Response Time-Optimized Distributed Cloud Resource Allocation

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1 Response Time-Optimized Distributed Cloud Resource Allocation Matthias Keller Holger Karl Computer Networks Group Universität Paderborn

2 Minimizing response times Latency-critical service Interactive, emergency service request t Response Time answer 21

3 Minimizing response times Latency-critical service Interactive, emergency service request t Response Time Time to compute the answer answer 22

4 Minimizing response times request Response Time answer t Queuing System: Time in Queue + Processing Time Time in System (TIS) 23

5 Minimizing response times Latency-critical service Interactive, emergency service Decision: Spend time on RTT or TIS request t Queuing System: Response Time answer Time in Queue + Processing Time Time in System (TIS) 24

6 Minimizing response times Latency-critical service Interactive, emergency service Decision: Spend time on RTT or TIS request Response Time Time in System (TIS) answer 25

7 Example: RTT + TIS Demand assignment Facility Location Solution with RTT only average response time Better RTT solution arrival rate 26

8 Example: RTT + TIS Demand assignment Facility Location Solution with RTT only average response time Better RTT solution RTT solution with TIS arrival rate 27

9 Example: RTT + TIS Demand assignment Facility Location Solution with RTT only average response time Better RTT solution RTT solution with TIS Surprise at runtime arrival rate 28

10 Example: RTT + TIS Demand assignment Facility Location Solution with RTT only With RTT + TIS average response time Better RTT solution RTT solution with TIS RTT+TIS solution arrival rate 29

11 Goal Given Network Data centres Objective Minimize response time Means Allocation of n VMs at data centres 30

12 Goal Given Network Data centres Objective Minimize response time Means Allocation of n VMs at data centres Characterise: How does response time depend on number n of VMs? Response Time Optimal Solutions Number of VMs 31

13 Two Approaches Accurate Solution Mixed Integer Convex Problem Convex TIS function for each data centre time in system utilization Tough to solve slow? 32

14 Two Approaches Accurate Solution Mixed Integer Convex Problem Convex TIS function for each data centre Approximate Solution Reformulation: Mixed Integer Linear Problem Linearization of TIS function time in system time in system original uniform utilization Tough to solve slow? utilization Accuracy? Speed? 33

15 Improve accuracy of linearization Objective: Minimize the maximum difference Control knobs Number of basepoints End point at asymptote Basepoint positions time in system difference to org Better original uniform utilization

16 Improve accuracy of linearization Objective: Minimize the maximum difference Control knobs Number of basepoints End point at asymptote Basepoint positions Evaluation in Paper time in system difference to org Better original uniform imamoto utilization

17 Evaluation of both approaches Convex Problem Reference Solution Tough to solve slow? Linear Problem Approximate Solution Accuracy? Speed? Linearization 36

18 Evaluation of both approaches Convex Problem Reference Solution Tough to solve slow? Linear Problem Approximate Solution Accuracy? Speed? Linearization Configurations 6 topologies, nodes à 50 random demand realizations 10 data centre fix 37

19 Evaluation of both approaches Convex Problem Reference Solution Tough to solve slow? Linear Problem Approximate Solution Accuracy? Speed? Linearization VM limit: 5 10 Configurations 6 topologies, nodes à 50 random demand realizations 10 data centre fix 38

20 Results Approximation Ratio 1.16 approx. ratio = Resp.time Linear Resp.time Convex approximation ratio Better 1.00 dfn-bwin small di-yuan norway topology atlanta zib54 ta2 large 39

21 Results Approximation Ratio 1.16 approx. ratio = Resp.time Linear Resp.time Convex approximation ratio Better 1.00 dfn-bwin small di-yuan norway topology atlanta zib54 ta2 large 40

22 Results Runtime Ratio 10 0 runtime ratio = Runtime Linear Runtime Convex runtime ratio Better 10-4 dfn-bwin small di-yuan norway topology atlanta zib54 ta2 large 41

23 Results Runtime Ratio 10 0 runtime ratio = Runtime Linear Runtime Convex runtime ratio Better Runtime Linear Runtime Convex s 0:28h dfn-bwin small di-yuan norway atlanta 7s 1:03h 5s topology 1:15h zib54 ta2 large 42

24 Results Runtime Ratio 10 0 runtime ratio = Runtime Linear Runtime Convex runtime ratio Better Runtime Linear Runtime Convex s 0:28h dfn-bwin small di-yuan norway atlanta 7s 1:03h 5s topology 1:15h zib54 ta2 large 43

25 Results Optimal Solutions More Resources: Shorter time in queuing system VMs at closer data centres Response Time (ms) RTT TIS di-yuan norway dfn-bwin Resource Limit (#VM) 44

26 Results Optimal Solutions More Resources: Shorter time in queuing system VMs at closer data centres Response Time (ms) RTT TIS di-yuan norway dfn-bwin Resource Limit (#VM) 45

27 In the paper Convex/Linear Problem Formulation Facility Location Problem & queuing model P-median facility location + convex cost function P-median facility location + piecewise linear cost function Piecewise Linear Function: Minimize maximal difference Convexity Proof Evaluation Pareto optimal solutions Compare linear/convex problem Approx. Ratio Runtime 46

28 In conclusion adjust your latency-sensitive service: Faster! Adapt to demand fluctuations swiftly Accurate! With queuing delay no surprises at runtime 47

TIMELY: RTT-based Congestion Control for the Datacenter

TIMELY: RTT-based Congestion Control for the Datacenter Authors: Radhika Mittal(UC Berkeley), Vinh The Lam, Nandita Dukkipati, Emily Blem, Hassan Wassel, Monia Ghobadi(Microsoft), Amin Vahdat, Yaogong