Proxy-based Distribution of Streaming Video over Unicast/Multicast ConnectionsBing Wang, Subhabrata Sen, Micah Adler, and Don TowsleyUmass CMPSCI Tech. Report 01-05

Contributions of This PaperDevelop a generalized allocation technique for minimizing the transmission cost.Develop schemes that use proxy prefix caching as an integral part of bandwidth-efficient delivery in Internet-like environment.Explore the impact of the developed transmission schemes coupled with the optimal cache allocation, the proxy cache size and availability of unicast versus multicast capability, on the resultant transmission cost.

Streaming Model

Parameters in The ModelGoal: minimize

Optimal Proxy Cache AllocationAi={mi | 0 mi ni} : the set of possible prefixes for video i.saving(mi) =Ci(0)-Ci(miu/bi) : the saving in transmission cost when caching an mi-unit prefix of video i over caching no prefix of the video at the proxy.Optimization problem:

Optimal Proxy Cache Allocation (continued)This problem is a variant of 0-1 knapsack problem.It can be solved by dynamic programming algorithm.B(i, j) : the maximum saving in the transition cost for the first i videos in a proxy cache of size j.

Time complexity: O(NSK), K=max1iN|Ai|

Unicast Suffix Batching (SBatch)Sbatch schedules the transmission of the suffix from the server to the proxy as late as possible.For any request arriving in time (0, vi], the proxy just forwards the single incoming suffix to the new client.Assuming a Poisson arrival process, the average number of request in time [0, vi] is 1+vii.

Unicast Patching with Prefix Caching

Unicast Patching with Prefix Caching (continued)The average number of requests is 1+ 1+i(vi+Gi).The total length of patches from the server for these requests is

therefore

Multicast Patching with Prefix Caching

Multicast Patching with Prefix Caching (continued)Case 1: The average total length of patches is (i Ti2)/2. Cost function:

Case 2: The average total length of patches from the server is i (Ti-vi)2/2, because the average number of arrivals in this time interval is i (Ti-vi) with average length of patch of (Ti-vi)/2.Cost function:

Multicast Merging with Prefix Caching (MMerge)Closest Target policy is adopted.Let pj be the probability of requiring a j-second prefix per unit of time for video i, 0jLi.