How to use SHARPE and SPNP - Duke...

How to use SHARPE and SPNP

Dr. Dan (Dong-Seong) Kim

University of Canterbury, New Zealand

[email protected] http://www.cosc.canterbury.ac.nz/dongseong.kim

mailto:[email protected]

University of Canterbury

University of Canterbury (UC) • originated in 1873 in the centre of Christchurch as

Canterbury College, the first constituent college of the University of New Zealand

• Ernest Rutherford – physicist – Nobel Prize in chem.

• John Key– politician currently Prime Minister of New Zealand

Computer Science and Software Engineering department at UC has been ranked in the top 101-150 Computer Science departments in the 2011 International QS World University Rankings.

http://en.wikipedia.org/wiki/Christchurchhttp://en.wikipedia.org/wiki/University_of_New_Zealandhttp://en.wikipedia.org/wiki/University_of_New_Zealandhttp://en.wikipedia.org/wiki/Ernest_Rutherfordhttp://en.wikipedia.org/wiki/John_Keyhttp://en.wikipedia.org/wiki/John_Keyhttp://en.wikipedia.org/wiki/Prime_Minister_of_New_Zealandhttp://en.wikipedia.org/wiki/Prime_Minister_of_New_Zealandhttp://en.wikipedia.org/wiki/Prime_Minister_of_New_Zealandhttp://www.topuniversities.com/university-rankings/world-university-rankings/2011/subject-rankings/technology/computer-science-information-systems?page=4http://www.topuniversities.com/university-rankings/world-university-rankings/2011/subject-rankings/technology/computer-science-information-systems?page=4

About myself

Lecturer (Assistant Professor in US) since Aug. 2011 • Full time/permanent

• Computer science and software engineering Dept.

• Research/teaching: Computer and Network Security

Postdoc at Duke U. from June 2008- July 2011 • (Kishor S. Trivedi group)

U of Maryland, USA in 2007 • Virgil D. Gligor group (former ACM SIGSAC chair)

Studied at KAU in Korea (BS, MS, PhD) • JongSou Park group (Penn. State PhD)

Security

Hardware/ Software

Network

Ubiquitous computing

Cyber physical systems

Intrusion Detection /Tolerance systems

Sensor Nets Dependability and Security

Cloud/VDC

Fault tolerance Reliability of Sat./UAV

Embedded System

REASSURE analysis (REliability, Availability, Security, SUrvivability, REsilience)

Smart Grid

Outline - SHARPE

Brief Intro. To SHARPE

Download

Analytic Modeling using SHARPE • Non-state space models

o Reliability Block Diagram (RBD)

o Fault Tree

o Reliability Graph

• State space models o Continuous Time Markov Chains (CTMC)

o Stochastic Petri nets/Stochastic Reward nets

• Hierarchical Models

• Others

6/81

Copyright © by Kishor S. Trivedi

Health & Medicine

Communication

Avionics

Entertainment Banking

Motivation: Dependence on Computer Systems

Dependability– An umbrella term

Trustworthiness of a computer system such that reliance can justifiably be placed on the service it delivers

Dependability

Attributes

Availability Reliability Safety Maintainability

Fault Prevention Fault Removal Fault Tolerance Fault Forecasting

Means

Threats Faults Errors Failures

IFIP WG10.4

Failure occurs when the delivered service no longer complies with the desired output.

Error is that part of the system state which is liable to lead to subsequent failure.

Fault is adjudged or hypothesized cause of an error.

Faults are the cause of errors that may lead to failures

Fault Error Failure

Reliability Availability

Dependability Measures

Dependability Attributes or Measures

• Reliability: “The ability of a system to perform a required function

under given conditions for a given time interval.” No recovery is

assumed after system fails (there can be recovery after a component

failure)

• Availability: “The ability of a system to be in a state to perform a

required function at a given instant of time or at any instant of time

within a given time interval.“

Reliability, Availability, Performance

Reliability-Based

• Availability: Steady-state, Transient, Interva

Downtime

• Reliability: R(t), System MTTF

Performance

• Throughput, Loss Probability, Response Time

“Does it work, and for how long?''

“Given that it works, how well does it work?''

Composite Performance and Availability

Need Techniques and Tools That Can Evaluate • Performance, Availability and Their

Combinations

“How much work will be done(lost) in a

given interval including the effects of

failure/repair/contention?''

Performability

Methods of Evaluation

Measurement-Based

• Most believable, most expensive

• Not always possible or cost effective during system

design

Model-Based

• Less believable, Less expensive

• Discrete-Event Simulation vs. Analytic

Numerical solution tool

Close-form

solution

Evaluation Methods

Model-based

Discrete-event simulation

Hybrid

Analytic Models

Quantitative evaluation

Measurement-based

Overview of SHARPE

SHARPE: Symbolic-Hierarchical Automated Reliability and Performance Evaluator

Well-known modeling tool (Installed at over 300 Sites; companies and universities)

Combines flexibility of Markov models and efficiency of combinatorial models

Ported to most architectures and operating systems

Used for Education, Research, Engineering Practice

Overview of SHARPE (cont.)

Graphical User Interface is now available

Used for analysis of performance, dependability

and performability

Hierarchy facilitates largeness & stiffness

avoidance

Steady-state as well as transient analysis

Written in C language

Architecture of SHARPE

Fault tree

Reliability graph

Reliability

Block

Diagrams

Task graph Pfqn, Mfqn

Hierarchical & Hybrid Compositions

Semi-Markov chain

Markov chain

Petri net

(GSPN & SRN)

Availability/Reliability Performance Performability

Non-state space models

Analytic models

Non-state space model types

Series Parallel reliability block diagrams

(RBDs)

Non-SP reliability block diagrams

(reliability graph: Relgraph)

Fault trees (FTs)

Fault trees with repeated events

Non-state space models (cont.)

Reliability block diagrams, Fault trees and

Reliability graphs

• Commonly used for reliability and availability

• These model types are similar in that they capture

conditions that make a system fail in terms of the

structural relationships between the system

components.


Non-state space modeling techniques (like RBDs, relgraphs and FTs) are easy to use and assuming statistical independence solve for system reliability, system availability and system MTTF; can find bottlenecks

Each component can have attached to it

• A probability of failure

• A failure rate

• A distribution of time to failure

• Steady-state and instantaneous unavailability


can be solved using fast algorithms assuming stochastic independence between system components (all implemented in SHARPE) • Sum of Disjoint Products (SDP) algorithms.

• Binary Decision Diagrams (BDD) algorithms.

• Factoring (conditioning) algorithms.

• Series-parallel composition algorithms.

• Bounding algorithm for relgraphs

Failure/Repair Dependencies are often present; • RBDs, FTs cannot easily handle these (e.g., shared repair,

warm/cold spares, imperfect coverage, non-zero switching time, travel time of repair person, reliability with repair).


Reliability block diagrams (Control-voice channel example)

Fault Tree (Control-voice channel example)

Reliability block diagrams

2 Control and 3 Voice Channels Example

control

control

voice

voice

voice

Description

Each control channel has a reliability Rc(t)

Each voice channel has a reliability Rv(t)

System is up if at least one control channel and at least 1 voice channel are up.

Reliability:

]))(1(1][))(1(1[)( 32 tRtRtR vc

Exercise: (non-) virtualized vs. virtualizedsystem

H. Ramasamy and M. Schunter, ‚Architecting Dependable Systems Using Virtualization,‛ In Workshop on DSN-2007.

Fault Tree

Markov chains

Markov chains

To model complex interactions between components, use models like Markov chains or more generally state space models.

Markov reliability models will have one or more absorbing states;

• Markov availability models will have n absorbing states

Many examples of dependencies among system components have been observed in practice and captured by continuous-time Markov chains (CTMCs).

Modeling Taxonomy

Abstract models


Hybrid

Analytic models

Non-state-space models

State-space models

State-Space Models

States and labeled state transitions

State can keep track of:

• Number of functioning resources of each type

• States of recovery for each failed resource

• Number of tasks of each type waiting at each resource

• Allocation of resources to tasks

A transition:

• Can occur from any state to any other state

• Can represent a simple or a compound event

Markov Availability model WebSphere AP Server

Application server and proxy server (with escalated levels of recovery)

• Delay and imperfect coverage in each step of recovery modeled

UA UR UB(1-r)rm

rrmqra

(1-q)ra

bbm

RE(1-b)bm

m

UOUPg ed2

1D

ed2dd1

(1-e)d2

UN

dm

1N

(1-d)d1

(1-e)d2

2N(1-d)d1

(1-e)d2

ed2 dd1

Failure detection By WLM

By Node Agent

Manual detection

Recovery Node Agent

Auto process restart

Manual recovery Process restart

Node reboot

Repair

State-Space model taxonomy

(discrete) State space

models

Markovian models

non-Markovian models

discrete-time Markov chains (DTMC)

continuous-time Markov chains (CTMC)

Markov reward models (MRM)

Semi-Markov process (SMP)

Markov regenerative process

Non-Homogeneous Markov

Can relax the assumption of exponential distributions

Problem with State Space Models

State space explosion problem or the largeness problem

Stochastic Petri nets (SPNs) and related formalisms for easy specification and automated generation/solution of underlying Markov model

Or use hierarchical (Multilevel) model composition.

• e.g. Upper level : FT or RBD, lower level: Markov chains

• Many practical examples of the use of hierarchical models exist

Markov Reward Models (MRMs)

Modeling any system with a pure reliability / availability model can lead to incomplete, or, at least, less precise results. • Gracefully degrading systems may be able to

survive the failure of one or more of their active components and continue to provide service at a reduced level.

• Markov reward model is commonly used technique for the modeling of gracefully degradable system

Two-State Markov Availability

Model in SHARPE

Availability measures

Steady-state Availability

Steady-state Unavailability

Transient Availability

Average Cumulative Downtime

Snapshot of the GUI

bind

lambda 0.0033

mu 1

end

* We define a model of type Markov with the name m2_state

markov m2_state readprob

*specify each transition and its rate

1 0 lambda

0 1 mu

end

* specify that state 1 is the initial state with probability 1

1 1

end * define variable A as the steady-state probability of

* the Markov chain m2_state being in state 1 var A prob(m2_state,1)

var U prob(m2_state,0)

var downtime 60*8760*U

*ask sharpe to compute and print A, U and downtime

expr A, U, downtime

*define function A(t) as the transient probability for the Markov chain

* to be in the up state 1 at time t

func A(t) tvalue(t;m2_state,1)

* we ask SHARPE to compute and print pointwise availability

* for time points 0 through 1000 in steps of 50 hours

loop t,0,1000,50

expr A(t)

end

end

Outputs from SHARPE

A: 9.9668e-01

U: 3.3223e-03

Downtime: 1.7462e+03

0.995

0.996

0.997

0.998

0.999

1

1.001

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

Time

insta

nta

neo

us a

vailab

ilit

y A

(t)

Outputs

Two component system: Markov availability model

Assume we have a two-component parallel redundant system with repair rate m.

Assume that the failure rate of both components is .

When both the components have failed, the system is considered to have failed.

Markov availability model (Cont.)

Let the number of properly functioning components be the state of the system. The state space is {0,1,2} where 0 is the system down state.

We wish to examine effects of shared vs. non-shared repair

2 1 0

2

m

m2

2 1 0

2

m

m

Non-shared (independent)

repair

Shared repair


Note: Non-shared case can be modeled &

solved using a RBD or a FT but shared case

needs the use of Markov chains.

m

m

A

2)1(1m

m

sysA


72

markov shared

2 1 2*lambda

* Could be also written

* 2 1 2/MTTF

1 0 lambda

1 2 mu

0 1 mu

end

Shared Case

bind mu 1

lambda 0.1

end var U prob(shared,0)

var downtime 60*8760*U

loop j ,2, 5, 0.5

bind lambda 1.0 *10^-j

expr downtime

end

end

Non-shared case


markov non_shared

2 1 2*lambda

1 0 lambda

0 1 mu

1 2 2*mu

end

Non-shared Case

bind mu 1

end var U prob(non_shared,0) var downtime 60*8760*U

loop j ,2, 5, 0.5

bind lambda 1.0 *10^-j

expr downtime

end

end

Copyright © 2008 by K.S. Trivedi 78


Non-shared case

Comparing Shared/Non-shared cases

CTMC: WFS example

WFS Example

A Workstations-Fileserver Example

Computing system consisting of:

• A file-server

• Two workstations

• Computing network connecting them

System operational as long as:

• One of the Workstations

and

• The file-server are operational

Computer network is assumed to be fault-free.

The WFS Example

Assuming exponentially distributed times to

failure

• w : failure rate of workstation

• f : failure rate of file-server

Assume that components are repairable

• mw: repair rate of workstation

• mf : repair rate of file-server

File-server has (preemptive) priority for repair

over workstations (such repair priority cannot

be captured by non-state-space models)

Markov Chain for WFS Example

Markov Availability Model for WFS

0_0

2_1 1_1

1_0 2_0

0_1

f

2w

2w

w

mw mw

w

mf mf mf f f

Since each state is reachable from every other state, the

CTMC is irreducible. Furthermore, all states are positive

recurrent (since it is a finite state CTMC).

In the previous figure, the label (i_j) of each state is

interpreted as follows: i represents the number of

workstations that are still functioning and j is ‘1’ or ‘0’

depending on whether the file-server is up or down

respectively.

Note that in the text, no component failures are

allowed from system failure states; this is commonly

assumed by many engineers in practice. Here we

allow component failures from system failure states to

show that this situation can also be modeled.

Markov Availability Model for WFS (cont.)

Model in SHARPE GUI

Outputs; steady state

Analysis Frame

Output Generated by SHARPE


Continuous Time Markov Chains are useful

models for performance as well as availability

prediction

Extension of CTMC to Markov reward models

make them even more useful

Attach a reward rate (or a weight) ri to state i of

CTMC. Let Z(t)=rX(t) be the instantaneous reward

rate of CTMC at time t

Markov Reward Models (MRMs) (Continued)

Define Y(t) the accumulated reward in the interval (0,t]

Computing the expected values of these measures is easy

For computing distribution of Y(t) see the Perfomability monograph edited by Haverkort, Marie, Rubino & Trivedi

t

dZtY0

)()(

3-State Markov Reward Model with Sample

Paths of X(t) and Z(t) Processes

r1 = 1.7

r2 = 1.0

r3 = 0.0

1 2 3

2

m2 m3

CTMC: Security models

Legend

R

IR CR IA CA

CIA

A

Dependability and Security Models

A Dependability and Security Model Classification

A Availability

C Confidentiality

I Integrity

R Reliability

Security Modeling Taxonomy

Analytic models


State-space models

Attack tree

SMP

CTMC

Security compromise of smart card

Confidentiality compromise

Availability compromise

Integrity compromise

Get PIN Unauthorized access

Dump communication

Applications/algorithm Data Protocol

Block access

Hardware damage

Denial Of service

Non-state space model: Attack Tree

Fault tree -> attack tree

I1 I2 I3

Non-state space model: Attack graph

Reliability graph -> attack graph

Will be covered in more detail • In security talk

Probabilistic Security Quantification

State transition diagram of system security states/ attacker behavior, and use Markov chains, Semi Markov Process, Stochastic Petri Nets

Attack (Response/countermeasure) Trees for incorporating both attacker and system behavior.

Hierarchical and fixed-point iterative models in future?

Security Quantification of SITAR

Security vs. attack rate

0.9550.96

0.9650.97

0.9750.98

0.9850.99

0.9951

0.33

2.33

4.33

6.33

8.33

10.3

3

12.3

3

threat level 3

threat level 1

Mean time to security failure vs. attack rate

0

5000

10000

15000

20000

25000

30000

1 2 3 4 5 6 7 8 9 10 11 12 13

threat level 3

threat level 1

System security

Mean time to severe security failure

Threat level 1

Threat level 3

State Space Explosion

State space explosion can be handled in two ways: • Large model tolerance must apply to specification, storage

and solution of the model. If the storage and solution problems can be solved, the specification problem can be solved by using more concise (and smaller) model specifications that can be automatically transformed into Markov models (GSPN and SRN models).

• Large models can be avoided by using hierarchical model composition.

Ability of SHARPE to combine results from different kinds of models • Possibility to use state-space methods for those parts of a

system that require them, and use non-state-space methods for the more ‚well-behaved‛ parts of the system.

Dependability and Security Evaluation Methods

Model-based


Hybrid

Analytic Models

Quantitative evaluation

Measurement-based

Hierarchical models

largeness

Combinatorial models

Efficiency, simplicity

State-space models

Dependency capture

VDC example

Introduction

VMware Virtualization • w/o virtualization vs. w virtualization

Introduction

VM live migration (e.g., VMotion in VMware) • enables the Live Migration of Virtual Machines

across hosts

How useful is this ?

Introduction

VMware

CPU utilization CPU utilization

VMware VMware

CPU utilization

OS

App App

OS

App

OS

App

OS

App

OS

Call for Upgrade

Upgrade Completion

VM live migration (VMotion) (cont)

host1 host2 host3

Introduction

VMotion

Bottle App

ESX Server 1 ESX Server 3 ESX Server 2

Bottle App Bottle App

VM live migration (VMotion) (cont) • automatic resource allocation to bottleneck

Introduction

VMware HA (High Availability) • provides easy to use, cost effective high

availability.

Resource Pool X Host failure

Revisit (non-) virtualized vs. virtualizedsystem

H. Ramasamy and M. Schunter, ‚Architecting Dependable Systems Using Virtualization,‛ In Workshop on DSN-2007.

A System Architecture

VMM1

Host1

VMM2

Host2

VM2

APP2

VM1

APP1

SAN

CPU

Mem

Power

NIC

Cooler

Hardware

Failure classification in virtualized two hosts

Failures

Hardware failures Software failures

(non-aging related Mandel bugs)

VMM Application VM Power

failure

Memory

failure

CPU

failure

Network

failure

SAN

failure

Cooler

failure

How can you represent this system using stochastic model?

Any idea?

A system availability model of virtualized two nodes (old)

System Failure

AND

HW1

CPU Mem Net Pwr

host1

VMM1 HW2

CPU Mem Net Pwr

host2

VMM2

SAN SAN

VMs VMs

A system hierarchical model of virtualized two hosts

System Failure

VM sub SAN

HW1

CPU1 Mem1 NIC1 Pwr1

Host1

VMM1

Coo1

HW2

CPU2 Mem2 NIC2 Pwr2

Host2

VMM2

Coo2

AND

OR

Compute equivalent failure and recovery rate in one host (subtree) in the fault tree And use it in VM Markov model

Markov submodel

CPU submodel

D1 RP

VMM1

host1

VMM2

host2

VM2

APP2

VM1

APP1

SAN

CPU Mem Power NIC Cooler

MTTFeq and MTTRequ computation of VM host

Top level is a host fault subtree (boxed)

1. Solve Markov submodels such as CPU, MEM, NIC, PWR, COO in the host fault subtree. • We can compute MTTFeq, MTTReq of the Markov

submodels

2. Compute MTTFeq and MTTReq of a host fault subtree model

3. Use MTTFeq and MTTReq values into VM sub Markov model to be shown

Ref: Dazhi Wang, MS Thesis

System flow review

A host fault subtree

VM sub Markov chain model

2) MTTF_eq/MTTR_eq

of a host fault subtree

HW1

CPU Mem NIC Pwr

Host

1

VMM1

Coo 1) MTTF_eq/MTTR_eq of

Markov submodels

Measure of interests

(availability)

CPU Mem NIC Pwr VMM Coo SAN

Input Parameters values of the Markov submodels

System Failure

VM sub SAN

HW1

CPU1 Mem1 NIC1 Pwr1

Host1

VMM1

Coo1

HW2

CPU2 Mem2 NIC2 Pwr2

Host2

VMM2

Coo2

AND

OR

3) Use MTTFeq and MTTReq

values into VM sub Markov

model to be shown

VMware HA (High Availability)

• After a host failure detection, restart VM on the other host

VM migration

• After the host is repaired, VM is moved to on the original host

Resource Pool

Host failure detected!

x Host failure

RP Host repair

started

UP Host repaired

restart

Revisit: HA and VM migration

Availability model of virtualized two nodes system : VMsub model

Up state

Down state

Host failure

Host failure

detected

VM is restarted

on other host

Host is repaired

VM is migrated

130

131/86

Input Parameters values in Markov submodels

For execution only, real value will be used

alpha_sp 2

lambda_cpu 2/8760

mu_cpu 2

lambda_mem 2/8760

mu_mem 2

lambda_net 2/8760

mu_net 2

mu2_net 1

lambda_pwr 2/8760

mu_pwr 2

mu2_pwr 1

lambda_coo 2/8760

lambda2_coo 2/8760

alpha_coo 1

mu2_coo 1

mu_coo 2

delta_vmm 1

b_vmm 0.9

beta_vmm 6

mu_vmm 1

lambda_vmm 1/2880

132/86

1) Compute MTTFeq and MTTReq of Markov submodels in the host fault subtree

Results from SHARPE execution

MTTFeq MTTReq

CPU 2.19050000e+003 5.00000000e-001

Memory 1.09550000e+003 5.00000000e-001

Network 2.19049994e+003 9.99942929e-001

Power 2.19000000e+003 4.99942929e-001

Cooler 4.38099977e+003 5.00399446e-001

VMM 2.88000000e+003 1.31666667e+000

133/86

2) Compute MTTFeq and MTTReq of host fault subtree model

MTTF equivalent : 3.49899881e+002

MTTR equivalent : 6.79629790e-001

They are used in VM sub Markov chain model in the next slides.

134/86

Steady state availability of system fault

tree

Steady state availability : 9.99770797e-001 -------------------------------------------

Down time : 1.20469077e+002 (min)

Other examples index


• Reliability Block Diagram (RBD): voice, IBM, NEC, CISCO

• Fault Tree: the same

• Reliability Graph

State space models

• Continuous Time Markov Chains (CTMC): o Simple two components failure-recovery: Bluebook

o Other failure-recovery model: IBM, NEC-VDC

o Software rejuvenation

o Security model: SITAR

o UAV model

• Stochastic Petri nets/Stochastic Reward nets o NEC-VDC, SITAR, NEC-warm rejuvenation, Disaster tolerance

Reliability models in practice

Availability models in practice

Expected interval availability

Stochastic Petri nets/SRN

UUXUUX UFaXUUX UUXUFaX

UUXUDaX h h

hd hd

vr vr

vdvd

v v

a a

ad ad

UDaXUUX

UPaXUUX UUXUPaX FUXUUX UUXFUX

DXXUUR UURDXX

2am

1a ac m

2am

(1 ) 1a ac m (1 ) 1a ac m

UFvXUUX

UDvXUUX

DXXUUU

hm

UUUDXX

UUXUFvX

UUXUDvX

UXXFUU

hh

UUUUXX

FUUUXX

hd hd

DUUUXX UXXDUU

hmvm vm

vr

1a ac m

2 vr2

UPvXUUX UUXUPvX

UXXUUU

(1− cv)r v

μv

cvr

v

(1− cv)r v

μv

cvr

v

Model with only 1st Host Failure (IEEE-TR)

UUXUUX UFaXUUX UUXUFaX

UUXUDaX h h

hd hd

vr vr

vdvd

v v

a a

ad ad

UDaXUUX

UPaXUUX UUXUPaX FUXUUX UUXFUX

DXXUUR UURDXX

2am

1a ac m

2am

(1 ) 1a ac m (1 ) 1a ac m

UFvXUUX

UDvXUUX

DXXFUU

hm

UUUDXX

UUXUFvX

UUXUDvX

UXXFUU

hh

UUUUXX

FUUUXX

hd hd

DUUUXX UXXDUU

hmvm vm

vr

1a ac m

2 vr2

UPvXUUX UUXUPvX

DXXURR

(1− cv)r v

μv

cvr

v

(1− cv)r v

μv

cvr

v

DXXDUU FUUDXX URRDXX DUUDXX

DXXUUU

UXXUUU

hhdhm

vr

2

hm

2 hd

2

vr2

UXXURR URRUXX

hm

UXXUUR

vr2

h

UURUXX

vr2

hm

vrvr

Model with 2nd Host Failure

Sensitivity of MTTF_VMs

Parameter Sensitivity – Model with only 1st Failure

Sensitivity – Model with 2nd Failure

lambda_h -1.99866136e+00 -1.99869163e+00

m_v 9.99931045e-01 5.20949060e-02

lambda_a 1.04508774e-03 1.04508774e-03

lambda_v 3.25669697e-05 3.25669696e-05

r_v -2.00199738e-05 -2.24829226e-05

mu_v -1.72413369e-05 -1.72413369e-05

The order of parameters in the sensitivity ranking is the same for both models

Obs: In the paper, the values for sens. of some parameters were wrong, due to a computation error that was detected and fixed now. But only the order of r_v and mu_v was swaped with this fix. (6th -> 5th, 5th -> 6th in the ranking)

Unavailability and MTTF_VMs

Metric Model with only 1st Failure Model with 2nd Failure

Unavailability 3.96688083e-10 4.01031499e-07

MTTF 3.85133268e+07 2.00774300e+06

MTTF and Unavailability are larger in the second model

SRN models

Refer to Trivedi’s SPN lecture notes if necc.

Open the SHARPE project file.

SPN model for WFS example

Modeling Practices using SHARPE

Performance models in practice

Performability models in practice

SPNP: Stochastic Petri Net Package.

Version 6.0

Outline - SPNP

Brief Intro. To SPNP

Download

Analytic Modeling using SPNP • Stochastic Petri nets/Stochastic Reward nets

• Others

SPNP

Modeling tool well-known (Installed at over 180 Sites;

companies & universities)

Ported to Most Architectures and Operating Systems

Used For Performance, Dependability and

Performability

Steady-State as well as Transient Analysis

Written in C Language

SPNP GUI supports animantion

Stochastic Reward Nets

Bipartite graph with two kinds of nodes:

places and transitions

Timed and immediate transitions

Inhibitor arc, variable cardinality arc,

guard function, and priority

Reward rate based measures

Fluid stochastic Petri net: fluid places and

fluid arcs

Characteristics

Structural characteristics:

• Marking dependency

• Resampling policies, for general distributions

Stochastic characteristics:

• Allow definition of reward rates in terms of net level entities

• Automatically generate the reward rates for the markings

Characteristics (cont.)

Non- Markovian SPNs as well as Fluid Stochastic Petri

Nets (FSPNs) can be described and solved

Besides the analytic numeric solution of Markovian

models discrete-event simulation is now available

A user-friendly GUI Interface is now available

Transition Type

Poisson

Binominal

Negative Binominal

2-stageHyperexponential

3-stageHypoexponential

Erlang

Pareto

Cauchy

Transition Type

Exponential

Deterministic(Constant)

Uniform(a,b)

Geometric(p)

Weibull(a,b)

Lognormal

Truncated Normal

Gamma

Beta

Available Distribution functions

Solution Techniques

SRN Model

Markovian Nets Non-Markovian Nets FSPNs

Extended Reachability Graph

(ERG)

Generate All Markings

(tangible + vanishing)

Generate Reward Rates

for Tangible Markings

make correspondance list

schedule transition events

schedule fluid events

change states

Compute statistics

and confidence interval

Discrete

Event

Simulation

(DES)

modify

clock

Steps in Analytic Numeric Analysis of Markovian SRN

Generates all markings of the SRN by considering all the enabled transitions in each marking. Classify the markings as Tangible and Vanishing markings.

Stochastic Reward Nets

Extended Reachability Graphs

Markov Reward Model

Solve MRM for Steady-State

Transient behavior using

known methods

Eliminates the vanishing markings

Discrete Event Simulation

FSPN (Fluid Stochastic Petri net)

Used as a model for: • Systems involving fluid variables

• Approximation of models with a large number of tokens

No need to generate the reachability graph

Possibility to give the number of replications or the desired relative error.

SRN models in SPNP

Some examples

References

K. Trivedi’s lecture notes on SHARPE demonstration

SHARPE portal

SPNP site at K. Trivedi’s homepage.

How to use SHARPE and SPNP - Duke...

Documents

Transcript of How to use SHARPE and SPNP - Duke...