagation delay in link \(e\) \\ \(L^{\text{S}}(e)\) & store-and-forward delay of the switch being the origin of link \(e\in\mathcal{E}^{\text{S}}\) \\ \(L(d,f,e)\) & delay produced by transmission of the burst of frames of flow \(f\) of demand \(d\) at link \(e\) \\ \(\tilde{L}(d,f,e)\) & overall latency of flows in set \(\mathcal{H}(d,f,e)\) \\ \(L(t)\) & the value of latency \(t\in\mathcal{T}(d,f,e)\) \\ \(L^{\text{max}}(d,f)\) & maximum one-way latency limit of flow \(f\) of demand \(d\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notation.