1. Clean Slate Project On the Optimality and Interconnection of VLB Networks Moshe Babaioff and John Chuang UC Berkeley IEEE INFOCOM 2007 Anchorage, Alaska, USA May 8, 2007

2. Clean Slate Project Babaioff & Chuang 20072 Main Points Universal optimality of Valiant Load Balancing (VLB) network under node failures (in paper) Interconnection of multiple VLB networks –Interconnection challenges –Generalization: m-hubs VLB –Support peering and transit relationships

3. Clean Slate Project Babaioff & Chuang 20073 Many challenges: –Traffic matrix can change over short and long timescales –Customers expect high availability and low congestion –Network operator must design for low congestion and high fault tolerance over the lifetime of the network Backbone Network Design 1 2 3 n … 4 r r r r r Network? r

4. Clean Slate Project Babaioff & Chuang 20074 Valiant Load-Balancing (VLB) [Zhang-Shen & McKeown; Kodialam et. al.] Clean-slate approach to backbone design: –Design a network that supports any legal traffic matrix (f ij ) i,j Input: –n : the number of nodes –r : bound on each node’s ingress and egress rates (hose model) Output: A network that supports any legal traffic matrix on the n nodes: –Capacity c ij on each edge (i,j) –A routing scheme that respects the edge capacities

5. Clean Slate Project Babaioff & Chuang 20075 f ij : rate from i to j Σ j f ij ≤r, Σ i f ij ≤r Two-stage routing of f ij : 1.i sends f ij /n to each node k 2.k forwards to j For any legal traffic matrix, flow of at most: Σ j f ij /n ≤r/n per stage per edge Total capacity: 2r(n-1) is optimal Additional results for heterogeneous nodes, fault tolerance Valiant Load-Balancing (VLB) [Zhang-Shen & McKeown] 1 2 3 n … 4 r r r 2r/n 1

6. Clean Slate Project Babaioff & Chuang 20076 VLB Interconnection How should multiple VLB networks interconnect with one another? –How to generalize the load- balancing routing algorithm –How to support different interconnection relationships, e.g., transit and peering –Are the efficiency and robustness properties of a single VLB network retained? 1 2 36 54 B C E A D ? ? ?

7. Clean Slate Project Babaioff & Chuang 20077 VLB Generalization: m-hubs VLB Each stream is equally load- balanced on m nodes (the hubs) –n-hubs = VLB –1-hub = star Fact: any m-hubs network can support any legal traffic matrix, and it has optimal network capacity of 2r(n-1). Capacity: 2(n-m)m (r/m) + m(m-1) (2r/m) = 2r(n-1) 2r/m r/m

8. Clean Slate Project Babaioff & Chuang 20078 Two networks connect at a set of m shared locations Network x has n x nodes, each with homogeneous rate of r x (possibly n 1 ≠n 2 and r 1 ≠r 2 ) There is a bound of R p on the total interconnection rate to/from a network Peering of Two Networks 1 2 36 54 B C E A D

9. Clean Slate Project Babaioff & Chuang 20079 “Two m-hubs VLB Peering Network” Two m-hubs VLB networks peering at the hubs 3-stage routing scheme: 1.traffic load balanced on the m hubs 2.traffic sent across peering edges 3.traffic delivered to destination Each network x has optimal capacity: 2r x (n x -1) Capacity of R p /m on each of the 2m directed peering edges –Total interconnection capacity of 2R p (optimal) 1 2 36 54 B C E A D

10. Clean Slate Project Babaioff & Chuang 200710 Peering of 2 Networks: Results Theorem: The “two m-hubs VLB peering network” can support any legal traffic matrix and has minimal capacity in each network and minimal interconnection capacity. Result extends to q>2 networks in the case of universally shared locations: all networks share m>0 locations Extension to node failures

11. Clean Slate Project Babaioff & Chuang 200711 Interconnection without Universally Shared Locations With three or more VLB networks, it may be infeasible to require a set of interconnection points universally shared by all networks –Networks have different coverage areas –Raises entry barrier for new networks; reduces evolvability Consider alternate VLB interconnection schemes –Transit vs. peering schemes –Note: routing stages will have to increase

12. Clean Slate Project Babaioff & Chuang 200712 1.Traffic load-balanced on local hubs 2.Traffic forwarded to peering nodes for destination network 3.Traffic sent across peering edges 4.Traffic load-balanced on destination network’s hubs 5.Traffic delivered to destination node VLB Bilateral Peering x1x1 x2x2 x3x3 xqxq 1.Traffic load-balanced on local hubs 2.Traffic forwarded to peering nodes for destination network 3.Traffic sent across peering edges 4.Traffic load-balanced on destination network’s hubs 5.Traffic delivered to destination node q: # of networks : hubs : data : destination

13. Clean Slate Project Babaioff & Chuang 200713 VLB Bilateral Peering Capacity for each network x: C x =2r x (n x -1)+2R p (q-2) (within constant factor of optimal) Interconnection capacity: R p (q-1)q (optimal for peering) RpRp RpRp RpRp RpRp RpRp x1x1 x2x2 x3x3 xqxq q: # of networks : hubs : data : destination

14. Clean Slate Project Babaioff & Chuang 200714 1.Traffic load-balanced on local hubs 2.Traffic forwarded to transit network Z 3.Traffic load-balanced on transit hubs 4.Traffic forwarded to peering nodes 5.Traffic forwarded to destination network (destination hubs) 6.Traffic delivered to destination node x q-1 VLB Transit (“VLB over VLBs”) z (transit) x1x1 x2x2 1.Traffic load-balanced on local hubs 2.Traffic forwarded to transit network Z 3.Traffic load-balanced on transit hubs 4.Traffic forwarded to peering nodes 5.Traffic forwarded to destination network (destination hubs) 6.Traffic delivered to destination node q: # of networks : hubs : data : destination

15. Clean Slate Project Babaioff & Chuang 200715 x q-1 VLB Transit (“VLB over VLBs”) Capacity of stub network x: 2r x (n x -1) Capacity of transit network z: 2r z (n z -1)+2R p (q-2) Interconnection capacity: 2R p (q-1) Theorem: Any interconnection network by a transit network must have at least these capacities in each network and at least as much interconnection capacity. Proves the optimality of VLB as the transit scheme. RpRp RpRp RpRp RpRp RpRp z (transit) x1x1 x2x2 q: # of networks : hubs : data : destination

16. Clean Slate Project Babaioff & Chuang 200716 VLB Peering vs. Transit Scheme Capacity PeeringTransit Intra- network Each network x: 2r x (n x -1)+2R p (q-2) (max (2r x (n x -1),R p (q-2)/2) is necessary for any interconnection by peering) Stub x: 2r x (n x -1) Transit z: 2r z (n z -1)+2R p (q-2) Inter- connection 2R p (q-1) q/2 (necessary for interconnection by peering) 2R p (q-1) (necessary for any interconnection by transit) Total S + 2R p (q-2)qS + 2R p (q-2) S= Σ y 2r y (n y -1)  Transit scheme more scalable in number of networks (q)

17. Clean Slate Project Babaioff & Chuang 200717 Summary Established universal optimality of VLB under node failures (not presented today) Generalized m-hubs VLB network serves as building block for VLB interconnection –m-hubs VLB design retains desirable properties of VLB while allowing diverse VLB networks to interconnect –Can support both peering and transit relationships –Established optimality for VLB transit, and within constant factor of optimality for VLB peering Open questions: –Support simultaneous transit and peering –Fault tolerance: failure of nodes, edges, transit networks –Strategic interaction between VLB networks