Software Architecture Metrics

Hany Ammar, Mark Shereshevsky, Ali Mili,Hany Ammar, Mark Shereshevsky, Ali Mili,Walid Rabie and Nicholay GradetskyWalid Rabie and Nicholay Gradetsky

Lane Department of Computer Science & Electrical

Engineering

hammar@wvu.edu; (smark, amili, rabie, grani)@csee.wvu.edu

Initiative Title: Architectural Level Software Metrics '01

FY2001 University SOFTWARE INITIATIVE PROPOSAL

for theNASA SOFTWARE IV&V FACILITY

  

Outline

Project OverviewHub Control Software (HCS) case studyDefinition of the entropy based metrics Definition of the Quantitative FactorsInformational Integrity Coefficient (IIC)Conclusions (achievements)Papers submitted Work In Progress

Future work (2nd year plans)

Project Overview

Developing a class of architectural metrics that quantify information flow in the architecture. Different metrics reflect:

Coupling vs. cohesion; Data flow vs. control flow; Static measurement vs. dynamic measurement;

Introducing a group of quantitative factors: mathematically defined functions, that are relevant with respect to qualitative attributes of the architectureEstablishing analytical relationship between the metrics and the quantitative factors Automating computation of the metrics

         

Product Artifacts Architecture,

Design, Code,

External Attributes: Maintainability,Testability,

Reliability,

Computable Metrics: Coupling, cohesion,

complexity, etc.

Error Propagation, ChangePropagation,

Requirements Propagation

impacts

computed for

Analytical Definitions

Mathematical Formula

have

have

Historical Data

Measurement Values

produce

ValidationAnalytical

Derivations

Quantified

 

•McCall's model of software quality [McCall 1977],

Three-level hierarchy of software attributes

Project Overview

Project Overview McCall's model of software quality in UML

Mathematical DefinitionsMathematical FormulaeAnalytical Relationship

Quantitative Factors

Error PropagationChange PropagationRequirements Propagation

Empirical Validation

Mathematical Derivation

Historical Data

Error ReportsChange Reports

<<uses>>

External Quality Attributes

MaintainabilityReusabilityReliabilityTestability

Computable Metrics

Entropy-based couplingEntropy-based cohesion

Software Product

Product Artifacts

Architecture SpecificationDesign ModelsCode

<<uses>>

Internal Quality Attributes

CouplingCohesionComplexity

Impact

measured by

have

have have

Quant. Factors Measurements

produce

Measurements

produce

correlation

has

has

has

Hub Control Software (HCS) Case StudyInternational Space Station

General HCS-ITCS scheme

HCS

ITCS

SCITCS

FRITCS

LRITCS

PPA mon

PFMC LT

PFMC MT

Scheduler

State manger

CMD Queue

O/P CMD Queue

N3-1 Data Access

RPCMN3-2 Data Access

Other HCS sub-systems

HCS case study: Hierarchical Architecture

Definition of entropy based metrics

Definition 1:Coupling: The coupling from A to B, denoted Coupling(A,B), is

the entropy of random variable VAB.

Cohesion: The cohesion of A is defined as coupling from A to A.

• Ensemble • CNTL , DATA E• p is the probability

distribution of E.• VAB is a random

variable defined by E and p

S

CNTL

A B

DATA

))(

1log()(B),Coupling(A

epep

Ee

HCS case study :ITCS Static Control Matrix

  Scitcs Fritcs Pfmc mt pfmc lt lritcs ppa mon

Scitcs 3.7 1.58 1.58 1.58    

Fritcs 2 3.91 0 0    

Pfmc mt 1 2 2 0    

pfmc lt 1 2 0 2    

lritcs            

ppa mon            

HCS case study :HCS Static Control Matrix (LEVEL 1)

  itcs N3 queues rpcm sch state man

itcs 1.06 0 1 0 0 0

N3 1 0 0 0 0 0

Queues 0 1 0 0 0 0

rpcm 0 0 0 2 0 0

sch 0 0 0 0 1 0

state man 0 0 0 0 0 1.58

Information Theoretic metrics

Method of data

collection

Aspect ofinform. exchange

Static(syntactic analysis,Comprehensive statistics)

Dynamic(running actual instances of the architecture)

Control Entropy of set of methods, with statically computedprobabilities

Entropy of set of methods, with dynamically computedprobabilities

Data Entropy of set of parameter values, with statically computedprobabilities

Entropy of set of parameter values, with dynamically computedprobabilities

HCS case study :ITCS Dynamic Control Matrix

  Scitcs Fritcs Pfmc mt pfmc lt lritcs ppa mon

Scitcs 3.31911948 1 1.5637897 1.19243058    

Fritcs 1.53948476 3.65269014 0 0    

Pfmc mt 0.73206669 1.46234979 1.9132505 0    

pfmc lt 0.80580491 1.48343604 0 1.93555927    

lritcs            

ppa mon            

HCS case study : HCS Dynamic Control Matrix (LEVEL 1)

  itcs N3 queues rpcm sch state man

itcs 1.17573608 0 0.590576 0 0 0

N3 0.988016215

0 0 0 0 0

Queues 0 1 0 0 0 0

rpcm 0 0 0 1.92612075 0 0

sch 0 0 0 0 0.999992 0

state man 0 0 0 0 0 1.584963

Definition of the Quantitative Factors

Quantitative Factors bridge the gap between qualitative attributes (which we want to assess) and computable metrics (which we can measure).

Some Quantitative Factors:• Error Propagation• Change Propagation• Requirements propagation

Definition of the Quantitative Factors: error propagation

B(x) is the state of B resulting from invoking B on input x. Suppose, due to a fault in A, the information transmitted from A to B is corrupted from the expected x to some erroneous x`.

The error propagation (EP) is a measure of the likelihood that an error in the message sent by A will propagate into B.

S

X

A B

xx` x` xOR

Error

Definition of the Quantitative Factors: error propagation

Continued

Definition 2:Error Propagation:The error propagation from A to B is defined as the following conditional probability:

EP(A,B) = Prob(B(x) B (x’) | x x’).

• This equation can be reduced to:

EP(A,B) = 1 – exp( – Coupling(A, B)) + exp( – Cohesion(B)).

Definition of the Quantitative Factors: error propagation

Continued

• From the analysis of the above equation: The higher the coupling from A to B – the higher is the

error propagation from A to B. The lower the cohesion of component B – the higher is

the error propagation from A to B.

• These observations, consistent with intuition, provide an analytical validation of our metrics. Our equation gives these relationships (which are not surprising by themselves) precise analytical form.

Informational Integrity Coefficient (IIC)

One of architecture quality guidelines is to maximize cohesion and minimize coupling of components.

We introduce a quantitative characteristic, which we call the informational integrity coefficient of an architecture which assesses its conformance to this guideline.

The coefficient is computed based on the information flow matrix.

IIC =

d

i

d

j

ij

d

i

ii

c

c

1 1

2

1

2

HCS case study :HCS-ITCS (flattened) Static Control Matrix

IIC = 0.749

MT

SC 3.7 1.58 1.58 1.58 0 0 0 0 0 0 3.32FR 2 3.91 0 0 0 0 0 1 0 0 0MT 1 2 2 0 0 0 0 0 0 0 0LT 1 2 0 2 0 0 0 0 0 0 0LRppa N3-1 0 1 0 0 2.81 0 0 0 0 0 0N3-2 0 1 0 0 0 2.81 0 0 0 0 0ACQ 0 0 0 0 0 0 1 0 0 0 0

RPCM 0 0 0 0 0 0 0 2 0 0 0sch 0 0 0 0 0 0 0 0 1 0 0state 1.58 0 0 0 0 0 0 0 0 1.58 0OCQ 0 0 0 0 2.32 2.32 0 0 0 0 1

OCQACQ RPCM sch state LR ppa N3-1 N3-2SC FR LT

HCS case study :ITCS Static Control Matrix

  Scitcs Fritcs Pfmc mt pfmc lt lritcs ppa mon

Scitcs 3.7 1.58 1.58 1.58    

Fritcs 2 3.91 0 0    

Pfmc mt 1 2 2 0    

pfmc lt 1 2 0 2    

lritcs            

ppa mon            

IIC = 0.795

HCS case study :HCS Static Control Matrix (LEVEL 1)

  itcs N3 queues rpcm sch state man

itcs 1.06 0 1 0 0 0

N3 1 0 0 0 0 0

Queues 0 1 0 0 0 0

rpcm 0 0 0 2 0 0

sch 0 0 0 0 1 0

state man 0 0 0 0 0 1.58

IIC = 0.861

IIC = 0.773

HCS case study :HCS-ITCS (flattened) Dynamic Control Matrix

MT

SC 3.32 1 1.56 1.19 0 0 0 0 0FR 1.53 3.65 0 0 0 0 0 0.98 0MT 0.73 1.46 1.91 0 0 0 0 0 0LT 0.81 1.48 0 1.93 0 0 0 0 0LRppa N3-1 0 1 0 0 2.62 0 0 0 0N3-2 0 1 0 0 0 2.62 0 0 0ACQ 0 0 0 0 0 0 0.99 0 0

RPCM 0 0 0 0 0 0 0 1.92 0sch 0 0 0 0 0 0 0 0 0.99state 1 0 0 0 0 0 0 0 0OCQ 0 0 0 0 2.19 2.21 0 0 0

ACQ RPCM schSC FR LT LR ppa N3-1 N3-2

HCS case study :ITCS Dynamic Control Matrix

  Scitcs Fritcs Pfmc mt pfmc lt lritcs ppa mon

Scitcs 3.31911948 1 1.5637897 1.19243058    

Fritcs 1.53948476 3.65269014 0 0    

Pfmc mt 0.73206669 1.46234979 1.9132505 0    

pfmc lt 0.80580491 1.48343604 0 1.93555927    

lritcs            

ppa mon            

IIC = 0.884

HCS case study : HCS Dynamic Control Matrix (LEVEL 1)

  itcs N3 queues rpcm sch state man

itcs 1.17573608 0 0.590576 0 0 0

N3 0.988016215

0 0 0 0 0

Queues 0 1 0 0 0 0

rpcm 0 0 0 1.92612075 0 0

sch 0 0 0 0 0.999992 0

state man 0 0 0 0 0 1.584963

IIC = 0.887

HCS case study : IIC ComparisonFlattened Architecture Vs Hierarchical Architecture

Architecture Static Dynamic

HCS-ITCS (flattened) 0.749 0.773

HCS_ITCS (Level 1) 0.861 0.887

ITCS (Level 0) 0. 795 0.844

N3 (Level 0) 1 1

Queues (Level 0) 1 1

The flattened architecture shows a lower IIC than the hierarchical architecture, this proves that the hierarchical architecture is more cohesive and less coupled

Conclusions (achievements)

We defined coupling and cohesion metrics for hierarchical architectures based on the information theory.  We introduced a normalized measure, the informational integrity coefficient (IIC) of an architecture based on the computed metricsWe derived the relationship between the coupling/cohesion metrics and the error propagation factor between components.

Papers submittedConferences

Annual International Computer Software and Applications Conference (COMPSAC 2001)Title: "Information-Theoretic Metrics for Software Architectures“– Status: Accepted for publicationAutomated Software Engineering Conference (ASE 2001) Title: "Quantifying Architectural Attributes of UML Specifications: A Framework and Its Automation" – Status: Submitted June 29, 2001

JournalsAutomated Software Engineering JournalTitle: "Quantifying Software Architectures: Definitions and Automation Plans“ – Status: submitted: May 11, 2001Transactions on Software Engineering JournalTitle: "Information Theoretic Metrics for Software Architectures" – Status: submitted: April, 2001

Future Work

Deriving a relationship between our coupling/cohesion metrics and the change propagation,Developing an automation methodology for computing the metrics given a UML description of the architecture,Validating the metrics using a NASA CASE Study

Canonical Architectural Style

Automation support for metrics computation

Software System

Conceptual view (RoseRT-UML)

Static Metrics

Quantitative factors (EP, CP)

In progressPlannedHas a view

Other views (UML, Rapide)

Dynamic Metrics

Tra

nsfo

rmatio

n

Information Integrity

Coefficient