Online Path Computation & Function Placement in SDNs

Transcription

1 Online Path Computation & Function Placement in SDNs Guy Even Tel Aviv University Moti Medina MPI for Informatics Boaz Patt-Shamir Tel Aviv University

2 Today s Focus: Online Virtual Circuit Routing Network: G = V, E, c V is the set of nodes E is the set of links c: E N + edge capacities Requests: paths r j = s j, t j, b j, d j, α j, β j s j source node t j destination node b j benefit (per time step) d j BW requirement α j, β j arrival/depart times β j is either known or unknown upfront. r 1 = r 2 = load(e) flow(e)/c(e)

3 Performance Measure - Competitive Ratio [Sleator, Tarajan 85] ALG : Online alg σ : sequence of path requests ALG σ : total benefit due to σ OPT σ : Max benefit from σ by a feasible allocation ρ ALG inf σ ALG(σ) OPT(σ)

4 unknown Duration known Online Versions ACC/REJECT Model ACC/STDBY Benefits: ACC/REJECT = accepted b j ACC/STDBY= t accepted(t) b j? [AAP93] C. R. = log V b max Tight Unbounded C. R. time Same as? ACC/REJECT New: C. R. = log V b max Known duration only arrivals (persistent requests)

5 Proposal: ACC/STDBY model r j arrives Unknown duration Active ACCEPT Route? STDBY Active? No preemption (!) No rerouting (!) Request pays b j per served time unit. end end Question: what about online competitive analysis?

6 unknown Duration known Online Versions ACC/REJECT Model ACC/STDBY Benefits: ACC/REJECT = accepted b j ACC/STDBY= t accepted(t) b j [AAP93] C. R. = log V b max Tight Unbounded C. R. time Same as ACC/REJECT New: C. R. = log V b max Tight Known duration only arrivals (persistent requests)

7 Online Persistent Routing Algorithm [AAP93] (known duration, ACC/REJ) State: accepted requests r j, path j acc. r j arrives: r j arrives Path Oracle REJECT Oracle(r j ) w e = exp(load(e)) Search for a path s j t j s.t. e pathj w(e) < b j Success: return(path j ) Fail: REJECT ACCEPT Allocate path j to r j load(e) flow(e)/c(e)

8 Our Algorithm (unknown duration, ACC/STDBY) State: accepted requests r j, path j, acc. STDBY list. r j arrives: r j arrives Path Oracle STDBY Active? Oracle(r j ) w e = exp(load(e)) Search for a path s j t j s.t. e pathj w(e) < b j Success: return(path j ) Fail: STDBY active ACCEPT Allocate path j to r j end end load(e) flow(e)/c(e)

9 Main Result (virtual circuit routing version) Thm. Small demands in each time step t, benefit t ALG benefit t OPT log V b max. Remarks: 1. Small demands: d max c min log V b max. 2. If served, request is served continuously until it ends. 3. Even when OPT is fractional, may preempt, may reroute, i.e., MCF in every time step. 4. Proof idea: repeating the game of persistent routing. 5. Asymptotically optimal! 6. Extends to the SDN modeling (next slide).

10 Modeling SDN Single source packets arrive from here Req served by any s t path. Needs mapping to N Network N = V, E V set of servers E set of links c: V E N + i.e, Processing, BW Online requests r j = G j, d j, b j, U j G j = (X j, Y j ) PR-graph d j : X j Y j N demand b j N + : benefit per served time step U j : X j Y j 2 V 2 E mapping Can be implemented by U x 1 = {v 17, v 23, v 97, } e can be implemented by v 0 p v k if i v i 1, v i U(e) PR-graph Action vertices enc/dec, comp/decomp s j x 1 x 2 x 3 e x 4 t j Single sink packets are destined to here

11 Examples Simple Routing I want to route a connection of 100 mbps from v to v PR-graph s e t U s = {v}, U t = {v }, U e = E, d e = 120 mbps Serial Processing Stream, Pass k transformations a 1,, a k in series. PR-graph s a 1 a k t U a i V implements a i Can model BW changes E.g., a j is COMPRESS. How? Set diff demands to diff PRedges.

12 Summary Need to allocate network resources in online fashion. Each request specifies sequence(s) of functions. Map desired functions to real network devices. Route the request between these devices. Security: want to avoid some nodes. Flexibility: customer does not want to commit to the duration upfront the duration is unknown. Maximum benefit: maximizing the benefit rate.

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