Cloud Computing in Space Jiangchuan Huang Systems Engineering, UC Berkeley, [email protected]

Christoph M. Kirsch Computer Sciences, University of Salzburg, Austria, [email protected]

Jiangchuan Huang

Raja Sengupta Systems Engineering, UC Berkeley, [email protected]

April 25, 2015

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Tasks Arriving in Time and Space K customers. Task = (Arrival time, Location, Size). M vehicles (real vehicles). Performance metrics: Average waiting time, Total distance traveled.

Applications. I I I Jiangchuan Huang

Map building, e.g., Google street view. Unmanned aerial vehicle based sensing. Mobile sensor network.

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Tasks Arriving in Time and Space

Traditional Vehicle Routing Problem [2], no performance isolation. I I I

Time, e.g., First Come First Served [1]. Location, e.g., Nearest Neighbor [1]. Size, e.g., Shortest Job First [5].

Customer 1: Customer 2:

0 1

0 2

0 3

0 4

0 5

0 6

0 7

0 8

0 9

In cloud computing, performance isolation (PI) means the resource consumption of one VM (customer) should not impact the promised guarantees to other VMs (customers) on the same hardware [3]. Jiangchuan Huang

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The Virtual Vehicle (VV) A VV with virtual speed v V is a replica of a real vehicle (RV) with speed v V . C11!

C11!

L11! RV1!

VV1!

RV5!

RV1!

C12!

C24! VV2! 2 C 3!

TM12!

D11!

L12!

C22!

RV5! C13!

C22!

TM13!

C21!

RV4!

(a) Customer View!

D12!

C12!

C24! VV2! 2 C 3!

L13!

C21!

RV2!

VV1!

C13! D13! RV3!

(b) Provider View!

Cyber-mobility, migrate between RVs. Physical mobility, move with an RV. Theorem 1: Each VV is a GI /GI /1 queue. I Jiangchuan Huang

virtual departure time (virtual deadline).

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Virtual Vehicle Queues and Real Vehicle Queues Virtual vehicle and virtual deadline create a soft real-time system. I I

Tardiness (TD) = max {Actual completion time - Virtual deadline, 0}. Delivery prob (DP) = Pr (Actual completion time  Virtual deadline).

Low TD and high DP indicate high performance isolation. Voronoi allocation: Theorem 2: Each RV is a ⌃GI /GI /1 queue. Tdead11 Tdead12 Tdead13! Ta11! Ta12! Ta13!

VV1# GI/GI/1#

Ta(11)! Ta(12)! Ta(13)!

Tak2! Tak3!

VVk" GI/GI/1#

t!

RV1# ΣGI/GI/1#

Tdead(m1) Tdead(m2) Tdead(m3)!

Tdeadk1 Tdeadk2 Tdeadk3! Tak1!

Tcomp(11) Tcomp(12) Tcomp(13)!

Tdead(11) Tdead(12) Tdead(13)!

t!

Voronoi## Alloca1on#

Ta(m1)! Ta(m2)!

Ta(m3)!

TaK1! TaK2! TaK3!

Jiangchuan Huang

VVK" GI/GI/1#

Ta(M1)!

Ta(M1)! Ta(M1)!

Tcomp(m1) Tcomp(m2) Tcomp(m3)!

RVm" ΣGI/GI/1#

Tdead(M1) Tdead(M2) Tdead(M3)! TdeadK1 TdeadK2 TdeadK3!

t!

t!

Tcomp(M1) Tcomp(M2) Tcomp(M3)!

RVM" ΣGI/GI/1#

t!

t!

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Gain, Migration Cost and Performance Isolation Gain:  = I I

#VVs #RVs ,

v V = v R . Two ways a provider can gain ( > 1):

Multiplexing gain, a customer may not utilize her virtual vehicle fully. Migration gain, the provider gains by migrating the VV hosting the task to another RV closer to the task location.

Migration cost (MC) = # bits of the VV * inter-distance * 1{migration} / inter-virtual departure time. I I

The migration cost has the same unit (bit-meters/second) as in [4]. Theorem 5: The migration cost is bounded.

Results I I

Jiangchuan Huang

A VV performs as well as an RV with high performance isolation. The provider can support a given number of VVs with significantly fewer RVs while guaranteeing high performance isolation and bounded migration cost.

Systems Engineering, UC Berkeley, Cloud Computing [email protected] in Space April Christoph 25, 2015 M. Kirsch 6 / 13 Com

CPCC System!

Allocation and Scheduling Policies •  # Customers (VV’s): K.! # Real Vehicles (RV’s): M.! Voronoi• allocation. !!!!!! {Ta1i}!

{Taki}!

RV1! RV2! RV4! Cki-1!

{TaKi}!

RV5!

{Td1i}! RV7!

RV3! Lki! Cki! RV6!

Dki!

{Tdki}! RV8! {TdKi}!

Scheduling: I I I

Earliest Virtual Deadline First (EVDF), task size known. Earliest Dynamic Virtual Deadline First (EDVDF), task size not known. Credit scheduling policy, task size not known.

Theorem 3 (Optimality): The EVDF achieves minimum tardiness. Jiangchuan Huang

Systems Engineering, UC Berkeley, Cloud Computing [email protected] in Space April Christoph 25, 2015 M. Kirsch 7 / 13 Com

Worst-Case Arrival Process

η"Arrival)Process)

The ⌘-arrival process: Arrival(i) = Virtual departure(i d1!

d2!

d3!

d4!

⌘). d5!

η = 1! Ta1!

Ta2! d1!

Ta3! d2!

Ta4! d3!

t!

Ta5! d4!

d5!

d4!

d5!

η = 2! Ta1, Ta2!

Ta3! d1!

Ta4! d2!

t!

Ta5! d3!

η = 3! Ta1, Ta2, Ta3!

Ta4!

Ta5!

t!

Theorem 4 (Worst-case): Assume the EVDF, the ⌘ = 1 process achieves maximum tardiness among all the renewal processes. I

Jiangchuan Huang

The VV is fully utilized under the ⌘ = 1 process, thus the gain observed is migration gain only.

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Performance Isolation - # RVs - Gain EVDF: Tardiness − M −κ Relation when η = 1 and TS =0 ki

EVDF: Delivery Probability − M − κ Relation when η = 1 and TS =0 ki

Delivery probability, DP

700%

Tardiness, TD

600% 500% 400% 300% 200% 100% 0% 10 8

100 6

1

0.8

0.6

0.4

0.2

0 10 8

100 6

80 60

4

40

2

20 0

# VVs / # RVs, κ

80 60

4

40

2 0

# VVs / # RVs, κ

# RVs, M

EVDF: Migration Cost − M − κ Relation when η = 1 and

TS ki

20 0

0

# RVs, M

=0

Migration cost, MC

1.005

1

0.995

0.99

0.985

0.98 10 8

100 6

80 60

4

40

2

# VVs / # RVs, κ

Jiangchuan Huang

20 0

0

# RVs, M

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Performance Isolation - # RVs - Gain EVDF: Contour of Tardiness when η = 1 and TS =0 ki

EVDF: Contour of Delivery Probability when η = 1 and TS =0 ki 10

9

9

8

5 0.0 0.02

κc

7

# VVs / # RVs, κ

5 2 0.0 0.0 0.01

6

5

5 02 1 0.0 0. 0.0

4

0.9

6

95

9 0.

4

0.

20

30

40

50

60

70

80

90

1

100

10

5

0.0 5 0.0 2 0. 01

2

10

20

30

40

# RVs, M S

V

EVDF: Contour of Tardiness when η = 1 and E[T ] = E[L] / 4v

70

80

90

100

3.5

κc < 5

κc < 5 3

2.5

0.05

0.05

2

5

05

0.0

05 0.

10

20

0

2 .0

30

40

2.5

2

0.9

2

0.9

0.0

2 0.0

0.

1.5

# VVs / # RVs, κ

3

# VVs / # RVs, κ

8 0.9 60 50 # RVs, M

EVDF: Contour of Delivery Probability when η = 1 and E[TS] = E[L] / 4vV

3.5

Jiangchuan Huang

98

0.

3

2

1

5

0.9

5

3

1

0.9

κc

7

0. 9

# VVs / # RVs, κ

8

0.9

10

1.5

0.0

1 .0

50 0 60 # RVs, M

70

9

0.

1

80

90

100

1

10

20

9 0.

30

40

50

60

5 0.9 70

0.95 80

90

100

# RVs, M

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Comparison of EVDF, EDVDF and Credit For a given # RVs and a guaranteed performance isolation. I I

EVDF achieves higher gain than EDVDF. EDVDF achieves higher gain than the credit scheduling policy.

EVDF, EDVDF and Credit: Contour of Tardiness

EVDF, EDVDF and Credit: Contour of Delivery Probability 2

EVDF EDVDF Credit

2.2

0.05 0.05

1.8

5 0.0 0.05

# VVs / # RVs, κ

0.05 0.02 0.02

0.05

5 00..005

0.9 0.9 0.9

1.7

1.8

02 2 0.0 .0

1.4

5 0.0

0.02

1.6

0.09.9.9 0

1.5 1.4 1.3 1.2

1

10

Jiangchuan Huang

20

30

50

00..99

1.1

0.02 40

60

# RVs, M

70

80

90

100

1

.955 00.9

0.

05

202 0.00.

9

1.2

0.

# VVs / # RVs, κ

2

1.6

EVDF EDVDF Credit

1.9

10

20

30

40

50

60

70

0.95 80

90

100

# RVs, M

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Conclusion and Acknowledgements Conclusion I I I I

I

The migration gain is significantly high while guaranteeing high PI. The migration gain increases with # RVs while guaranteeing the same PI. The migration cost is bounded. The virtual vehicle concept works best when the task sizes are small and the vehicle spends more time traveling to tasks than it does standing still. EVDF has better performance than EDVDF, and EDVDF has better performance than the credit scheduling policy.

Research supported in part by I I

Jiangchuan Huang

The National Science Foundation (CNS1136141) The National Research Network RiSE on Rigorous Systems Engineering (Austrian Science Fund S11404-N23).

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Dimitris J Bertsimas and Garrett Van Ryzin. A stochastic and dynamic vehicle routing problem in the euclidean plane. Operations Research, 39(4):601–615, 1991. G. B. Dantzig and J. H. Ramser. The truck dispatching problem. Management Science, 6(1):pp. 80–91, 1959. Diwaker Gupta, Ludmila Cherkasova, Rob Gardner, and Amin Vahdat. Enforcing performance isolation across virtual machines in xen. In Proceedings of the ACM/IFIP/USENIX 2006 International Conference on Middleware, pages 342–362. Springer-Verlag New York, Inc., 2006. P. Gupta and P.R. Kumar. The capacity of wireless networks. Information Theory, IEEE Transactions on, 46(2):388–404, 2000. Adam Wierman. Scheduling for today’s computer systems: bridging theory and practice. PhD thesis, Pittsburgh, PA, USA, 2007.

Jiangchuan Huang

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Jiangchuan Huang

Thanks!

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