Formal Description of a DECIDE System

DECIDE distributed self-adaptive systems comprise n > 1 components that cooperate to achieve a set of common objectives. Each component within DECIDE executes the self-adaptation workflow shown in Figure 5.1. We use Cfg_i and Env_i to denote the set of possible configurations and the set of possible environment states for the i-th component, respectively. Thus Cfg_i corresponds to parameters that the local control loop of component i can modify, and Envi represent parameters that the component

can only observe. Additionally, the i-th component has mi ≥ 1 QoS attributes attri1∈

V1, attri2∈ V2, . . . , attrimi ∈ Vmi, where the value domainVj of thej-th attribute could

be R, R+, B = {true, false} etc. The mi QoS attributes are classified into the following

types (Figure 5.2): i) system-level QoS requirements; ii) system-level cost; iii) local- level (i.e., component-specific) QoS requirements; and iv) local-level cost, and satisfy the following conditions:

1. Local capability analysis & sharing of capability

summary 2. Receipt of peer capability summaries 3. Selection of local contribution-level agreement 4. Execution of local control loop none

major peer change(s) major local change

major change?

Figure 5.1: Decentralised self-adaptation workflow of a DECIDE component.

1. For any component i, the value of its j-th QoS attribute depends on the current configuration c ∈ Cfgi and the current environment state e∈ Envi, and can be

obtained through the quantitative verification of the following

attrij(e, c) = fij(e, c, Mi(e, c)|= Φij) (5.1)

where Mi is a Markov model parametrised by the state of the environment the

component operates in and the configuration selected by its local control loop, Φij is a probabilistic temporal logic formula, and f (·, ·, ·) is a function that can

be evaluated in O(1) time.

2. Attributes attri1, attri2, . . . , attrim, m < mi, are associated with the m > 0

system-level QoS requirements of the DECIDE distributed system. Formally, thej-th system QoS requirement, 1_{≤ j ≤ m, is specified as}

expr_j(attr1j, attr2j, . . . , attrnj) ./j boundj (5.2)

where a non-exhaustive list of options for the expression expr_j, relational operator ./j and bound boundj is shown in Table 5.3.

3. Attribute attri,m+1 is a measure of the system-level cost associated with the cur-

rent environment state and configuration of component i. Accordingly, Vm+1 =

R+ and the system-level costPn_i=1= attri,m+1 needs to be minimised subject to

system-level

QoS requirements system-level cost requirementslocal QoS local cost

Figure 5.2: QoS attributes of a DECIDE component and their roles in defining system- and local-level QoS requirements.

Table 5.3: Categories of DECIDE system-level QoS requirements from (5.2)

Vj exprj(attr1j, attr2j, . . . , attrnj) ./j∈ boundj∈

Types of QoS requirements

R+ Pni=1wiattrij,wi> 0 weights {<, ≤, ≥, >} R+

throughput, energy

usage, response

time [0, 1] Qn

i=1wiattrij,wi> 0 weights {<, ≤, ≥, >} [0, 1] reliability, availability

B booleanExpr(attr1j, attr2j, . . . , attrnj) {=, 6=} B liveness, security

them QoS requirements being satisfied.

4. Attributes attr_i,m+2, attri,m+3, . . . , attri,mi−1 represent local-level QoS require-

ments. We have Vm+2 = Vm+3 = . . . = Vmi−1 = B, and the local requirements

are satisfied iff

attrij = true for j = m + 2, m + 3, . . . , mi− 1. (5.3)

5. Attribute attr_{i,mi ∈ R+} represents local cost associated with the current environ- ment state and configuration of component i. This value needs to be minimised, subject to system and local QoS requirements being satisfied.

Example 5.1. The set of configurations for UUVi of our distributed n-UUV system is Cfg_i = Sp_{i × {0, 1}}ni_{, where (sp}

i, xi1, xi2, . . . , xini) ∈ Cfgi give the UUV speed spi

and sensor configurationsxi1, xi2, . . . , xini selected by the local control loop. The set of

environment states for UUVi is Envi= Rni+, where (ri1, ri2, . . . , rini) ∈ Envi gives the

measurement rates for the ni sensors.

We use the CTMC model in Figure 2.3 to model the l-th sensor of the i-th UUV and denote this model Mil2. The Markov model Mi(e, c) used to compute the QoS

attributes of UUV i in (5.1) is obtained through the parallel composition of the ni

sensor models: Mi= Mi1k Mi2k . . . k Mini.

Given the model Mi, the CSL formulae and the functions in Table 5.4 are used in

(5.1) to establish the QoS attributes for requirements R1–R6. Them = 2 system-level

2

The indices of the model parameters from Figuree 2.3 are adjusted accordingly to suit then-UUV system; thus, the configurable parameterxibecomesxil, the sensor rateribecomesril, etc.

Table 5.4: QoS attributes for UUVi, where valij is the value ofMi(e, c)|=Φij

j Vj Φij attrij = fij(e, c, valij)

1 R+ R=?“measurement”C≤60



vali1

2 _B P≥1[F oni1|oni2| . . . |onini] vali2

3 _R+ R=?“energy”C≤60



vali3

4 _B R_≤e“energy”max i C ≤60 vali4 5 _B Vni l=1  readil⇒ P≥pmin i [X accurateil]  vali5 6 B R=?“energy”C≤60  w1vali6+ w2sp−1

requirements, R1 and R2, are given by the following instances of (5.2):

R1: n X i=1 attri1≥ 1000 R2: _ 1≤i1<i2≤n

(attri12∧ attri22) = true

(5.4)