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Deriving a Good Trade-off BetweenSystem Availability and Time Redundancy
Nils [email protected]
System Software and Distributed Systems Group,Universitat Oldenburg, Germany
June 30, 2009
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 1 / 19
Table of contents
1 Motivation
2 New Availability Metric
3 Results from Analysis and Simulation
4 Conclusion
5 Future Work
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 2 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
Trade-off between time (steps to wait for intended service)and availability increase (to get intended service)in distributed systems
How much ddelay is desired? ⇒ as short as possible...
How available should your system be? ⇒ as high as possible...
What is a good trade-off in between delay and availability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 3 / 19
Orientation
masking nonmasking
self-stabilizing
t ime for stabil ization
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 4 / 19
Instantaneous Window Availability
request response
fault
masker
system
user
system
service unavailable service available
k+1k k+1k
request response
time redundancy
maximal
(a) (b)
k+2 k+w
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 5 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
Availability
Availability : A =MTTF
MTBF(1)
instantaneous availability: at some arbitrary time k the system isavailable: A(k)limiting availability: the same, as k approaches ∞analysis determines limiting, but for simulation we can only choosehigh kat some arbitrary point k, what are the chances that we get theintended (correct) service?and what would happen if the system fails but we can wait for atmost w timesteps for the system to recover?Instantaneous Window Availability (IWA): given that a system isnot available at k , what is the availability increase if we wait for atmost w steps?How many steps must one wait to achieve a certain overallavailability?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 6 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithm
convergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithm
convergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithm
convergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithm
convergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithm
convergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithm
convergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithm
convergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithmconvergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
a
b c
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithmconvergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
a
b c
a
d
e
b c
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
System Model
serial execution semantics
central demon/scheduler/monitor
shared memory model
perfect fault detection
fault model: transient faults strike mem register with static probability
distributed self-stabilizing algorithmconvergence: ∃t ≥ t0 : c(t) |= Pconsistency: ∀tl > tk : c(tk) |= P ⇒ c(tl) |= P
two systems:
a
b c
a
d
e
b c
distributed self-stabilizing breadth first search (BFS) [Dol00]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 7 / 19
Methods
1 Analysis: build state space (3p: 6561, 5p: ∼7 Billion), form IWA inPCTL with final argument, calculate with PRISM [KNP07]
P =?[F <= 100”state6523”{true}{min}]
2 Simulation: build system, execute n steps, see, if c(t) |= P, if not,count i until c(t + i) |= P [MDT08]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 8 / 19
Methods
1 Analysis: build state space (3p: 6561, 5p: ∼7 Billion), form IWA inPCTL with final argument, calculate with PRISM [KNP07]
P =?[F <= 100”state6523”{true}{min}]
2 Simulation: build system, execute n steps, see, if c(t) |= P, if not,count i until c(t + i) |= P [MDT08]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 8 / 19
Methods
1 Analysis: build state space (3p: 6561, 5p: ∼7 Billion), form IWA inPCTL with final argument, calculate with PRISM [KNP07]
P =?[F <= 100”state6523”{true}{min}]
2 Simulation: build system, execute n steps, see, if c(t) |= P, if not,count i until c(t + i) |= P [MDT08]
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 8 / 19
Results 3p System - Analysis
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.00
0.05
0.10
0.15
0.20
0.25
0.30
Analysis, 3 Processes, BFS
0.010.050.1
Window Size w, w > 0
IWA
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 9 / 19
Results 3p System - Simulation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.00
0.05
0.10
0.15
0.20
0.25
0.30Simulation, 3 Processes, BFS
0.010.050.1
Window Size w, w > 0
IWA
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 10 / 19
Results 3p System - Simulation - Standard Deviation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40Simulation, 3 Processes, BFS, μ±σ
0.010.050.1
Window Size w, w > 0
IWA
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 11 / 19
Results 3p System - Simulation - Standard Deviation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Comparison, 3 Processes, BFS, p(fault) = 0.01, μ±σ
Analysis
Window Size w, w > 0
IWA
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 12 / 19
Results 3p System - Simulation - Standard Deviation
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829300.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50Comparison, 3 Processes, BFS, p(fault) = 0.01, μ±2*σ
Analysis
Window Size w, w > 0
IWA
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 13 / 19
Comparison - Analysis & Simulation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.00
0.05
0.10
0.15
0.20
0.25
0.30Comparison, 3 Processes, BFS, p(fault) = 0.01
SimulationAnalysis
Window Size w, w > 0
IWA
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 14 / 19
Results 5p System - Simulation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.00
0.01
0.02
0.03
0.04
0.05
Simulation, 5 Processes, BFS300,000 Experiments
0.010.050.1
Window Size w, w > 0
IWA
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 15 / 19
Conclusion
Relation: IWA vs. Delay
Notion of IWA necessary to argue for trade-off.
Analysis & Simulation coincide well.
Limits of analysis (state space explosion) obvious,for simulation important for larger systems
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 16 / 19
Conclusion
Relation: IWA vs. Delay
Notion of IWA necessary to argue for trade-off.
Analysis & Simulation coincide well.
Limits of analysis (state space explosion) obvious,for simulation important for larger systems
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 16 / 19
Conclusion
Relation: IWA vs. Delay
Notion of IWA necessary to argue for trade-off.
Analysis & Simulation coincide well.
Limits of analysis (state space explosion) obvious,for simulation important for larger systems
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 16 / 19
Conclusion
Relation: IWA vs. Delay
Notion of IWA necessary to argue for trade-off.
Analysis & Simulation coincide well.
Limits of analysis (state space explosion) obvious,for simulation important for larger systems
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 16 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Future Work
1 Framework for the Automatic Derivation of Trade-off solutions
find Pareto-optimal solutionsmore dimensions (consistency, frequency, ...)distributed analysis to cope with complex systems
2 Real world experiments with WSNs: constistency vs. availability vs.energy consumption vs. collisions vs. code strength vs. delay vs. ...
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 17 / 19
Abhishek Dhama, Oliver E. Theel, and Timo Warns.Reliability and Availability Analysis of Self-Stabilizing Systems.In SSS, pages 244–261, 2006.
Shlomi Dolev.Self-Stabilization.MIT Press, Cambridge, MA, USA, 2000.
Nils Mullner, Abhishek Dhama, and Oliver Theel.Derivation of Fault Tolerance Measures of Self-Stabilizing Algorithmsby Simulation.In Proc. of AnSS’08, pages 183–192. April 2008.
Edsger W. Dijkstra.Self-Stabilizing Systems in Spite of Distributed Control.Commun. ACM, 17(11):643–644, 1974.
M. Kwiatkowska, G. Norman, and D. Parker.Stochastic Model Checking.InProc. of SFM’07, volume 4486 of LNCS (Tutorial Volume), pages220–270. Springer, 2007.
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 18 / 19
Thank your for your attention!
Questions?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 19 / 19
Thank your for your attention!
Questions?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 19 / 19
Thank your for your attention!
Questions?
Nils Mullner (Universitat Oldenburg) Trade-off: System Avbl vs Time Redundancy 19 / 19