Dynamic On-Line Group-Tree Matching: A Performance Study

Dynamic On-Line Group-Tree Matching:A Performance Study Jun-Hong Cui (UCONN) Li Lao (UCLA) M. Y. Sanadidi (UCLA) Mario Gerla (UCLA)

Outline • Motivation • Problem Formulation • A Generic Dynamic On-Line Algorithm (GDOA) • Complexity analysis • An upper bound • Performance Evaluation • Conclusions ISCC 2005, Spain

Background • Multicast • Efficient for multi-user applications • Multicast state scalability problem • Two issues: • Multicast forwarding state information in routers • Control overhead due to multicast tree maintenance • Aggravated when there are a large number of groups • Solution: • Aggregated multicast: solve both issues ISCC 2005, Spain

Aggregated Multicast • The key idea • Force multiple groups to share one aggregated tree • Multiplex and de-multiplex packets on edge routers • Perfect match vs. leaky match: • Perfect match: group and tree are same • Leaky match: tree is bigger than group • A trade-off • aggregation vs. bandwidth waste ISCC 2005, Spain

Aggregated Multicast D T0 (g0, g1) g0, g1: perfect match g2: leaky match B C E A (g0, g1, g2) (g0, g1, g2) Multicast Groups Aggregated Trees ISCC 2005, Spain

The Key Problem How to match groups to trees? ISCC 2005, Spain

Group-Tree Matching • Notations • Network model: G(V, E) • Multicast group g • Native Tree: tn(g) • Bandwidth waste of using t: • Aggregation Degree: • Goal • Maximize aggregation degree AD for a given bandwidth waste threshold bth ISCC 2005, Spain

Problem Formulation (I) • Static Pre-defined Trees • Assume all the groups are known in advance • Input: G(V, E), grps, and bth • Output: a minimum number of trees T such that every group is covered by at least one tree without violating bth and AD is maximized • Useful for multicast pre-provisioning based on long-term traffic measurement • Proved to be NP-complete ISCC 2005, Spain

Problem Formulation (II) • Dynamic On-Line Trees • Groups dynamically join and leave • Establish, modify and tear down a set of trees and assign a group to a tree (without violating bth), such that the number of trees is minimized • Useful for on-line systems • This is the problem we focus on • We present a generic dynamic on-line algorithm • GDOA ISCC 2005, Spain

GDOA (I) • Dynamic Join (g) • For each existing tree t • If (tcan cover g without exceeding bth) • tis a candidate tree • Else • t is extended to te to cover g • te becomes a candidate tree if it satisfies the bandwidth requirement for the remaining groups matched to it • If there is at least one candidate tree • The one with the minimum bandwidth waste is selected • Else • A new tree is computed ISCC 2005, Spain

Example F g2 bth = 1 g1 g0 D T0 B C E A g0 g1 g2 g0 g2 Multicast Groups Aggregated Trees ISCC 2005, Spain

GDOA (II) • Dynamic-Leave (g) • Identify the tree t which covers g • Shrinktif possible • For each group g’covered by t • Mark all the nodes used to deliver data for g’ • Delete all unmarked nodes from t ISCC 2005, Spain

Example F (g0, g1) (g0) (g0) D T0 B C E A (g1) (g0) (g0, g1) Multicast Groups Aggregated Trees ISCC 2005, Spain

An Upper Bound • Difficult to obtain optimal solution due to dynamics • Our idea: run an optimal Static Pre-defined Tree algorithm whenever groups join and leave • A Greedy algorithm (UBAA-Greedy) • For each group, enumerate all possible trees • Candidate trees • Identify the groups covered by each candidate tree • Determine the minimum set of trees that cover all the groups – equivalent to Minimum Set Cover • UBAA-Greedy provides near-optimal solutions ISCC 2005, Spain

Compare Dynamic Heuristics • GDOA • Simple-GDOA (ASSM) [GLOBECOM’02] • A simplified version of GDOA • No tree extension and shrinking • MTBF [GLOBECOM’02] • For a domain with ne edge routers, ne aggregated trees, with each rooted at one edge router • Groups with the same source edge router share one tree • Add Filters in routers to stop unnecessary data forwarding • More filters equivalent to more group state ISCC 2005, Spain

MTBF Filter • The aggregated trees do not take group member distribution into consideration • If a group is small compared with the aggregated multicast tree, a lot of filters need to be installed F g2 g1 g0 D T0 B C E A g0 g1 g2 g2 g0 ISCC 2005, Spain

Performance Evaluation • Network topology • AT&T backbone network with 54 nodes • Group membership • Random Node Weighted Model • Performance metrics • Aggregation Degree • State Reduction Ratio • Tree Control Overhead • Compare GDOA, Simple-GDOA, MTBF ISCC 2005, Spain

How Good is GDOA? ISCC 2005, Spain

GDOA vs. Simple-GDOA ISCC 2005, Spain

GDOA vs. MTBF ISCC 2005, Spain

Conclusions • We formulate the group tree matching problem • We propose a generic dynamic on-line algorithm (GDOA) • We provide an approach to determine the upper bound on the performance of GDOA • We quantitatively compare the performance of GDOA and some existing dynamic heuristics ISCC 2005, Spain

Dynamic On-Line Group-Tree Matching: A Performance Study