Advances in Applied Information Science
MATLAB Graphical User Interface For Study Through Modelling And
Simulation Of The Waiting Systems Without Priorities
MIHAELA OSACI, MANUELA PĂNOIU, CAIUS PĂNOIU, IONEL MUSCALAGIU
Department of Electrical Engineering and Industrial Computer
“Politehnica” University of Timisoara, Engineering Faculty of Hunedoara
Revolutiei no. 5, Hunedoara
ROMANIA
mihaela.osaci@fih.upt.ro http://www.fih.upt.ro
Abstract: - The scope of the paper is to create an interactive graphical user interface in MATLAB by
using the utility Guide to study, by modelling and simulation, the waiting systems without priorities.
This interface can be used both for teaching and for operational research studies of the systems that
are suitable for these models, in fields such as: production planning, telecommunications, traffic
control, computer performance prediction, medical services, air traffic, etc.
Key-Words: - Interactive graphical user interface, waiting systems without priorities, waiting models.
with known distribution.
The knowledge of the service mechanism
requires knowledge of the system topology, rule
according to which the service is performed, also
called ”service discipline” [1], [3] (e.g. FIFO
(First−In First−Out) – first come, first served), and
the distribution of the number of customers served
per unit time, or the service length distribution. The
service mechanism is also characterized by the
assumed known system capacity, i.e. maximum
number of customers that may exist at a given time
in the system or, equivalent, the maximum length of
the queue.
The unknown elements of the waiting
model are: waiting time in queue, waiting time in
the system, queue length, number of customers in
the queue and number of customers in the system.
All these unknowns are random variables and, by
solving the waiting model, we aim to determine
their distribution or an average value, depending on
the known elements.
A waiting model is denoted by A / S / c: (L,
d) [3], where: A – distribution of time between two
consecutive arrivals, S – service length distribution,
c – number of service stations (channels), L –
maximum length of the queue, d – service
discipline.
The most accurate results from the waiting
theory were obtained in those systems where the
arrival rate of the consumers and/or the station
service rate are governed by an exponential negative
probability. In most waiting systems, at least the
arrival rate of the consumers in the system is
1 Introduction
The waiting theory (or the theory of waiting threads,
or the queueing theory) [1], [2] deals with the study
of evolution of the systems which have clusters
(standby systems). In practice, the waiting theory is
mainly used to highlight the shortcomings in an
existing system in service and to show the directions
to streamline its operation. The study of a waiting
system is realised with a waiting model. A generic
waiting model consists of the following three
elements [1], [2]:
- The customers (consumers) requesting a
service;
- The service station (server) which has the
purpose to meet the customer demands; in a
waiting system, the service station may
have one post or multiple identical posts
(finite or infinite number), working in
parallel;
- The waiting thread or queue that forms
when the customers must wait.
The models of the waiting systems differ
between them by: the probability laws governing the
arrival and serving of the customers, number of
posts in the service station, discipline of the waiting
thread and the structure of the consumer population
(finite or infinite number of consumers).
The known elements of a waiting model
are: the flow of system inputs and the service
mechanism. The entries are characterized either by
the number of customers arriving per unit time, or
the intervals between two consecutive arrivals.
Either of these two quantities is a random variable
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Advances in Applied Information Science
exponential negative, because the consumers’
arrivals can be modelled using a Poisson
distribution [1].
2 Grafical Interfaces For Models Of
The Waiting Systems Without
Priorities
The graphical user interfaces for the simulation
model of the waiting systems without priorities are
programmed with the utility Guide from Matlab [4].
The main graphical user interface of the application
(Fig. 1) offers access possibility to the programmed
model interfaces.
Fig. 2 The interface of the model
Exp(λ)/Exp(µ)/1:(∞,FIFO) and the graphic of the
probability to have a certain number of customers in
queue
2.The model Exp(λ)/Exp(µ)/1:(m, FIFO).
Compared to the previous model [3], the maximum
length of the queue is m<∞. The model interface
and the graphical representation of the probability to
have a certain number of customers in queue are
shown in Fig. 3.
Fig. 1 The main graphical interface of the
simulation model
Each interface allows entering the input
parameters for simulation, the simulation of the
output values and the graphical representation of the
probability to have a certain number of customers in
queue.
The application allows the simulation of
four models for the waiting systems without
priorities.
1.Exp(λ)/Exp(µ)/1:(∞,FIFO). In this model,
the entries are made according to the Poisson
distribution [3], and the interval between two
consecutive arrivals has an exponential distribution
with parameter λ, as can be easily seen. The services
are made using a negative exponential distribution,
i.e. the length of the service as a random variable
has the exponential negative distribution with
parameter µ. The service distribution is FIFO. The
model interface and the graphical representation of
the probability to have a certain number of
customers in queue are shown in Fig. 2.
ISBN: 978-1-61804-113-5
Fig. 3 The interface of the model
Exp(λ)/Exp(µ)/1:(∞,FIFO) and the graphic of the
probability to have a certain number of customers in
queue for this model
2.The model Exp(λ)/Exp(µ)/c:(∞, FIFO).
These models [3] generalize the waiting models
with a single service station, having parallel service
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Advances in Applied Information Science
stations (identical in terms of serving time) and the
service discipline FIFO. The model interface and the
graphical representation of the probability of having
a number of customers in queue are represented in
Fig. 4.
3 Analysis On The Modelling Of The
Real System By Using The Waiting
Models Without Priorities
The operation of the computer systems, either
sequential or parallel, is based on the organization
of waiting threads for access to the shared resources
of the system (processor, memory, peripherals) [5],
[6], [7]. So, for each resource there is a waiting
system, in which the resource represents the service
station, and the system tasks are the customers [6],
[8].
So, the average quantities of interest
(average number of consumers in the queue and in
the system, the average waiting time in threads and
in the system) can provide a clear image of the
overall system performance and the ways for
improving.
If the time required to complete the parallel
program is finite, we can use: for the
multiprocessing operating systems [2], [5] - the
model Exp(λ)/Exp(µ)/c:(m,FIFO), for the network
operating systems and the really distributed
operating systems [5],[7], where the number of
execution threads equals the number of processors –
modelled with waiting network [2], each node of the
network being modelled with the model
Exp(λ)/Exp(µ)/1:(m,FIFO). If the execution time of
the parallel program becomes very long [6], and the
number of processes executed in the system
increases significantly, we shall use the models
Exp(λ)/Exp(µ)/c:(∞,FIFO)
or
Exp(λ)/Exp(µ)/1:(∞,FIFO).
Fig. 4 The interface of the model
Exp(λ)/Exp(µ)/c:(∞,FIFO) and the graphic of the
probability to have a certain number of customers in
queue
3.The model Exp(λ)/Exp(µ)/c:(m, FIFO).
This model [3] represents the case of the waiting
system with Poisson arrivals, exponential services,
more stations serving in parallel (identical in terms
of serving time), limited number of customers, m,
and the service discipline, FIFO.
4 Conclusion
The waiting theory is a very useful tool for
predicting the performance of the waiting systems.
So, the average quantities of interest (average
number of consumers in the queue and in the
system, the average waiting time in threads and in
the system) can provide a clear image of the overall
system performance and the ways to improve them.
The paper presents an application realised in
the Matlab medium, used to simulate the waiting
systems without priorities. This application can be
used either as teaching software, or in the
operational research, for improving the operation
parameters of the waiting systems.
Fig. 5 The interface of the model
Exp(λ)/Exp(µ)/c:(m,FIFO) and the graphic of the
probability to have a certain number of customers in
queue
ISBN: 978-1-61804-113-5
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