Transcript Multi-Actor Hidden Markov Inference Model (MAHMI) for

RAIDs Performance Prediction
based on Fuzzy Queue Theory
Carlos Campos Bracho
ECE 510 Project
Prof. Dr. Duncan Elliot
Outline






Goal
Introduction.
RAIDs Performance Analysis based on
Queue Theory (QT) .
RAIDs Performance Analysis based on Fuzzy
Queue Theory (FQT) .
Performance Evaluation of different RAIDs
using FQT ( Pending).
Conclusion.
Goal

To explore how Fuzzy Queing Theory can
be used to predict the performance of
RAIDs disks.

To investigate how both RAIDs level and
the workload influence service time, disk
utilization and response time.
Introduction
Roughly speaking, in the study of
processor as well as memory performance,
we deal basically with two fundamental
techniques: measurement and simulation.
With I/O systems, given the probabilistic
nature of I/O events, the study of I/O
performance is basically carry out by an
analytical model known as Queuing Theory .
Introduction
Within the context of Queuing Theory, there
are some parameters (such as the
interarrival and services times), which are
required to have a certain probability
distributions.
However, when a real queuing system (i.e.
RAIDs disks) is in the planning stage, these
parameters are described most of the times
by linguistic terms ( such as fast, moderate
or slow) or are estimated by experts.
RAIDs Performance Analysis
based on Queue Theory (QT) .
Benefits:
Using a (Fuzzy) Queue model will allow us
to predict important RAIDs performance
parameters such as the average time a job
spends in the RAIDs queue, the average
number of jobs in the RAIDs queue, the
probability of having a given number of jobs
in the RAIDs queue, among others.
RAIDs Performance Analysis
based on Queue Theory (QT) .
Basic assumptions:




A RAID disk is modeled as a single-open
queue system.
There is a Job-flow balance in the RAID disk.
One-step RAID disk’s behavior.
The average job-arrival rate and the average
rate are independent of the RAID disk’s state.
RAIDs Performance Analysis
based on Queue Theory (QT) .
Notation:












s : RAIDs Average time required to service a job.
 = 1/s : RAIDs average service rate time.
 : average arrival rate.
 =  /  : Traffic intensity at RAIDs .
r : RAIDs Average response time.
w : Average time a job spends waiting at RAIDs.
q : Average number of jobs at RAIDs.
n : Number of jobs at RAIDs.
U : Utilization of RAIDs.
umber of jobs at RAIDs.
a : The number of arrivals that occur within the fixed observation interval T.
d : Number of departures during observation interval T.
RAIDs Performance Analysis
based on Queue Theory (QT) .
More notation ( w.r.t stochastic queue model) :
It is completely specified with six parameters ( Kendall notation),
which are ( A/ S/ c/ B/ N/ D):


A: Arrival Process: This stochastic process describes when jobs arrive at the queue.
What is actually more useful, though, is knowing the times between arrivals of jobs
(interarrival times).

S: Service Process: This stochastic process describes the distribution of times
required to service a job when it leaves the queue and enters one of the servers.

c: Number of servers ( disks in our case)

B: Refer to the total number of jobs that can be in the system, including both those
in the queue and those being served. Most real systems have finite maximum queue
sizes due to their having limited amounts of buffer memory.

N: Refer to the total number of jobs that can enter in the system

D: It specifies the order in which jobs are removed from the queue and passed to a
server.
RAID 0,1,4 Modelling



A RAID 0 containing N disks will be modeled as N
separate M/M/1 (Fuzzy) queues.
A RAID 1, considering a read-only workload will be
modeled as an M/M/#mirrors (Fuzzy) queues. In
addition, a write-only workload will be modeled as
an M/M/1 (Fuzzy) queue.
A RAID 4 containing N disks, considering a readonly workload will be modeled as M/M/ N-1 (Fuzzy)
queues. In addition, a write-only workload will be
modeled as an M/M/1 (Fuzzy) queue.
Basic RAIDs Model: A single-queue with
N disks (servers) model.
A single-queue model of a system consists of one or more servers (i.e.
RAIDs disks) that process jobs entering the system. A single queue
temporarily stores (buffers) jobs that must wait to be processed while
jobs that arrived earlier are being processed.
Basic RAIDs Model: single-server
(disk) (M/ M/ 1) system.
.
The state of a system described by a birth-death process is the
number of jobs in the system, n. A birth occurs when a job enters the
system and increases n by 1. The departure of a job from the system
is called a death, and causes n to decrease by 1.
Basic RAIDs Model: single-server
(M/ M/ 1) system.
.
A discrete-state process which follow
the last assumptions is known as
Markov Process.
Basic RAIDs Model: single-server
(M/ M/ 1) Fuzzy system.
.
For the case, in which the interarrival
process as well as the service time is
unknown, a Fuzzy Markov Process
will be used. Under this context, the
transitions
probabilities
will
be
considered as intervals not just a single
real numbers.
Conclusions
Queuing Theory provide us with a
framework for predicting the RAIDs
performance under the assumption
mentioned before. However, in many
real-applications, these assumptions
are not completely satisfactory.
Conclusions

Fuzzy Queuing Theory provide us
with a more realistic model for
predicting the RAIDs performance
under
conditions
of
uncertainty
( in this case for not knowing in
advance the behavior of the interarrival
time as well as the service time), and
without the assumption of poisson
distribution.
References



Ching Kao. Parametric programming
to the analysis of fuzzy queues. Fuzzy
Sets & Systems,1999.
J. Buckley. Fuzzy Probability and
Statistics. Springer 2006.
H&P. Computer Architecture.Morgan &
Kauffman. 2003.
Questions ????