Network model Server with a broadcast channel Server · K users: cache size m ④File File Placement v 2@ Transmission Niles:={F1,…,F} Popularity( decreasing 2 File P={m1,…,p Request 2 Fil Request · Random request W; W2={n,…,fk,fk∈ FUser1user2 User K Rate for Wi is r(Wi Expected rate R(K,,P)=〉r(W)PW) 1Network Model 9 • Server with a broadcast channel • K users: cache size M • N files: ℱ = 𝐹1, …, 𝐹𝑁 • Random request 𝑊𝑖 • Expected rate: Popularity (decreasing): 𝒫 = 𝑝1,… , 𝑝𝑁 𝑊𝑖 = 𝑓𝑖1, … , 𝑓𝑖𝐾 , 𝑓𝑖𝑘 ∈ ℱ Rate for 𝑊𝑖 is 𝑟(𝑊𝑖) 𝑅 𝐾, ℱ,𝒫 = ෍ 𝑖=1 𝑁 𝐾 𝑟(𝑊𝑖)𝑃(𝑊𝑖) User 1 File 1 ... File N User 2 ... User K Server File Placement User 1 File 1 ... File N User 2 ... User K 1 Server File Placement User 1 File 1 ... File N User 2 ... User K File Request File Request 1 2 2 2 2 Server File Placement User 1 File 1 ... File N User 2 ... User K File Request File Request File Transmission 1 2 3 2 2 2 Server