SLIDE 17 List of Variables & Equations
A video stream i is sent to user i at a data rate of 𝑠𝑗 The AP channel utilization is 𝛽𝑗 The throughput of stream i is: 𝑈𝑗 = 𝛽𝑗𝑠𝑗 The data transmission must meet the wireless channel utilization constraint: 𝑗=1 𝑂
𝛽𝑗 ≤ 1
The number of processing cycle needed to transcode a stream: 𝑑𝑗 The total available processing cycles is: C 𝑦𝑗 is used to indicate if a stream is transcoded 𝑦𝑗 = 1 or not 𝑦𝑗 = 0 Then the transcoding constraint is: 𝑗=1 𝑂
𝑑𝑗𝑦𝑗 ≤ 𝐷
The desired video rate is: 𝑇𝑗 𝑒 The final transmitted video rate (after transcoding if necessary) is: 𝑇𝑗 𝑢 The transcoder can only reduce the video resolution, i.e., decreasing the video rate.
Therefore: 𝑇𝑗
𝑢 < 𝑇𝑗 𝑒 𝑗𝑔 𝑦𝑗 = 1 𝑢𝑠𝑏𝑜𝑡𝑑𝑝𝑒𝑗𝑜 , and 𝑇𝑗 𝑢 = 𝑇𝑗 𝑒 𝑗𝑔 𝑦𝑗 =
0 𝑜𝑝 𝑢𝑠𝑏𝑜𝑡𝑑𝑝𝑒𝑗𝑜
If 𝜀 denotes the protocol overhead, which includes the lower layer headers and overhead to
transmit video data, then, the required bandwidth to transmit the video stream is 𝑈𝑗 = 𝛽𝑗𝑠
𝑗 = 𝜀𝑇𝑗 𝑢