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ARCHITECTURAL STYLE SELECTION

Software Architecture Design process considers many candidate

designs from which few will be eliminated immediately and others will be

considered for evaluation. The toughest task of software architect is selecting

the appropriate design from these competing designs for the software to be

developed. This chapter proposes a hybrid model to evaluate the candid

architectural styles with respect to quality attributes. The set of candid

architectural styles are derived from the mapping of architectural styles with

vastu mandalas. The brief description about vastu mandalas and their

mappings are presented in this chapter.

5.1 VASTU VEETHIS, MANDALAS AND LOKAS

Vastu is an art of living from which one can derive maximum benefits.

It is based on the effects of natural forces and elements. Vastu Vidya is the

study of effective utilization of natural elements in the living place. Vastu

Shastra deals with the dos and don’ts in Vastu Vidya. If a person has an in-

depth knowledge of Vastu Vidya, he can change the Vastu according to his

requirements. The origin of vastu, the two design patterns of vastu and the

mandalas which act as the base for the vastu are explained in the chapter 2.

Vastu consists of Central energy that is termed as central object,

Veethis, Mandalas and lokas. Veethis means layer or loop or level of energy.

Mandala consists of these veethis with or without the central object. Loka

consists of mandalas with central object or without central object [77].

The levels that are used in defining mandalas are called as veethis in

Vastu. The name of each mandala depends on the number of veethis and the

existence of a central object. There are four important veethis namely Brahma

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Veethi, Deva Veethi, Manushya Veethi, and Paisacha Veethi. Fig 5.1 and 5.2

depict veethis in grid and elliptic representation respectively. Brahma Veethi

is around the core of the mandala with high energy. Deva Veethi is away from

Brahma Veethi with less energy than Brahma Veethi. Manushya Veethi is

farther away from the earlier veethis and has an appropriate energy for the

evolving of life. Paisacha Veethi is the outer veethi, where energy is the least.

Fig 5.1 Four veethis of Vastu-grid representation

Fig 5.2 Four veethis of Vastu-elliptic representation

Veethis and existence of central object form thirty two mandalas that

are depicted in the following fig 5.3. Vastu not only defines these thirty-two

mandalas, but also says which structure is suited for what purpose. Mandala

means container of essence. The mandalas are in spatial dimensions that

portray how matter can be distributed in a given space. The purpose behind

these mandalas and veethis is to place the rooms in a way that works for the

well being of the dwellers by balancing the natural elements and forces

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[77].The thirty-two mandalas are divided into four divisions. These divisions

are named as Lokas. Each Loka consist a list of mandalas that follow the two

patterns discussed in chapter 2. Mathematically this may be represented as

{[x=True and n=0…4/5…8/9…12/13…15]}, {[x=False and

n=1…4/5…8/9…12/13…16]}. The pictorial representation of this is given in

fig 5.3.

Fig 5.3 Vastu patterns, Mandalas and Lokas

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The four Lokas are Manduka Loka { [x=True and n=0, 1, 2, 3, 4],

[x=False and n=1, 2, 3, 4] } Dyauh Loka { [x=True and n=5, 6, 7, 8], [x=False

and n=5, 6, 7, 8] }, Deva Loka{ [x=True and n=9, 10, 11, 12], [x=False and

n=9, 10, 11, 12] }, and Manushya Loka{ [x=True and n=13, 14, 15], [x=False

and n=13, 14, 15, 16] } (fig 5.3). Each Loka consist of four veethis as depicted

in fig 5.4.

Fig 5.4 Four Lokas and existence of four veethis

If Lokas are considered as veethis, then Manduka Loka will become a

Brahma veethi, Dyauh loka will become a Deva veethi, Deva Loka will

become a Manushya veethi and Manushya Loka will become a Paisacha

veethi. This is shown in fig 5.3. Nine different mandalas in Manduka Loka are

explained below with their mappings as per Vastu literature [77].

Sakala Mandala: This mandala represents an undivided space. Fig 5.5 depicts

this mandala, which has the undivided space of energy in the rectangle

boundary, mathematically {x=True and n=0}. Any open space with boundary

represents sakala mandala.

Fig 5.5 Sakala Mandala

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Pechaka Mandala: This mandala represents the pattern of one loop that

contains energy, mathematically {x=False and n=1}. The same is represented

in fig 5.6. An example of this mandala is a public bath place in which

bathrooms are built in the loop around a central place. Another example is a

public worship place in which many people worship in the loop around a

central place.

Fig 5.6 Pechaka Mandala

Pitha Mandala: Pitha means a container that has energy in the center as well

as in a loop around it, mathematically {x= True and n=1}. Fig 5.7 contains

the central object of energy with a single loop of energy.

Fig 5.7 Pitha Mandala

Mahapitha Mandala: Mahapitha means a big basket that is characterized by

two loops of energy, mathematically {x=False and n=2}. This structure,

shown in fig 5.8, contains more energy than the Pitha Mandala because it has

more loops. The energy loops may not always be concentric, but they can

overlap each other. An Example of this mandala is two bodies with a

difference in mass orbiting around a common barycenter, like the Charon-

Pluto system.

Fig 5.8 Mahapita Mandala

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Upapitha Mandala: Upapitha means additional to pitha and this is

characterized by two energy loops with a central energy space, mathematically

{x= True and n=2}. Fig 5.9 represents this mandala, which has a central object

and two loops of energy. An example of this mandala is two moons around the

planet Mars.

Fig 5.9 Upapitha Mandala

Ugrapitha Mandala: It means forceful pedestal. It has the pattern of three

energy loops, as shown in fig 5.10, mathematically {x=False and n=3}. An

example of this mandala is algol triple star systems.

Fig 5.10 Ugrapitha Mandala

Sthandila Mandala: Sthandila means an open ground or the place of rest that

is represented in fig 5.11, mathematically {x=True and n=3}. Pattern of this

mandala has three energy loops with a central energy space. This mandala is a

near complete mandala, because it has the three energy loops meant for human

habitants. This mandala is used for planning villages on an open ground. The

fields will be in the center of the village and three major settlements or paths

(veethis) are planned around the fields.

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Fig 5.11 Sthandila Mandala

Manduka Mandala: It has the pattern of four loops of energy. This is the first

complete mandala as it has all four veethis, mathematically {x=False and

n=4}. Manduka means the structure of the universe. Manduka Mandala is also

called Chandita Mandala, which means a mandala that is grateful/thankful.

Most of the temples built are examples of this mandala. Fig 5.12 shows the

pattern of this mandala and temples built using the pattern of Manduka

Mandala.

Fig 5.12 Manduka Mandala

Paramasayika Mandala: This mandala is characterized by four loops with

central energy, mathematically {x=True and n=4}. Fig 5.13 represents the

pattern of this mandala. Parama means excellent or all encompassing. Sayika

refers to being in regular order. So, Paramasayika indicates being in an all

encompassing order. An example for this mandala is our Milky Way Galaxy.

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Fig 5.13 Paramasayika Mandala

A traditional house built based on the Paramasayika Mandala will have

an open courtyard at the center. This is the center of high energy. Around the

center, there can be a walkway, which is the first veethi called Brahma Veethi,

so that the energy from the center can flow towards the rooms in the next

veethis. As the energy in this veethi is higher, the rooms (halls, living rooms)

where people spend most of their time can be built there. The next veethi Deva

Veethi involves the creation of matter and energy and so the dining rooms and

bedrooms of the newly married can be built here. This will have an energy

lesser than the Brahma Veethi. The next veethi will surely have a lesser energy

compared to this veethi. Hence, storage rooms, granaries, treasure chests and

bedrooms of elders can be built in Manushya Veethi. The next veethi Paisacha

Veethi may have a garden filled with trees and a high raised platform.

Similarly, the above said four Loka divisions Manduka Loka, Dyauh

Loka, Deva Loka and Manushya Loka are also mapped to earth, Solar system,

galaxy and universe respectively [77]. The next section explains how exactly

the patterns of vastu fit into the software architecture.

5.2 MAPPING OF VASTU MANDALAS TO SOFTWARE

ARCHITECTURAL STYLES

As discussed in chapter 2, the two patterns in Vastu are veethis, with a

central object and without a central object. This classification is very similar to

the two broad categories of software systems, like systems operating in

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centralized mode and distributed mode. Patterns in vastu are similar to

architectural patterns and styles available in a literature.

The monolithic architecture is the single, undivided system structure

with interconnected components. The same pattern of architecture was

proposed 2000 years ago in Vastu as a Sakala Mandala. The Sakala Mandala

is the representation of a monolithic architecture with interconnected parts.

The Pechaka Mandala, which symbolizes the structure with one loop of

energy, is mapped to the single layer of pipe and filter architectural pattern.

The client–server architecture pattern with the central database is mapped to

Pitha Mandala as Pitha Mandala represents the structure with the central

object and one loop. The loop can also be mapped to Pechaka mandala.

Similarly, the blackboard architecture pattern will also fit into Pitha Mandala.

Mahapitha Mandala is mapped to the distributed client–server

architecture pattern. The inner loop of Mahapitha Mandala is mapped to

distributed servers and the outer loop is mapped to distributed clients.

Upapitha Mandala is mapped to remote procedure call pattern. The inner loop

in this mandala is mapped to remote procedures residing in various systems

and the outer loop is mapped to the main program routine. The inner loop may

query the centralized database. The result of the query will be returned to the

outer loop. Ugrapitha Mandala consists of three loops. This mandala is

mapped to the distributed three-tier architecture pattern [111]. The inner loop

is mapped to distributed database servers; the middle loop is mapped to a

collection of application servers, and the outer loop to clients.

Sthandila Mandala is mapped to the three layer central data store

architectural pattern [89]. The central object is mapped to the database. The

inner loop is mapped to data access components; the middle loop is mapped to

business object components, and the outer loop to UI components and clients.

Manduka Mandala is mapped to the distributed multilayered architecture

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pattern of four layers [89]. The first innermost loop is mapped to the database

and services; the second inner loop is mapped to data access components; the

third loop is mapped to web service components and business components and

the outer loop to the collection of UI components, clients, and UI access

components.

Paramasayika Mandala is mapped to the multilayered web architecture

[112]. The central object is mapped to the database. The first innermost loop is

mapped to the server side framework; the second inner loop is mapped to

business components; the third loop is mapped to web service components and

the outer loop to the collection of UI components, clients, and UI access

components. According to vastu, it is a complete mandala with central object

and four veethis. Hence, it is implied that any architecture consisting of at

least four layers and a central database will be a complete structure.

The nine different mandalas existing in the Manduka Loka division are

mapped to different architectural patterns. As depicted in section 5.1, the four

Loka divisions Manduka Loka, Dyauh Loka, Deva Loka and Manushya Loka

can have one or more loops in them. These loops can also be suitably mapped

to appropriate architectural styles like the above.

Further, the four Lokas mentioned above can be appropriately mapped

like Manduka Loka mapped to Earth, Dyuah Loka mapped to solar system,

Deva Loka mapped to the galaxy, Manushya Loka mapped to the Universe.

These Loka divisions are mapped to distributed computing within the

organization, campus, region, country, around the world and perhaps the entire

universe. The type of distributed systems built using these four Lokas may be

called ‘super distributed system’ ‘ultra distributed system’, ‘ultra super

distributed system’ and ‘supreme distributed system’.

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With the super distributed system, information distribution may be

within the earth. Ultra distributed system may be designed for communication

and data distribution in earth and moon, an Ultra super distributed system may

be designed for communication among planets in the galaxy. Supreme

distributed system may be for intergalaxy communication in the Universe.

Thus, vastu can help us in building any kind of complex system.

Comparative analysis of Vastu mandalas and software architecture

styles has been done based on the important characteristics of software

architecture [113]. They are structure, communication and control. One or two

criteria have been taken for the investigation based on judgment of

practitioners. Criteria considered are physical deployment for structure, shared

data & duplicated shared data and message passing for communication,

concurrent & sequential for control. Table 5.1 below displays the analysis of

architecture styles with respect to the above chosen criteria.

Criteria details:

a) Physical deployment: number of levels (separation of concerns) the

components and connectors of the style can be deployed

b) Shared data: whether shared data can be used at the level

c) Duplicate shared data: if the shared data is not being used, whether

duplicate or copy of it can be used at the given level

d) Message passing: whether data can be passed using a message passing

mechanism at the level

e) Concurrent: computations can be done simultaneously for intra level

f) Sequential: computations can be done sequentially for intra level or

inter level

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Pipe and Filter architecture style deals with the data stream processing.

This may be on a single level of sequential operation of the incremental data

transfer. But the same style can be used in two stages with data sharing and

concurrency. Hence this style falls under the Pechaka, pitha, Mahapitha and

Upapitha mandalas. Batch sequential architecture style is non interactive and

not supporting concurrent operations. Hence this style is placed under pechaka

mandala if it is on a single level. The same style can be mapped to pitha,

Mahapitha, Ugrapitha and Manduka when the series of operations is done at

various levels in a sequential order.

Blackboard architecture style contains Blackboard, controller and

knowledge sources. The controller and knowledge sources may be on a single

level or in two levels with Blackboard as a central object. So, this style falls

under pitha and Upapitha mandalas. Repository stye is highly efficient when

dealing with large amount of data. But it finds difficult to distribute. So, this

style is considered to map the Pitha Mandala.

Main subroutine style has a main program that acts as a controller and

subroutines that do tasks with or without shared data. This suggests having

two levels with or without central object. So, this style maps Mahapitha and

Upapitha mandalas. Master slave architecture style consists of multiple

parallel tasks. The task that controls all the others is the master and the

remaining tasks are slaves. One master task always drives one or more slave

tasks. It is very advantageous when creating multi-task applications. However,

this style is considered better to map the Mahapitha, Upapitha, Ugrapitha,

sthandila and paramasayika mandalas.

The client server style fits in two, three and four levels without central

object and one, two and three levels with central object. So, this style maps to

pitha, Mahapitha, Upapitha, Ugrapitha, sthandila and Manduka mandalas.

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Table 5.1 Mapping Table

Shared data

duplicate

shared data Msg passing Concurrent Sequential

1 √ √ √ √ Х √ Pechaka , Pitha

2 √ √ √ √ √ Х Mahapitha, Upapitha

3 Х NA NA Х NA NA

4 Х NA NA Х NA NA

1 √ √ Х √ Х √ Pechaka , Pitha

2 √ Х Х √ Х √ Mahapitha

3 √ Х Х √ Х √ Ugrapitha

4 √ Х Х √ Х √ Manduka

1 Х NA NA Х NA NA

2 √ √ √ √ Х √ Mahapitha, Upapitha

3 Х NA NA NA NA √

4 Х NA NA NA NA √

1 Х NA NA Х NA NA

2 √ √ √ √ √ Х Mahapitha, Upapitha

3 √ √ √ √ √ Х Ugrapitha, Sthandila

4 √ √ √ √ √ Х Manduka, Paramasaykia

1 √ √ Х Х √ Х Pitha

2 Х NA NA Х NA NA

3 Х NA NA Х NA NA

4 Х NA NA Х NA NA

1 √ √ Х Х √ √ Pitha

2 √ √ Х Х √ √ Upapitha

3 Х NA NA Х NA NA

4 Х NA NA Х NA NA

1 Х NA NA Х NA NA

2 √ √ √ √ Х √ Mahapitha, Upapitha

3 √ √ √ √ Х √ Ugrapitha, Sthandila

4 √ √ √ √ Х √ Manduka, Paramasaykia

1 √ √ Х √ √ √ Pitha

2 √ √ √ √ √ √ Mahapitha, Upapitha

3 √ √ √ √ √ √ Ugrapitha, Sthandila

4 √ Х √ √ √ √ Manduka

1 Х NA NA Х NA NA

2 Х NA NA Х NA NA

3 √ √ √ √ Х √ Ugrapitha

4 Х NA NA Х NA NA

1 Х NA NA Х NA NA

2 Х NA NA Х NA NA

3 √ √ √ √ Х √ Ugrapitha

4 Х NA NA Х NA NA

1 Х NA NA Х NA NA

2 Х NA NA Х NA NA

3 √ √ √ √ Х √ Ugrapitha

4 Х NA NA Х NA NA

1 Х NA NA Х NA NA

2 Х NA NA Х NA NA

3 √ √ √ √ √ √ Ugrapitha

4 Х NA NA Х NA NA

Communication

Physical

deployment

Service oriented

Mapped

Mandalas

Client

server

Broker

MVC

PAC

No.of

Levels

Control

Layered

Pipe & Filter

Batch

sequential

Main

Subroutine

Master

Slave

Repository

Blackboard

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Layered architecture style deals with two or more than two levels. So,

other than sakala, pechaka and pitha mandalas all other mandalas are mapped

to this style. Monolithic kernel maps the indivisible interconnected structure

sakala mandala. Here we are not discussing about this. The following table 5.2

summarizes the mapping.

Table 5.2 Summary of Mapping

Mandalas Architectural Styles

paramasayka Master slave, Layered

Manduka Batch Sequential, Master slave, Layered, Client server

Sthandila Master slave, Layered, Client server

Ugrapitha Batch Sequential, Master slave, Layered, Client server , Broker, MVC,

PAC, Service oriented

Upapitha Pipe & Filter, Main subroutine, Master slave, Blackboard, Layered,

Client server

Mahapitha Pipe & Filer, Batch Sequential, Main subroutine, Master slave, Layered,

Client server

Pitha Pipe & Filer, Batch Sequential, Repository, Blackboard,

Client server

Pechaka Pipe & Filer, Batch Sequential

The next section deals with the level of support provided by the

software architectural styles to a set of quality attributes and thus they are

related to vastu mandalas. A detailed analysis is presented based on the quality

attributes and vastu mandalas.

5.3 MANDALAS AND QUALITY ATTRIBUTES

Table 5.3 shows the tradeoff between Mandalas and quality attributes.

Quality attributes play vital role in the design or selection of architectural style

for a system. A number of common quality attributes are listed in [89] [90].

They are not same. All the quality attributes have been taken for evaluation.

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The assessment of architectural styles is based on [90]. The meaning of

symbols used in table 5.3 as follows: “++” represent a strong support of the

architectural style with respect to the specific quality attribute. “+” means

some support. “O” stands no support, unsure or neutral. “—“indicates the

negative impact and “- -““means high negative impact.

Table 5.3 Tradeoff between Vastu mandalas and Quality attributes

Further analysis is done by taking numerical value for quality attribute.

Numerical values are more towards the stakeholders’ requirements, as human

minds tendency to analyse accurately is more as reported in the literature.

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Masterslave o o o o o o o o o + ++ o o o o o

Layered Arch ++ + ++ + + − + o - - − o + o o o o

Batch Sequential o ++ o o + + o o o − o o o o - - o

Masterslave o o o o o o o o o + ++ o o o o o

Layered Arch ++ + ++ + + − + o - - − o + o o o o

ClientServer − − o o + + − ++ − o − + o o o o

Masterslave o o o o o o o o o + ++ o o o o o

Layered Arch ++ + ++ + + − + o - - − o + o o o o

ClientServer − − o o + + − ++ − o − + o o o o

BrokerArch ++ − + + + + o − − o o o o o o o

Masterslave o o o o o o o o o + ++ o o o o o

Layered Arch ++ + ++ + + − + o - - − o + o o o o

MVC + o o + o + + o o o o - - o o + +

ClientServer − − o o + + − ++ − o − + o o o o

BrokerArch ++ − + + + + o − − o o o o o o o

Service oriented + o o o ++ − + o o o o + + o o o

Presentation

Abstraction

Control(PAC) + o + + + − + o − + o o o o + o

Pipe & Filter + + o + + + o o o ++ o + o o - - −

Blackboard Arch − − − o + o o o + ++ o + o o o o

MainSubroutine − o o o − o o - o o + o o o o o

Masterslave o o o o o o o o o + ++ o o o o o

Layered Arch ++ + ++ + + − + o - - − o + o o o o

ClientServer − − o o + + − ++ − o − + o o o o

BrokerArch ++ − + + + + o − − o o o o o o o

Batch Sequential o ++ o o + + o o o − o o o o - - o

Pipe & Filter + + o + + + o o o ++ o + o o - - −

MainSubroutine − o o o − o o - o o + o o o o o

Masterslave o o o o o o o o o + ++ o o o o o

Layered Arch ++ + ++ + + − + o - - − o + o o o o

ClientServer − − o o + + − ++ − o − + o o o o

Batch Sequential o ++ o o + + o o o − o o o o - - o

Pipe & Filter + + o + + + o o o ++ o + o o - - −

Blackboard Arch − − − o + o o o + ++ o + o o o o

Repository Arch − o o − + o + o o o − + − o − o

ClientServer − − o o + + − ++ − o − + o o o o

Batch Sequential o ++ o o + + o o o − o o o o - - o

Pipe & Filter + + o + + + o o o ++ o + o o - - −Pechaka

Mandala Vs Quality Attributes

Paramasayka

Manduka

Ugrapitha

Pitha

Maha pitha

Sthandiala

Upapitha

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Discrete ordinal integer values are being used in table 5.4 to map the

symbols of table 5.3.

Table 5.4 Trade off table with numerical Values

The following scheme is used to map symbols into numerical values to

obtain the table 5.4 that represents the tradeoff with numerical values.

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Masterslave 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0

Layered Arch 4 2 4 2 2 -2 2 0 -4 -2 0 2 0 0 0 0

Batch Sequential 0 4 0 0 2 2 0 0 0 -2 0 0 0 0 -4 0

Masterslave 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0

Layered Arch 4 2 4 2 2 -2 2 0 -4 -2 0 2 0 0 0 0

ClientServer -2 -2 0 0 2 2 -2 4 -2 0 -2 2 0 0 0 0

Masterslave 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0

Layered Arch 4 2 4 2 2 -2 2 0 -4 -2 0 2 0 0 0 0

ClientServer -2 -2 0 0 2 2 -2 4 -2 0 -2 2 0 0 0 0

BrokerArch 4 -2 2 2 2 2 0 -2 -2 0 0 0 0 0 0 0

Masterslave 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0

Layered Arch 4 2 4 2 2 -2 2 0 -4 -2 0 2 0 0 0 0

MVC 2 0 0 2 0 2 2 0 0 0 0 -4 0 0 2 2

ClientServer -2 -2 0 0 2 2 -2 4 -2 0 -2 2 0 0 0 0

BrokerArch 4 -2 2 2 2 2 0 -2 -2 0 0 0 0 0 0 0

Service oriented 2 0 0 0 4 -2 2 0 0 0 0 2 2 0 0 0

Presentati0n

Abstracti0n

Control(PAC) 2 0 2 2 2 -2 2 0 -2 2 0 0 0 0 2 0

Pipe & Filter 2 2 0 2 2 2 0 0 0 4 0 2 0 0 -4 -2

Blackboard Arch -2 -2 -2 0 2 0 0 0 2 4 0 2 0 0 0 0

MainSubroutine -2 0 0 0 -2 0 0 -2 0 0 2 0 0 0 0 0

Masterslave 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0

Layered Arch 4 2 4 2 2 -2 2 0 -4 -2 0 2 0 0 0 0

ClientServer -2 -2 0 0 2 2 -2 4 -2 0 -2 2 0 0 0 0

BrokerArch 4 -2 2 2 2 2 0 -2 -2 0 0 0 0 0 0 0

Maha pitha Batch Sequential 0 4 0 0 2 2 0 0 0 -2 0 0 0 0 -4 0

Pipe & Filter 2 2 0 2 2 2 0 0 0 4 0 2 0 0 -4 -2

MainSubroutine -2 0 0 0 -2 0 0 -2 0 0 2 0 0 0 0 0

Masterslave 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0

Layered Arch 4 2 4 2 2 -2 2 0 -4 -2 0 2 0 0 0 0

ClientServer -2 -2 0 0 2 2 -2 4 -2 0 -2 2 0 0 0 0

Batch Sequential 0 4 0 0 2 2 0 0 0 -2 0 0 0 0 -4 0

Pipe & Filter 2 2 0 2 2 2 0 0 0 4 0 2 0 0 -4 -2

Blackboard Arch -2 -2 -2 0 2 0 0 0 2 4 0 2 0 0 0 0

Repository Arch -2 0 0 -2 2 0 2 0 0 0 -2 2 -2 0 -2 0

ClientServer -2 -2 0 0 2 2 -2 4 -2 0 -2 2 0 0 0 0

Pechaka Batch Sequential 0 4 0 0 2 2 0 0 0 -2 0 0 0 0 -4 0

Pipe & Filter 2 2 0 2 2 2 0 0 0 4 0 2 0 0 -4 -2

pitha

Mandala Vs Quality Attributes

Paramasayka

Manduka

Sthandiala

Ugrapitha

Upapitha

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Now it is clear that the value 4 represents a strong support, 2 represents

support, 0 represents neutral, -2 represents negative impact and -4 represents a

high negative impact. Based on this implication the maximum, minimum and

average level of support for each quality attribute with respect to each mandala

is calculated and presented in table 5.5.

Table 5.5 Max, Min and Average support

The following graphs are obtained by using the table 5.5. These graphs

for mandalas clearly portray different levels (Max, Min, Avg) of support for

various quality attributes.

Fig 5.14 (a) shows that paramasayka mandala can provide a strong

support to Maintainability, portability and Reliability at the maximum. On an

average it provides a support to these three quality attributes, whereas at the

minimum level it will be neutral to these attributes. As the minimum level

doesn’t give negative impact, either the Master slave or Layered architectural

styles or a combination of both can be used to achieve these quality attributes.

Max

Min

AV

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Maintainability 4 0 2 4 -2 1 4 -2 2 4 -2 2 4 -2 1 4 -2 0 2 -2 -1 2 0 1

Testability 2 0 1 4 -2 1 2 -2 -1 2 -2 -0 2 -2 -0 4 -2 1 4 -2 0 4 2 3

portability 4 0 2 4 0 1 4 0 2 4 0 1 4 -2 1 4 0 1 0 -2 -0 0 0 0

Flexibility 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 -2 0 2 0 1

Reusability 2 0 1 2 0 2 2 0 2 4 0 2 2 -2 1 2 -2 1 2 2 2 2 2 2

Simplicity 0 -2 -1 2 -2 1 2 -2 1 2 -2 0 2 -2 1 2 -2 1 2 0 1 2 2 2

Availability 2 0 1 2 -2 0 2 -2 0 2 -2 1 2 -2 0 2 -2 0 2 -2 0 0 0 0

Security 0 0 0 4 0 1 4 -2 1 4 -2 0 4 -2 0 4 -2 0 4 0 1 0 0 0

Performance 0 -4 -2 0 -4 -2 0 -4 -2 0 -4 -1 2 -4 -1 0 -4 -1 2 -2 0 0 0 0

Concurrency 2 -2 0 2 -2 -1 2 -2 0 2 -2 0 4 -2 1 4 -2 0 4 -2 1 4 -2 1

Reliability 4 0 2 4 -2 1 4 -2 1 4 -2 0 4 -2 1 4 -2 1 0 -2 -1 0 0 0

Scalability 2 0 1 2 0 1 2 0 1 2 -4 0 2 0 1 2 0 1 2 0 2 2 0 1

cost 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 -2 -0 0 0 0

Lifetime 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Usability 0 0 0 0 -4 -1 0 0 0 2 0 1 0 -4 -1 0 -4 -1 0 -4 -2 -4 -4 -4

Supportability 0 0 0 0 0 0 0 0 0 2 0 0 0 -2 -0 0 -2 -0 0 -2 -0 0 -2 -1

Mandala Vs Quality Attributes

PechakaParamasayka Manduka Ugrapitha Upapitha Mahapitha PithaSthandila

111

Fig 5.14 (a) Paramasayka Mandala with Quality attributes

Fig 5.14 (b) shows that Manduka mandala provides strong support to

Maintainability, Testability, portability, security and Reliability at the

maximum level. Even this mandala supports these attributes at the average

level; Maintainability, Testability and Reliability are not supported at the

minimum level. Hence any one of the style under Manduka mandala can be

used to reach portability and security; whereas a combination of architectural

styles can be used to obtain all five quality attributes.

Fig 5.14 (b) Manduka Mandala with Quality attributes

Fig 5.14 (c) portrays that sthandila mandala has a strong support for

Maintainability, portability, security and Reliability at the maximum level.

Portability alone can be achieved as a neutral at the minimum level. Hence it

is advised not to select any of the style under this mandala to get these four

-6

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Manduka

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quality attributes. But the combination of styles under this mandala can be

used to get these four attributes as they are supported at average level.

Fig 5.14 (c) Sthandila Mandala with Quality attributes

Fig 5.14 (d) represents that Ugrapitha mandala posses a strong support

for Maintainability, portability, security, Reusability and Reliability.

Maintainability, Security and Reliability will be excluded from the list as they

have a negative impact at the minimum level. So, any one of the styles under

this mandala can be used to achieve Portability and Reusability. All five

quality attributes can be obtained when we use a combination of all styles

under this mandala.

Fig 5.14 (d) Ugrapitha Mandala with Quality attributes

Fig 5.14 (e) briefs that Upapitha mandala provides a strong support for

Maintainability, portability, security, concurrency and Reliability at the

maximum level. These five attributes are having a negative impact at the

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Ugrapitha

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minimum level. Hence, choosing any one of the styles under this mandala to

achieve these attributes is not profitable. As Testability is having a negative

impact at the average level, the combination of styles can also obtain the

remaining four quality attributes.

Fig 5.14 (e) Upapitha Mandala with Quality attributes

Fig 5.14 (f) explains that Mahapitha mandala gives a strong support for

Maintainability, Testability, portability, security, concurrency and Reliability

at the maximum level. As all attributes are having a negative impact excluding

portability which is neutral, choosing any one style to achieve these attributes

is unprofitable at the minimum level. Hence all styles under this mandala can

be combined to achieve these six quality attributes.

Fig 5.14 (f) Mahapitha Mandala with Quality attributes

Fig 5.14 (g) explains that Pitha mandala supports strongly for

Testability, security and concurrency. As no attribute is supported at the

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Mahapitha

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minimum level, selecting one among the styles under this mandala can be

avoided. The combination of these styles can achieve all three attributes at the

average level.

Fig 5.14 (g) Pitha Mandala with Quality attributes

Fig 5.14 (h) tells that Pechaka mandala posses a strong support for

Testability and concurrency. As Concurrency has negative impact at the

minimum level, choosing one style under the mandala is not appropriate. But

the style combination may meet these two attributes at the average level.

Fig 5.14 (h) Pechaka Mandala with Quality attributes

This analysis clearly shows the support of a collection of attributes with

respect to mandala at the strongest level. Details about varying level support

of attributes can also be obtained easily from these graphs. This section clearly

shows the symbol to numerical value conversion and calculating maximum,

minimum and average level support for each attribute.

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Pechaka

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It is clearly shown in the above analysis that set of quality attributes are

suitably mapped to vastu mandalas and the level of support they provide. The

architecture styles classified under these mandalas, exhibit the same level of

support for a set of quality attributes. The next section proposes a new hybrid

model to select the suitable mandala and to derive the best architectural style

from that mandala.

5.4 HYBRID MODEL

This section introduces a new hybrid model that deals with the

dependent and independent criteria for the selection of the best architectural

style. The solution of the problem encompasses the architectural mining,

building a hybrid model and the style selection with the balanced quality

attributes. The high level steps or stages are shown in the fig 5.15.

(Refer fig 5.16 (a))

(Refer fig 5.16 (b))

Fig 5.15 Stages in the proposed hybrid model

The initial stage of this model is architectural styles classification

which is completely described in the previous section. The mapping table 5.2

and trade off table 5.3 are the sources available for this stage. Set of

architectural styles mapped under a mandala and their level of support are

Architecture styles classification

Mandala Selection

Best architecture style selection

Table

List of Architecture styles

Given Application

Quality attributes values

Best Architecture style

116

given in these tables. This is available before the process starts. Fig 5.16 (a)

explains the Mandala selection stage in detail.

Fig 5.16 (a) Detailed steps of Mandala selection stage

consistent

1

Judgment on

No.of Levels

Judgment on

central object

Judgment matrix construction:

M =

[ 𝑀11 𝑀12 … 𝑀19

𝑀21 𝑀22 … 𝑀29

𝑀31 𝑀32 … 𝑀39

… … … …

𝑀91 𝑀92 … 𝑀99]

Derivation of Priority Vectors:

PV =

[ 𝑝𝑣11𝑝𝑣21𝑝𝑣31𝑝𝑣41𝑝𝑣51𝑝𝑣61𝑝𝑣71𝑝𝑣81𝑝𝑣91]

Check

consistency

of matrix

Not consistent

Calculate Wtotal = PVlij * Wl + PVOij *Wo

PVl , PVo

Wl , Wo

SRS document with

Layered view

Pick up Ms = M ( Wtotal (MAX))

Display ASi (Ms)

Mapping

Table

List of Architectural styles

117

Fig 5.16 (b) Detailed steps of Style selection stage

Judgment on

Quality attributes

Judgment on

Architecture styles

Judgment matrices construction:

C=

[ 𝑄1/𝑄1 𝑄1/𝑄2 𝑄1/𝑄3 … 𝑄1/𝑄𝑁

𝑄2/𝑄1 𝑄2/𝑄2 𝑄2/𝑄3 … 𝑄2/𝑄𝑁

𝑄3/𝑄1 𝑄3/𝑄2 𝑄3/𝑄3 … 𝑄3/𝑄𝑁

… … … … …

𝑄𝑁/𝑄1 𝑄𝑁/𝑄2 𝑄𝑁/𝑄3 … 𝑄𝑁/𝑄𝑁]

,

[ 𝑄1/𝐴𝑆1 𝑄1/𝐴𝑆2 … 𝑄1/𝐴𝑆𝑁

𝑄2/𝐴𝑆1 𝑄2/𝐴𝑆2 … 𝑄2/𝐴𝑆𝑁

𝑄3/𝐴𝑆1 𝑄3/𝐴𝑆2 … 𝑄3/𝐴𝑆𝑁

… … … …

𝑄𝑁/𝐴𝑆1 𝑄𝑁/𝐴𝑆2 … 𝑄𝑁/𝐴𝑆𝑁]

,

[ 𝐴𝑆1/𝐴𝑆1 𝐴𝑆1/𝐴𝑆2 … 𝐴𝑆1/𝐴𝑆𝑛

𝐴𝑆2/𝐴𝑆1 𝐴𝑆2/𝐴𝑆2 … 𝐴𝑆2/𝐴𝑆𝑛

𝐴𝑆3/𝐴𝑆1 𝐴𝑆3/𝐴𝑆2 … 𝐴𝑆3/𝐴𝑆𝑛

… … … …

𝐴𝑆𝑛/𝐴𝑆1 𝐴𝑆𝑛/𝐴𝑆2 … 𝐴𝑆𝑛/𝐴𝑆𝑛]

Construct Supermatrix

Obtain weighted supermatrix

Get Limit matrix

Obtain Stochastic Supermatrix

Select the highest scored

Architecture style

Best Architectural style

Quality Attributes

Derivation of Priority

Vectors

Check

consistency

of matrix

Not consistent

consistent

Weights

1

118

Then the judgment matrices and priority vectors are derived. After

ensuring the consistency, the priorities of the mandalas are calculated with

respect to each criterion. Then the high scored mandala is selected from the

total of the weighted priorities of two criterions. The list of architectural styles

under this mandala is extracted from the mapping table 5.2. This is given as an

input to the next stage depicted in fig 5.16 (b) that deals the best architectural

selection.

This stage gets the geometric mean value of user’s judgment on quality

attributes and their priorities as input. Based on this judgment, the judgment

matrices are built and their priority vectors are calculated. After confirming

the matrices’ consistency, supermatrix is constructed from them. Based on the

weights given to each cluster by the architect, the weighted supermatrix is

constructed and then it is converted to stocahastic matrix in order to maintain

the balance of quality attributes. The limit of this matrix lists out the score for

architecture styles and quality attributes. The high scored architectural style is

the best style to implement the given application. The next subsection explains

the second stage of this hybrid model in detail.

5.4.1 Mandala Selection

This section discusses the process to find out the best mandala under

which the given application falls. The Inputs for this process are the given

application and the classification table. The output of this process is the

shortlisted architecture styles.

The best mandala for the application is chosen based on the number of

levels/layers and the existence of the central object. This process considers

nine alternative mandalas in order to select the best mandala as shown in fig

5.17. They are Sakala, Pechaka, Pita, MahaPita, UpaPita, UgraPita, Sthandila,

Manduka and Paramasayikya mandala.

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Fig 5.17 Manadala Selection

The selection process comprises following steps.

a. Judgments on Mandalas:

The exact estimation of the applicable information is the critical step in

many decision-making methods where the qualitative information elicitation is

required. Quantifying the information in terms of absolute values is most

important in making the right decision. Therefore, the relative importance, or

weight, of the alternatives in terms of each criterion of a given problem is

determined in most of the problems. The pairwise comparison approach is

used to determine the relative importance of each alternative in terms of each

criterion [114]. In this approach the decision-maker choose one single

pairwise comparison’s value among available discrete choices. Each choice is

a linguistic phrase. The selected linguistic choice is quantified by using a

scale, which maps the decision maker’s discrete linguistic choices to a discrete

set of numbers that represent the importance. As per the psychological

experiments, more than seven objects cannot be compared simultaneously

[115]. The Weber law states that constant percentage of the stimulus

increment will make a change in sensation [116]. This is the basis behind the

scales shown in table 5.6 with a unit difference between successive values.

Go

al

No. of Loops Object Existence

Sakala Pechaka Pith

a

Maha pitha Upa pitha Ugra pitha Sthandila Manduka Parama

saikya

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Table 5.6 Scale of Relative importance

Reciprocals

A reciprocal, such as 1/3, is used for the other judgment in the matrix

involving the pair. For example, if the judgment 3 is entered in cell (i,j), the

judgment 1/3 is automatically entered in cell (j,i). A matrix with this special

form is called a reciprocal matrix.According to this scale, the available values

for the pairwise comparisons are members of the set: {9, 8, 7, 6, 5, 4, 3, 2, 1,

1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9}

In this research, initially the best mandala that suits for the architecture

is to be determined. The first step is to compare pairs of mandalas using

fundamental scale for pairwise comparison. For each comparison, it is decided

which mandala is weaker with respect to the number of levels giving the

mandala a weight of 1. The mandalas are denoted by Mj (j=1,2,…9). When

comparing two mandalas M1 and M2, a value of 1 is assigned, if mandala M1 is

equally important as Mandala M2 .If M1 is strongly favored then maximum

value 9 is assigned over M2. The intermediate strength of importance is

assigned by values between 1 and 9. If the value of comparing (M1, M2) is

between 1 and 9, then comparing (M2, M1) has a reciprocal value. Similarly a

Intensity of

Importance

Definition

1 Equal

2 Equally to Moderately more dominant

3 Moderately more dominant

4 Moderately to Strongly more dominant

5 Strongly more dominant

6 Strongly to Very Strongly more dominant

7 Very Strongly more dominant

8 Very Strongly to Extremely more dominant

9 Extremely more dominant

121

comparison is done on the pairs of mandalas with respect to object existence.

The next step is to construct matrices based on these judgments.

b. Mandala Weighted Matrix construction:

The next step is to transfer the weights to a matrix.

M =

[ 𝑀11 𝑀12 … 𝑀19

𝑀21 𝑀22 … 𝑀29

𝑀31 𝑀32 … 𝑀39

… … … …

𝑀91 𝑀92 … 𝑀99]

Now, the complete Judgment matrix is obtained. The next step is to derive the

priority vectors from this matrix.

c. Derivation of Weighted Priority Vectors:

Priority vectors list the relative weight of each mandala of each

criterion. This process results in two priority vectors. They are PVl for the

number of loops and PVo for object existence. Priority vectors are calculated

as follows:

1. Calculate the sum of elements of each column of ‘M’ matrix

𝑀𝑖𝑗 = ∑ 𝑀𝑖𝑗 9𝑖=1 (5.1)

2. In each column, divide each element by the sum value of

column

𝑋𝑖𝑗 = 𝑀𝑖𝑗

∑ 𝑀𝑖𝑗 9𝑖=1

(5.2)

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and obtain the matrix X =

[ 𝑋11 𝑋12 … 𝑋19

𝑋21 𝑋22 … 𝑋29

𝑋31 𝑋32 … 𝑋39

… … … …

𝑋91 𝑋92 … 𝑋99]

3. Calculate the mean value of each row

𝑃𝑉𝑖𝑗 = ∑ 𝑋𝑖𝑗

9𝑗=1

9 (5.3)

and get the priority vector PV =

[ 𝑝𝑣11𝑝𝑣21𝑝𝑣31𝑝𝑣41𝑝𝑣51𝑝𝑣61𝑝𝑣71𝑝𝑣81𝑝𝑣91]

The next step makes use of this priority vector to ensure the consistency of the

matrix and helps to select the best style.

d. Ensuring the Consistency of Matrix:

If all the comparisons are perfectly consistent, then the following

relation should always be true for any combination of comparisons taken from

the judgment matrix. It is a crucial thing to determine how consistent the

comparisons are, during the pairwise comparisons. Consistency ratio less than

0.1 indicate good consistency. Two consistency ratios exist: CRl for a number

of levels and CRo for object existence. Consistency ratio could be calculated

by the following way:

CR =( (λmax- n)/(n-1))/RI (5.4)

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Where λmax is largest eigenvalue of matrix, n is order of matrix and RI is

random consistency index.

Consistency vector CVij =

[ 𝑐𝑣11𝑐𝑣21𝑐𝑣31𝑐𝑣41𝑐𝑣51𝑐𝑣61𝑐𝑣71𝑐𝑣81𝑐𝑣91]

can be calculated using the following

formulae

CVij = (Xi1PV11 + Xi2PV21 + Xi3PV31+ . . . +Xi9PV91) / Wi1 (5.5)

The largest eigen value λmax is calculated by taking the average of consistency

vectors given as follows

λmax = ∑ 𝐶𝑉𝑖19

𝑖=1

9 (5.6)

Now, using the λmax value, consistency index (CI) is calculated using the

formula

CI = (λmax - n) / n-1 =( λmax -9) / 8 (5.7)

If the CI value obtained using formula (7) is 0, then the judgment matrix

formed by the pairwise comparison is a perfectly consistent one. Otherwise,

the consistent ratio should be calculated as division of Consistency Index (CI)

by the Random consistency index (RI) value which is depicted in the formula

(5.8)

CR = CI /RI where RI is the Random consistency Index (5.8)

RI value is obtained from the following table 5.7 where the upper row is the

order of the random matrix and the lower row is the corresponding index of

consistency for random judgments.

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Table 5.7 Random Consistency Index

If the CR is less than 0.1, then the judgment matrix is the consistent

matrix and the priority vector is a true priority vector. Now, using the priority

vector the best criteria can be selected as described in the next section.

Otherwise, the judgment matrix should be adjusted to obtain the consistent

matrix. The next step uses the consistent matrices’ priority vectors to obtain

the result.

e. Selection of suitable mandala & List out styles:

The priority vectors of each criterion are multiplied by weight of

respective criteria and then summed up to obtain the total score.

Wtotal = PVlij * Wl + PVOij *Wo (5.9)

Where Wl and Wo are the weightage assigned to the criteria number of levels

and object existence.

Finally the mandala with the highest total score in Wtotal is chosen. The

corresponding list of architectural styles of the chosen mandala is listed out

from the table 5.2. The next subsection discusses the selection of the best style

from the list of styles shortlisted in this section.

5.5.2 Selection of best architecture style

As quality attributes are interdependent and their ratio differs from each

architectural style, a different methodology is applied here that deals with the

interconnections (dependence and feedback) between factors of complex

structure in the decision making process as shown in fig 5.17. The goal of this

process is to select the best architectural style from the alternative styles

available by evaluating the criteria listed as quality attributes. As Quality

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attributes are interdependent, self loop is added in the criteria box. The two

arrow marks between criteria and alternatives specify that quality attributes

have impact on architectural styles and vice versa. The steps involved in

selecting the right style are given below.

Fig 5.17 Best style selection

The selection process involved comprises of following steps.

a. Judgments on Quality Attributes and Architecture styles:

Pairwise comparisons of the criteria elements are done. With respect to

each quality attribute, two levels of comparison are done. Comparisons of

Quality attribute Vs Quality attribute and Quality attributes Vs Architecture

styles are done and relative importance weights are determined using a

fundamental scale. And also, pairwise comparisons of architectural styles are

performed. The set of comparison matrices C is obtained.

C =

[ 𝑄1/𝑄1 𝑄1/𝑄2 𝑄1/𝑄3 … 𝑄1/𝑄𝑁

𝑄2/𝑄1 𝑄2/𝑄2 𝑄2/𝑄3 … 𝑄2/𝑄𝑁

𝑄3/𝑄1 𝑄3/𝑄2 𝑄3/𝑄3 … 𝑄3/𝑄𝑁

… … … … …

𝑄𝑁/𝑄1 𝑄𝑁/𝑄2 𝑄𝑁/𝑄3 … 𝑄𝑁/𝑄𝑁]

,

[ 𝑄1/𝐴𝑆1 𝑄1/𝐴𝑆2 … 𝑄1/𝐴𝑆𝑁

𝑄2/𝐴𝑆1 𝑄2/𝐴𝑆2 … 𝑄2/𝐴𝑆𝑁

𝑄3/𝐴𝑆1 𝑄3/𝐴𝑆2 … 𝑄3/𝐴𝑆𝑁

… … … …

𝑄𝑁/𝐴𝑆1 𝑄𝑁/𝐴𝑆2 … 𝑄𝑁/𝐴𝑆𝑁]

,

[ 𝐴𝑆1/𝐴𝑆1 𝐴𝑆1/𝐴𝑆2 … 𝐴𝑆1/𝐴𝑆𝑛

𝐴𝑆2/𝐴𝑆1 𝐴𝑆2/𝐴𝑆2 … 𝐴𝑆2/𝐴𝑆𝑛

𝐴𝑆3/𝐴𝑆1 𝐴𝑆3/𝐴𝑆2 … 𝐴𝑆3/𝐴𝑆𝑛

… … … …

𝐴𝑆𝑛/𝐴𝑆1 𝐴𝑆𝑛/𝐴𝑆2 … 𝐴𝑆𝑛/𝐴𝑆𝑛]

Goal : Select the best style

Performance Reliability Availability Usability Flexibility

Style 1

Style n

Style 2

Style 3

126

b. Derivation of Weighted Priority Vectors:

A set of priority vectors is calculated by the same formulas 5.1 to 5.8

used in section 5.4.1. This set represents the relative importance weights of the

pairwise comparison matrices.

c. Unweighted Supermatrix:

The interrelationships of all quality attributes and architectural styles in

the system are represented by placing the relative importance weights of

pairwise comparison matrices within a supermatrix. The row and column of

the matrix have an entry of a list of alternative mandalas, a list of quality

attributes and the goal. The unweighted supermatrix is represented by

AS1 AS2 . . . ASN

Q11 Q12 Q13 . . . Q1N Q11 Q12 Q13 . . . Q1N Q11 Q12 Q13. . .Q1N

Q11

Q12

Q13

AS1 Q14 W11 W12 . . . W1N

.

.

.

Q1N

Q11

Q12

Q13

AS2 Q14 W21 W22 . . . W2N

.

.

.

Q1N

Q11

CW = Q12

Q13

AS3 Q14 W31 W32 . . . W3N

.

.

.

Q1N

. .

. . . . . . . . . . . . . .

. .

Q11

Q12

Q13

Q14 WN1 WN2 . . . WNN

ASN .

.

.

Q1N

127

Where Wik is the block matrix of priority vectors of the influence of quality

attribute in the ith architecture style with respect to kth architecture style,

ASi is ith architecture style

And Qij is the jth quality attribute of ith architecture style

d. Stochastic supermatrix:

In general the supermatrix is rarely stochastic because, in each column,

it consists of several eigenvectors which each sums to one, and hence the

entire column of the matrix may sum to an integer greater than one. The

supermatrix must first be reduced to a matrix, each of whose columns sums to

unity, resulting in a column stochastic or simply a stochastic matrix. If the

matrix is stochastic, the limiting priorities depend on its reducibility,

primitivity, and cyclicity.

In each block of the supermatrix, a column is either a normalized

eigenvector with possibly some zero entries, or all of its elements are equal to

zero. In either case it is weighted by the priority of the corresponding cluster

on the left. If it is zero, that column of the supermatrix must be normalized

after weighting by the cluster’s weights. This operation is equivalent to

assigning a zero value to the cluster on the left when weighting a column of a

block with zero entries and then re-normalizing the weights of the remaining

clusters. Such a supermatrix is called as weighted supermatrix.

e. Limit matrix:

The weighted supermatrix is now column stochastic from which one

then derives the limiting supermatrix. The limit matrix can be obtained by

raising the matrix to largest powers so that the powers will converge to the

limit matrix or converge to the cycle of matrices where limit matrix is the

average of these matrices. The Limit Matrix is the weighted Super matrix,

128

taken to the power of k+1 to have the converged or stable values, where k is

an arbitrary number [117].

In the case of hierarchies the larger powers of the scaled supermatrix

eventually go to zero and thus we are left with a limit matrix containing all

zeros. It is given by the formula

where S is the scaled supermatrix, and L is the number of levels in the

hierarchy (or alternatively L is the first integer for which SL+1 = 0). In essence,

one raises the supermatrix to powers to find the power at which all entries

become zero; the sum of those powers is the limit matrix. The values of this

limit matrix are the desired priorities of the elements with respect to the goal.

The highest scored architectural style is selected from the limit matrix as a

right architectural style for the given application.

This chapter explained the solution for the most critical problem faced

in the software development process. The first attempt towards our ancient

architectural science vastu is carried out to find out the correlation between

vastu and software architecture. The patterns available in vastu are mapped to

software architectural styles. A new hybrid model proposed here uses the

stakeholders’ requirements to select the right architectural style dynamically

with balanced quality attributes. Next chapter validate the proposed model

with a case study.