REACTIVE AUTONOMIC SYSTEM PERFORMANCE

MODELING AND SELF-MONITORING WITH

CATEGORY THEORY

Olga Ormandjieva, Heng Kuang and Stan Klasa

Department of Computer Science and Software Engineering, Concordia University

Montreal, Quebec, H3G 1M8, Canada

Keywords: Reactive Autonomic System, Performance Modeling, Self-monitoring, Category Theory, Representational

Theory of Measurement, Decision Making.

Abstract: The research presented in this paper was motivated by the need to build performance self-monitoring and a

decision-making process into Reactive Autonomic Systems (RAS). In order to achieve RAS compliance in

terms of the imposed performance policies, we formalize RAS modeling and performance control in a

single framework based on a representational theory of measurement and category theory. Category theory

is expressive enough to capture qualitative and quantitative knowledge about heterogeneous RAS

requirements and their interrelationships, as well as a decision-making mechanism, in one formal

representation, where structure and reasoning are inextricably bound together. Thus, category theory

provides a computational mechanism which enables this knowledge to be applied to performance data and

RAS information structures in order to arrive at valid conclusions.

1 INTRODUCTION

The main obstacle to further progress in the IT

industry is software complexity, since the difficulty

of managing massive computing systems goes well

beyond the capabilities of IT administrators. Some

of that complexity derives from the real-time and

reactive nature of software systems. One of the

solutions to the emerging complexity problem is

autonomic computing, which helps by using

technology to manage technology. As a result, low

level complexities are hidden from end users or

removed altogether (IBM Corporation, 2006) (IBM

Tivoli, 2005). With autonomic behavior, real-time

reactive systems can increasingly self-manage, and

be more adaptive to their environment.

Current formal methods have not adequately

addressed the issue of verifying policies on behavior,

such as performance requirements, which constitute

one of the most important nonfunctional

requirements for Reactive Autonomic Systems

(RAS).

According to (ISO/IEC 9126-1:2001, 2001),

level of performance is “the degree to which the

needs are satisfied, represented by a specific set of

values for quality characteristics.” Performance

characteristics can be quantified through

measurement procedures which provide

measurement methods and functions, as well as a

meaningful analysis algorithm for combining

measurement data along with decision making

criteria.

The research proposed in this paper addresses the

following challenges:

z The requirement of the performance-critical

characteristics of the RAS for specification

and for theoretically valid measurement data;

z The need for performance self-assessment to

be regulated by policies which state the

constraints on system performance

fluctuations at runtime.

In order to achieve RAS compliance with the

imposed performance requirements, we formalize

RAS and performance modeling in a single

framework (RASF) based on a representational

theory of measurement and category theory.

Category theory is expressive enough to capture

qualitative as well as quantitative knowledge about

heterogeneous RAS requirements and their

interrelationships, and a decision-making

325

Ormandjieva O., Kuang H. and Klasa S. (2009).

REACTIVE AUTONOMIC SYSTEM PERFORMANCE MODELING AND SELF-MONITORING WITH CATEGORY THEORY .

In Proceedings of the 4th International Conference on Software and Data Technologies, pages 325-330

DOI: 10.5220/0002257003250330

 SciTePress

mechanism in one formal representation, where

structure and reasoning are inextricably bound

together. Furthermore, category theory allows for a

formal graphical representation of the syntax and

semantics of models which goes beyond existing

graphical languages, such as UML, where the

semantics of the models is informal or semi-formal.

The rest of this paper is organized as follows:

Section 2 surveys related work. RAS modeling is

described in section 3. Section 4 introduces

performance modeling. RAS and performance

models are integrated into an RASF Metamodel in

section 5, and further formalized in terms of

category theory in section 6. Our conclusions are

presented and future work directions outlined in

section 7.

2 RELATED WORK

This section gives a brief overview of related work

on performance modeling and self-monitoring in

autonomic systems.

IBM Research has developed a framework called

Policy Management for Autonomic Computing

(PMAC) (IBM Tivoli, 2005), which provides a

standard model for the definition of policies and an

environment for the development of software objects

that can hold and evaluate policies.

The paper (Abdelwahed and Kandasamy, 2006)

describes a model-based control and optimization

framework for designing autonomic systems which

continually optimizes their performance by changing

workload demands as well as operating conditions.

The performance management problem of interest

can be considered to be one of sequential

optimization under uncertainty, and a look-ahead

control approach is used to optimize system

behavior forecast over a limited prediction horizon.

The basic control concepts are then extended to

tackle distributed systems where multiple controllers

must interact with one another to ensure the overall

performance goals.

The research presented here differs from work

previously done in the area in an important way: the

RAS components, the measurement procedure, and

the performance are modeled as categories within

the same formal framework, which makes it possible

to formalize the self-monitoring policies, verify both

their consistency and their completeness, and

consequently build performance self-monitoring into

the RAS implementation.

3 RAS MODELING

Systems designed to be reactive and autonomic

(RAS) are complex and built from potentially very

large numbers of elements which are highly

autonomic and reactive, but which are also socially

interactive. The formal and comprehensive

framework used for modeling and controling

performance in RAS, the RASF, is built on a 4-tier

layered structure (see Figure 1), which includes

Reactive Autonomic Objects (RAO), Reactive

Autonomic Components (RAC), Reactive

Autonomic Component Groups (RACG), and

Reactive Autonomic Systems (RAS).

Figure 1: RASF tiers.

The RASF structure is made up of distributed

RACG with their asynchronous communication. The

RAC is a set of synchronously communicating

RAO, where one of the RAO is designated as the

leader of the workers. The autonomic behavior, such

as self-monitoring or self-analyzing, is implemented

by the RAC leaders, group supervisors, and system

managers in the RAC, RACG, and RAS tier

respectively.

The current trend in autonomic system

development is towards the direct or dynamic

composition of autonomic components through task

workflows. We abstract the behavior of the RAS to a

collection of communicating task processes. The

workers are mainly responsible for reactive tasks,

while the leader works on autonomic tasks such as

coordinating self-monitoring at the component level.

The assumption here is that each group performs an

autonomic task process, and so there is no

dependency between the task processes of different

groups. RACG are required to react in real time to

requests from the system manager for the fulfilment

of a task process. The task workflows are scheduled

by TACG supervisors, while individual tasks from

the specified workflow are assigned to RACs in the

group and then optimized, given the resource

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constraints of the RAO in real time. The task

workflow requires both communication and

synchronization of individual tasks to ensure reliable

performance by the supervised group, governed by

RAS policies.

RAS performance policies impose restrictions on

task process communication and synchronization,

and so need to be considered as an integral part of

the RAS self-management capability. To allow for

managing group task process performance, we need

to express performance in quantifiable terms by

devising an appropriate performance measurement

model. We describe next the hierarchical modeling

of that performance.

4 MODELING PERFORMANCE

In our approach, performance is modeled as a

hierarchical information structure. The performance

model proposed in this paper ensures that all

standard aspects of quality are considered from both

the internal and external points of view. It is

decomposed into four qualitative performance

characteristics: i) reliability (the capability of the

software product to maintain a specified level of

performance when used under specified conditions

(ISO/IEC 9126-1:2001, 2001); ii) fault tolerance (the

capability of the software product to maintain a

specified level of performance in cases of software

faults (ISO/IEC 9126-1:2001, 2001); iii) efficiency

(the capability of the software product to provide

appropriate performance, relative to the amount of

resources used, under stated conditions (ISO/IEC

9126-1:2001, 2001); and iv) performance

compliance (the capability of the RAS to adhere to

response time, as well as to throughput policies,

which are related to task execution and collaboration

respectively). Those high-level characteristics are

repeatedly refined, and in each of the

decompositions the offspring (sub) characteristics

can contribute partially or fully towards satisfying

the parent. The lowest level corresponds to the

quantifiable performance sub characteristics of the

RAS tasks computed by applying a measurement

method − a logical sequence of operations applied

directly to the source, that is, to a task or task

process. The result of applying a measurement

method is called a base measure. The base measures

are then combined by a measurement function to

obtain the derived measures required for

characterizing the parent (indicator) in accordance

with the associated rules for the interpretation of

measurement data (ISO/IEC 15939, 2007).

An indicator provides an estimate or evaluation

of the utility of the performance characteristic,

which is derived from an analysis of the

measurement data (values) and with respect to a

defined decision criterion. “Utility” in this context

means a property in any task process which tends to

produce a quality benefit or to prevent disruption

(failure behavior or unacceptably low reliability) to

an RAC, a RACG, or the whole system.

The combined utility of all indicators serves as a

basis for performance self-management decision

making on the part of the RACG supervisor.

The self-management decision-making process

can be modeled as a set of alternative rules linking

the performance utility of a task process to certain

actions to outcomes (Roberts, 1979). For example,

the input is task process performance utility and the

output is the action required to improve the task

process performance level in the RAS. If decisions

are being made in a situation of certainty, then we

choose that action the certain outcome of which

maximizes (minimizes) the utility of the task

process, depending on the rewards associated with

each outcome of an action (Roberts, 1979). The

outcome of the action consists of changes to the task

process which are executed. Their effect on the

performance utility of the task process is then

evaluated. The reward associated with the outcome

will increase if the utility of the task process

increases following the change. Otherwise, the

reward decreases.

One of the possible solutions to increasing

performance visibility and explicitly linking it to the

task processes in such systems is to enforce their

integration by applying metamodeling.

5 RASF METAMODEL

The RASF metamodel proposed in this paper is

aimed at encompassing models of different kinds of

requirements: functional (task process) and

nonfunctional (performance), which form the

foundation of the software system information

structure. The task processes are scheduled by the

RACG supervisor and are decomposed into

individual tasks. The performance of the task

processes has to conform to RAS policies,

specifically those on synchronization and

communication. This is controlled by first collecting

measurement data on those processes, and then

analyzing the data according to the decision criteria,

determining the utility of the task process, and

taking action intended to further increase task

process utility.

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RACG SupervisorGroup Task Process

Indicator

Policy

Individual Task

Decision CriteriaDerived measure

Synchronization

reliability

Communication

Decision-Making Rules

Base measure

Measurement Method Measurement Function

efficiency

Analysis

Model

compliance fault tolerance

Utility Function

-Reward

OutcomeAction

Applied on

schedule

measure

Control

-Utility

Performance

Figure 2: RASF (partial) metamodel.

Knowledge on RAS task processes, the

performance hierarchy of measurable characteristics

in line with the RAS self-management decision-

making policies, and the rules and the relationships

among them are represented in the metamodel

structure in Figure 2. Figure 2 depicts the semantics

of the relationships between different constructs of

the RASF Metamodel in terms of a UML diagram. It

should be noted, however, that such a diagram does

not formally capture the semantics of the constructs

or their relationships. This lack of formalism is an

obstacle in the process of formalization and

consequent automation of the performance modeling

and self-management mechanisms. Furthermore, the

theoretical validity of the measurement procedures

and the decision-making process cannot be

established from this semi-formal notation.

This lack of formalism prompted us to exploit

the idea of a uniform graphical formalization of the

metamodeling of RAS behavior and performance

self-management within the RAS life cycle based on

the representational theory of measurement and

category theory.

6 RASF METAMODEL WITH

CATEGORY THEORY

Category theory is a branch of mathematics that, par

excellence, addresses “structure”, which is the main

motivation behind this research: the structure

emerges from interactions between elements as

captured by arrows, and not extensionally as in set

theory. Compared with other methods of formalizing

software concepts, category theory is not a semantic

domain in which the description of components and

connectors is formalized, but rather involves the

semantics of interconnections, configurations,

instantiation, and composition, which are important

aspects of engineering RAS with both autonomous

and autonomic behavior. Moreover, automation may

be achieved using category theory.

Category theory provides the basic building

blocks of metamodeling using the fundamental

notions of category, object, morphism, and functor.

Informally, a category may be regarded as a

collection of heterogeneous objects and morphisms

which model the social life of these objects, that is,

their interactions. A category can be defined as zero

or more objects bound together, where each object

may be either a primitive or a category. In addition,

a category may be augmented, diminished, or joined

with other categories to produce a new category.

Formally, a category consists of objects: A, B, C,

etc., and arrows (morphisms) f: A → B where, for

each arrow f, there are given objects: dom(f), cod(f)

called the domain and the co domain of f, and

indicated as A = dom(f) and B = cod(f) respectively.

Central to category theory is the notion of

composition: given arrows f: A → B and: B → C

with cod(f) = dom(g), there is an arrow: g ◦ f : A →

C called a composite of f and g. For each object A,

there is a given arrow: id

: A → A called the identity

arrow of A. The category must satisfy the following

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laws: i) Associativity: h ◦ (g ◦ f) = (h ◦ g) ◦ f for all f:

A → B, g: B → C, h: C → D; ii) Unit: f ◦ id

= f =

◦ f for all f: A → B. A functor F: C → D between

categories C and D is a structure-preserving

mapping of objects to objects, along with arrows to

arrows: i) F(f: A → B) = F(f): F(A) → F(B); ii) F(g

◦ f) = F(g) ◦ F(f); iii) F(id

) = id

F(A)

Category theory for RAS self-management has

adopted an approach of correction by construction,

through which components are specified, proved,

and composed so as to preserve their properties. In

an abstract sense, we are dealing with arrow

diagrams of task processes where the existing arrows

represent cooperation channels in a very general

way. This gives us the justification for associating

the Task Process category with the PATH category,

as described in (Pfalzgraf, 2004), where the

morphisms are sequences (paths) of consecutive

arrows, each node representing a task and each

arrow being a structure-preserving mapping, that is,

a morphism. This defines the composition of arrows

in a natural way (concatenation of consecutive

arrows), and this composition is associative. The

identity arrow with respect to each object in Task

Process will be assumed to exist by definition;

according to graph theory, it is a loop to the

corresponding node.

The Task Process category represents the

empirical relational structure in the measurement

procedure, and it includes the task categories and

their relations. The Base Measure category

represents the numerical relational structure to

which the empirical relational structure is mapped.

The measurement procedure is deemed valid if it is a

structure-preserving (homomorphic) function. It is

easy to see that the mapping Measurement Method

(MM): Task Process → Base Measure between the

categories Task Process and Base Measure is a

functor of objects to objects along with arrows to

arrows satisfying the functor property outlined

earlier. The base measures can be further combined

using categorical products and mapped to derived

measures (characterizing different performance

characteristics) by a morphism Measurement

Function (MF): Base Measure x Base Measure x

…→ Derived Measure.

In software engineering decision making, we

often consider multidimensional alternatives with a

variety of quality characteristics or from several

points of a view. Such situations arise when we are

trying to explain a dependent variable, such as

performance utility, on the basis of a number of

independent variables, such as reliability, fault

tolerance, etc. In order to calculate a utility function

of multidimensional alternatives, we need to define a

collection of alternatives. We think of the set of

alternatives as a Cartesian product of all considered

attributes characterizing performance expressed as

Reliability x Fault Tolerance x Efficiency x

Compliance, and the set of decision criteria, where

Reliability is a set of all possible values of the

domain of the utility function morphism for

reliability, and so on. The categorical product

relations p0, p1, p2, p3, and p4 are the

corresponding projections of the product Reliability

x Fault Tolerance x Efficiency x Compliance x

Decision Making Criteria to Decision Making,

Reliability, Fault Tolerance, Efficiency and

Compliance respectively (see Figure 3). Such a

product corresponds to all possible alternatives

representing the values of the Indicator.

The functor Utility Function: Reliability x Fault

Tolerance x Efficiency x Compliance x Decision

Making Criteria → Performance Utility in Figure 3

maps the Indicator alternatives to a sample scale

where performance utility is qualitatively

categorized as Excellent, Acceptable, or

Unacceptable. These performance categories provide

feedback on performance utility, and help determine

whether or not the task processes in the RAS satisfy

the performance policies or need improvement. The

functors Method (MM), Measurement Function

(MF), and Utility Function have to satisfy the

postulates of the representational theory of

measurement. By definition, each functor is a

structure-preserving mapping and thus guarantees

the theoretical validity of the performance

assessment.

We model performance self-management as a

decision-making process in category theory as

sequences of consecutive arrows linking

Performance Utility to Actions to Outcomes. The

generic functor Decision Rule: Preference Utility →

Actions maps each object of Preference Utility to an

object in Actions. Each action has to be mapped to

an outcome, or set of outcomes, and each outcome is

associated with a reward that affects the decision

criteria (or policies). The outcome is meant to

improve task process performance, and the

execution of the prescribed changes is modeled with

the generic functor Execute: Outcomes → Task

Process.

The diagram in Figure 3 can be abstracted as a

concatenation of consecutive arrows Measurement

Method (MM), Measurement Function (MF), Utility

Function, Decision Rule, Execute. The diagram

commutes, which guarantees reliable self-

assessment on task process performance and valid

decision making based on performance utility.

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THEORY

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Indicator Category

Preference Utility Category

Task Process