=Paper=
{{Paper
|id=Vol-1260/paper5
|storemode=property
|title=Positioning Traffic in NoSQL Database Systems by the Use of Particle Swarm Algorithm
|pdfUrl=https://ceur-ws.org/Vol-1260/paper5.pdf
|volume=Vol-1260
|dblpUrl=https://dblp.org/rec/conf/woa/Wozniak14
}}
==Positioning Traffic in NoSQL Database Systems by the Use of Particle Swarm Algorithm==
https://ceur-ws.org/Vol-1260/paper5.pdf
Positioning traffic in NoSQL database systems by
the use of particle swarm algorithm
Marcin Woźniak
Institute of Mathematics
Silesian University of Technology
Kaszubska 23, 44-100 Gliwice, Poland
Email: Marcin.Wozniak@polsl.pl
Abstract—In this paper, application of particle swarm al- (using methods like [21] or [20]) server responses to the
gorithm in positioning and optimization of traffic in NoSQL requests, but this goes according to the income queue. Earlier
database is discussed. Sample system is modeled with independent requests must be served first and others according to arrival
2-order hyper exponential input stream of packets and exponen- time. The problem is to position this system for most efficient
tial service time distribution. Optimization is solved using particle operation (we shall define optimal service, vacation and in-
swarm algorithm for various scenarios of operation.
come parameters). In this paper NoSQL database system will
be positioned for most efficient service and lowest possible cost
I. I NTRODUCTION of work by the use of particle swarm optimization algorithm
In modern computer science, artificial intelligence (AI) (PSO).
as well as evolutionary computing (EC) is one of most
important fields, widely applied in various tasks. There are II. A PPLIED MASS SERVICE MODEL
many applications of AI in sciences and industry. The power
of such approaches lies within the dedicated mechanisms is For NoSQL database systems various methods of modeling
used to simulate sophisticated phenomenon. On the other and simulation can be applied. Mainly we try to analyze
hand some techniques of EC were proven very efficient for the model, which describes operation. Operation model is
searching optimal solutions, easy to implement and precise. defined for applied queueing system (QS). Service description
Let us give same examples. AI applied to create learning of NoSQL database, where dedicated QS is applied to optimize
sets are discussed in [1], [2]. Some aspects of positioning operation cost defines Tservice , Tincome and Tvacation , which
computing network models by the use of EC are presented describe average time of service, average income time and
in [3], [4] and [5]. Moreover, AI is used for the optimization average vacation time (backup, conservation and etc.), respec-
of industry processes [6], [7], [8]. AI is also applied for tively. All these are independent random variables, where the
systems which require dedicated solutions [9], [10], [11], as symbols in time t are:
well as for agents oriented programming and object oriented • τ1 — the first busy period starting at t = 0;
refactoring techniques [12], [13], [14], [15]. In NoSQL systems • δ1 — the first idle time (first vacation time and first
we use dedicated solutions to increase performance. These standby time);
applications are especially designed for given purposes, please • h(τ1 ) — the number of packets served during τ1 ;
see [16]. We must build applications to serve clients requests, • X(t) — the number of packets in the system at t.
search in database, maintain service and more. All these
aspects demand special mechanisms like dedicated sorting In this paper is discussed simulation and positioning of NoSQL
and indexing algorithms and queueing systems to administrate database traffic modeled with dedicated QS, where we define
incoming requests. Dedicated sorting algorithms help to or- only one request arrival and response departure.
ganize large data sets as fast as possible. Some examples of
dedicated sorting algorithms are discussed in [17], [18], [19] A. Analytical results
and [20]. While in [18] and [20] is presented dedicated version
of quick sort, where implemented modifications enabled faster Modeling traffic in NoSQL systems is non-trivial problem.
sorting. In [17] is discussed dedicated merge sort, which even Classical cost structure is considered in [25]. While in [26],
more efficient version is presented in [21]. Moreover extended [27], [28] are presented most important aspects of positioning
research on these situations are discussed in [22] and [23], and cost optimization. Various queueing models for applied
where research on efficient methods of indexing and sorting type of the server are investigated in [29], [30], [31], [32],
large NoSQL systems are presented. Here will be discussed [33], [34], [35]. Please see also [36] and [37] for a review of
another important aspect of optimal service in large NoSQL important results on modeling and positioning.
systems - traffic simulation and positioning.
In this paper are applied results of the research on similar
Traffic in the network and therefore efficient service can objects, see [38] and [39] for joint transform of first busy
increase Quality of Service (QoS) [24]. We can simulate period, first idle time and number of packets completely served
the network traffic, where NoSQL database server is serving during first busy period in GI/G/1-type systems. More on
various clients. Clients send requests and server collects them generally distributed service times and infinite buffers can be
to proceed actions. After processing knowledge in database found in [40] and [41]. All these research results are helpful to
model and position QS of different type as discussed in [42] then for model of traffic finally we have:
[43], [4] and [44]. Where in [42] or [43] was given an idea
to apply evolutionary computation (EC) in QS simulation and ∂
En τ1 = − Bn (s, 0, 1) , (6)
positioning. An extension of the research for sophisticated QS ∂s s=0
were published in [4]. And finally main analytical model with similarly we have:
detailed description and assessments for traffic in the system
was given in [44]. Let us see the model of QS for NoSQL ∂
En δ1 = − Bn (0, %, 1) . (7)
database traffic. ∂% %=0
To model NoSQL server operation was used a finite-
buffer H2 /M/1/N -type QS, similar to server traffic modeling III. A PPLIED PARTICLE S WARM O PTIMIZATION
ALGORITHM
functions discussed in [45] and [46]. Let it be here presented
only a brief description, just to help in understanding NoSQL Particle swarm optimization algorithm (PSO) has been
positioning and simulation problem (for details please see shown in [47]. In the initial form PSO was modeling behaviors
[44]). Incoming requests describes 2-order distribution func- that can be observed in young birds or fish, which in the
tion: cluster behave in a very specific way. Thanks to the ease of
implementation and adaptation to different tasks PSO algo-
F (t) = p1 1 − e−λ1 t + p2 1 − e−λ2 t , t > 0, (1)
rithm has become one of the most commonly used algorithms
where λi > 0 for i = 1, 2 and p1 , p2 ≥ 0. Inter-arrival times in it’s original or modified versions. In [48] is presented
are mixed of two exponential distributions with parameters adaptivity of this methods to different initial conditions of
λ1 and λ2 , which are being “chosen” with probabilities p1 positioned object. While in [49], [50] and [51] many possible
and p2 . In the system, there are (N − 1) places in queue aspects of application of various EC methods in engineering
and one for packet in the service. System starts working at optimization are discussed. In [52] PSO application in relay
t = 0 with at least one packet present. After busy period the times is presented. Finally discussion on theoretical aspects of
server begins vacation which is modeled with 2-order hyper convergence and stability can be found in [53], [54] and [55].
exponential distribution function: Let us discuss behavior of typical swarm.
V (t) = q1 1 − e−α1 t + q2 1 − e−α2 t , t > 0. (2)
In the swarm similar operations are performed by many
individuals of the same species. In action, individuals com-
Interpretation of parameters αi , i = 1, 2 and q1 , q2 is similar municate with each other in a manner characteristic for the
to that for λi , i = 1, 2 and p1 and p2 . If at the end of vacation species. Communication helps to exchange information and as
there is no packet present in the system, the server is on a result the whole swarm is moving in a certain direction or
standby and waits for first arrival to start service process. If behaves like one big organism. PSO algorithm uses the insights
there is at least one packet waiting for service in the buffer that emerge from the observation of swarms of fish or insects
at the end of vacation, the service process starts immediately that are looking for food or a safe place. This process can
and new busy period begins. be described in mathematical model. If we accept the goal of
optimizing criterion function of the object, we can talk about
Functions F (·) and V (·) help to simulate operation of optimizing algorithm.
the examined NoSQL system, where inter-arrival times and
vacation are defined in (1) and (2). In the research PSO is used PSO algorithm searches the space of test solutions by
to find optimal set of parameters λi , pi , µ and αi . To describe matching trajectories of individuals (particles) in a quasi-
minimal amount of resources to perform all operations rn (c1 ) stochastic way. A particular individual is a vector and it’s
is defined: movement is the result of stochastic and deterministic com-
ponents of movement model. Stochastic component corre-
Qn (c1 ) r(τ1 )En τ1 + r(δ1 )En δ1 sponds to random walk. In contrast, deterministic component
rn (c1 ) = = , (3)
En (c1 ) En τ1 + En δ1 of the movement model is distance between particles, or
other feature, which is modeled in mathematical equation. In
where the symbols are: r(τ1 )-fixed unit operation costs during
subsequent periods individual particles move in looking for
busy period τ1 , r(δ1 )-fixed unit operation costs during idle
the global optimum, where because of stochastic component
time δ1 , En τ1 -means of busy period τ1 and En δ1 -idle time δ1
this movement also has a random character. This combination
on condition that system starts with n packets present. In (3)
gives ability to efficiently search the test area of the simulated
are used means of busy period and vacation (idle) time. The
or positioned object. If during motion the particle is on a
explicit formula with detailed information and description for
new position, which is characterized by better properties of
conditional joint characteristic functions of τ1 , δ1 and h(τ1 ) is
the optimum, for this position it updates the knowledge. In
presented in [4] and [44]. Here let us briefly discuss modeling
further exploration particle accepts found value as the optimum
of applied QS. General equation to calculate this values is:
and starts searching in relation to this value. In each iteration
Bn (s, %, z) = E{e−sτ1 −%δ1 z h(τ1 ) | X(0) = n}, 2 ≤ n ≤ N, of the algorithm, the particles can communicate with each
(4) other and share information about the sought optimum. If we
where s ≥ 0, % ≥ 0 and |z| ≤ 1, n ≥ 1. Details on this consider that all particles in the swarm want to reach the sought
equation are discussed in [17], [4] and [44], where using it we optimum criterion function for the positioned object, in the end
can define, components of (3) total cos of work: we can take as the optimum best of all-values. In this way,
entire swarm is communicating between it’s individuals while
En e−sτ1 = E{e−sτ1 | X(0) = n} = Bn (s, 0, 1), (5) looking for the global optimum of the criterion function.
A. PSO model Algorithm 1 Basic PSO applied to position NoSQL database
system traffic
Actions taken while searching for the optimum criterion 1: Define all coefficients: α–optimum value memory factor,
function of the object are written as mathematical equations. β–optimum position memory factor, generation– number
The model of particle swarm movement keeps the communica- of iterations in the algorithm, particles–number of parti-
tion between particles based on a deterministic factor, but also cles in the swarm,
introduces randomness of the movements. To build the model 2: Dedicated criterion function: lowest cost of NoSQL system
of the swarm behavior in the solution space of the object are operation (3),
used the following assumptions: 3: Create at random initial population,
4: t:=0,
• Points in the search space are seen as potential solu- 5: while t ≤ generations do
tions to moving particle swarm. 6: Move particles according to (9) and (8),
7: Sort particles according to the value of criterion func-
• Each particle is seeking for optimum, which is deter- tion,
mined by it’s position in the space. 8: Evaluate population and take best ratio of them to next
• At the end of PSO iteration, the particles interact with generation,
other particles and change information. 9: Rest of particles take at random,
10: Next generation: t + +,
• As a result of communication global optimum is 11: end while
selected, relative to which all particles are continuing 12: Best particles from the last generation are potential
their search. optimum.
• Number of moving particles is determined.
IV. R ESEARCH RESULTS
In the model, we mean a particle moving in a virtual way. We
only model the choice of the optimum to which particle has Research results help to predict possible response time and
moved. Selected points in the study area are compared, and optimize service cost rn (c1 ) considered in different variants:
among them is chosen the global optimum, see also [56] for under-load, critical load and overload. PSO simulations were
details on convergence and stability of PSO. performed for r(τ1 ) = 0.5 and r(δ1 ) = 0.5. It means
that modeled NoSQL database system uses 0.5 energy unit
PSO algorithm for each particle takes the form of xti whose each vacation and work period. For other system types these
i components correspond to dimensions of the test space. Each values may be changed in (3), what makes presented model
particle is moving at the speed vit appropriate for the swarm flexible and easily applicable. All presented research results
in a particular PSO iteration. These values vary in subsequent are averaged values of 100 PSO samplings for 20 particles
iterations of the algorithm. Speed of movement of the particles in 80 iterations with α = 0.4 and β = 0.4. In each iteration
is described by the formula: best ratio = 90%, what means that 72 best particles were
moved to next generation and 8 were taken at random. This
vit+1 = vit + α · 1 · [g∗t − f (xti )] + β · 2 · [xt∗ − xti ], (8) helped to search entire object space for optimum values, where:
where the symbols are: vit –speed of i particle in t iteration, • Average service time: Tservice = µ1 ,
α–optimum value memory factor, β–optimum position mem- • Average time between packages income into the sys-
ory factor, 1 , 2 ∈ [0, 1]–random values, g∗t –optimum for t tem: Tincome = λp11 + λp22 ,
iteration, xt∗ –optimum position for t iteration, f (xti )– fitness
function value for i particle in t iteration, xti –position of i • Average vacation time: Tvacation = αq11 + αq22 ,
particle in t iteration.
• Examined system size: N = buffer size +1.
Equation repositioning particle swarm movement in each Scenario 1.
iteration of the PSO algorithm is defined using formula: PSO was performed to find set of parameters for lowest cost
of work. In Table I are optimum values for all parameters that
xt+1
i = xti + (−1)K · vit , (9) affect NoSQL server work. PSO positioned NoSQL system
where the symbols are: xti –position of i particle in t iteration, TABLE I. O PTIMAL PARAMETERS µ, λi , αi , pi , qi FOR i = 1, 2 AND
vit –speed of i particle in t iteration, K–random factor to change LOWEST VALUE OF (3).
motion direction. The initial coordinates of the particle swarm λ1 λ2 α1 α2 p1 p2 q1 q2
position and their speed we take at random. However, it is 2.9 2.3 1.43 0.32 1.78 1.3 6.1 3.5
possible also to apply some boundary criteria that will allow µ 0.6 rn (c1 ) 0.34
additional control of the swarm. Tservice Tincome Tvacation
[sec] 1.67 1.18 15.20
These two equations allow to change position of each
particle and therefore search entire space for the optimum of to operate at minimum costs, if the service and vacation are
the modeled object. Let us now see possible implementation results from Table I. PSO was also arranged to position the
of PSO, which is presented in Algorithm 1. system in various scenarios.
Scenario 2. average on-line shop or customer service). Calculated values
NoSQL Tservice = 2[sec], what means that request service of Tservice and Tincome gave positioning for lowest cost of
takes about 2[sec]. Research results are shown in Table II. work. If the system works with calculated parameters QoS
is still very high, but also cost of service is possibly lowest,
TABLE II. O PTIMAL PARAMETERS µ, λi , αi , pi , qi FOR i = 1, 2 AND what means better profit for the owner. In the article, have
LOWEST VALUE OF (3).
been examined newly proposed methods for QS simulation
λ1 λ2 α1 α2 p1 p2 q1 q2 and positioning (see also [4] and [44]). EC methods like PSO
2.13 3.15 0.94 0.78 79.70 0.89 2.30 12.10 are excellent for simulation or positioning of different objects.
µ 0.5 rn (c1 ) 0.37
PSO method helps to simulate complicated objects and because
Tservice Tincome Tvacation
[sec] 2.08 37.70 17.96
of the free design, calculations are easy to perform. The experi-
ments confirmed PSO efficiency in simulation and positioning
the system in various scenarios representing common traffic
situations.
Scenario 3.
NoSQL Tservice = 0.5[sec]. This situation represents NoSQL
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