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QUEUING CONFIGURATION IN SATELLITE
COMMUNICATION
S. Maragathasundari
Associate professor, Department of Mathematics, Kalasalingam Academy of Research and
Education Krishnankoil, (India).
E-mail: maragatham01@gmail.com.
ORCID: https://orcid.org/0000-0003-1210-6411
G. Ammakkannu
Associate Professor, Department of Mathematics, Kalasalingam Academy of Research and
Education, Krishnankovil, (India).
E-mail: ammakannu1975@gmail.com.
ORCID: https://orcid.org/0000-0002-8789-2093
P. Manikandan
Assistant Professor, Department of Electronics and Communication Engineering,
Kalasalingam Academy of Research and Education, Krishnankovil, (India).
E-mail: maanip85@gmail.com.
ORCID: https://orcid.org/0000-0002-5737-0235
Recepción: 25/10/2019 Aceptación: 24/08/2020 Publicación: 30/11/2021
Citación sugerida:
Maragathasundari, S., Ammakkannu, G., y Manikandan, P. (2021). Queuing conguration in satellite
communication. 3C Tecnología. Glosas de innovación aplicadas a la pyme, Edición Especial, (noviembre, 2021),
179-197. https://doi.org/10.17993/3ctecno.2021.specialissue8.179-197
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ABSTRACT
Satellite correspondence frameworks have been utilized for a considerable length of time to
give xed point and versatile administrations to the business and military markets around
the world. The procedure completed in satellite correspondence is changed over as a
Queuing issue and the issue is settled by methods for Supplementary variable technique of
Queuing. It results in the derivations of the Queue execution proportions of the framework
which causes the procedure to recognize the deformities in the process. It likewise gives
the thought regarding the uplift of the methods in satellite correspondence systems which
prompts a smooth running of the communication in a protable manner. Numerical outline
and Graphical portrayal given toward the end makes an intricate thought regarding the
lining procedure occurring in satellite correspondence.
KEYWORDS
Delay, Compulsory vacation, Reneging, Feedback service.
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1. INTRODUCTION
Services incorporate two-way media communications, route, and TV and radio telecom.
As in most present-day remote frameworks, satellite correspondences transfer speeds have
developed after some time with advanced information rates beginning from kilobits every
second (Kbps) to current framework wide limit of more than 100 gigabits for each second
(Gbps).
Graphic 1. Satellite communication.
Source: own elaboration.
There is currently extraordinary improvement in the arrangement of new high throughput
satellite broadband arrangements equipped for conveying web, voice, video and other
special interchanges administrations. Real administrators and supporters either have
propelled or are making arrangements for a wide scope of uses, including purchaser as
well as gas and oil, calamity recuperation, aeronautical, oceanic, military and other mission
basic prerequisites. For each satellite arrangement, there is a lot bigger arrangement of
earthbound based frameworks, or ground stations, extending from satellite control oces
to end-client gadgets. The approval, support and investigating of these ground stations
regularly requires a mix of indoor and outside testing of various RF and IF subsystems and
segments. Lam (1980) studied this paper in general about the models on multilevel diversity
coding.
Fantacci and Zoppi (2000) studied the performance of dierent polling systems used in
wireless local networks where the transmission channel exhibits a non-stationary behavior.
Yeung and Zhang (1999) discussed about the maximum channel throughput of CSMA
approaches unity in the limit of very long queues. Giambene and Kota (2006) suggested a
Satellite
Uplink
Ground stations
Downlink
www.explainthatstu.com
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work in detail about the interaction of dierent layers that can be permitted to improve the
higher-layer goodput as well as user satisfaction.
Hung, Montpetit, and Kesidis (1998) describes an ATM-based satellite network, focusing
on the networking (ATM) aspects of the design. Chang and Lin (1993) studied the
performance of VSAT-based satellite wide area networks. Basic geostationary and non-
geostationary satellite constellations are considered. Financial success of satellite personal
communication systems was examined by Lutz (1998). Louvros, Pylarinos, and Kotsopoulos
(2007) investigated a new model which is proposed with a dedicated queue for each
transceiver in the cell.
Zaim (2003) calculated a new call and hand-o call blocking probabilities in LEO satellite
networks carrying voice calls. Maragathasundari (2015) derived the execution measures
for a mass section queuing model of three periods of organization with dierent journey
strategies. Maragathasundari et al. (2017) described a non-markovian queuing model of
restricted admissibility and service interruption in which entry was taken after a Poisson
method. Zhu et al. (2012) discussed about the Load Balancing Routing Based on Agent for
Polar-orbit LEO satellite networks. Maragathasundari and Karthikeyan (2016) investigated
a mass queuing model with short and long escape.
1.1. COMMUNICATIONS SATELLITES
Communications satellites are “space mirrors” that can help us bounce radio, TV, Internet
data, and other kinds of information from one side of Earth to the other.
1.2. UPLINKS AND DOWNLINKS
In the event that you need to send something like a TV communicates from one side of
Earth to the next, there are three phases included. To start with, there’s, where information
is channeled up to the satellite from a ground station on Earth. Next, the satellite procedures
the information utilizing various installed transponders (radio recipients, intensiers, and
transmitters). These lift the approaching sign and change their recurrence, so approaching
sign don’t get mistook for active ones. Various transponders in a similar satellite are
utilized to deal with various TV stations carried on various frequencies. At last, there’s the
downlink, where information is sent down to another ground station somewhere else on
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Earth. Despite the fact that there’s generally only a solitary uplink, there might be a large
number of downlinks, for instance, if numerous individuals are getting a similar satellite
TV signal without a moment’s delay. While a correspondences satellite may transfer a sign
between one sender and beneciary (started up into space and withdraw once more, with
one uplink and one downlink), satellite communicates commonly include at least one uplink
(for at least one TV stations) and dierent downlinks.
The above communication progression is converted as a Queuing problem. The problems
faced in the process are diagnosed and the corresponding performance measures of the
Queuing system of the satellite communication are derived. The communication procedure
is explained in terms of Queuing parameters as Stages of service, Delay, compulsory
vacation, Reneging and feedback service
1.3. STAGE 1: DELAY PROCESS
Much like some other correspondences’ medium: inertness is the time taken for data to go
from the inception to the goal and possibly for the reaction to return.
Dormancy in satellites is particularly progressively evident due to the exceptionally long
separations that the sign must go into space and back. The separation voyaged relies upon
the area of the satellite and along these lines its circle. There are three primary satellite sorts
utilized in satellite correspondences:
1) Geostationary/geosynchronous/GEO: these satellites stay in a generally xed
position in the sky contrasted with a situation on the equator. In this way you
don’t have to modify your reception apparatus and it is dependably in a known
relative position in the sky. These satellites are around 32,786km from the Earth.
2) Low Earth Orbit (LEO): The Iridium satellites are just 781km from the surface
there are bunches of them and they cooperate like a ying cell arrange.
3) Medium Earth Orbit (MEO): It has another player nancially with O3b circling
at 8063km, they will have less satellite, giving lower dormancy than GEO however
more limit and less satellites than Iridium.
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1.4. COMPULSARY VACATION
On-orbit satellite servicing will elongate the life of some very expensive satellites. Its
application areas are very broad where each one has its own importance based on scientic,
economic, strategic, and societal benets. Repair and maintenance of the satellites in space
keep a unique and valuable asset operational, essentially improving it beyond its design
lifetime or the reliability of its subsystems. It improves overall mission robustness and oers
a unique capability to improve risk posture through post-launch operations.
The process of on-orbit satellite is very simple. For the purpose, a service spacecraft is built
with robotic arms. The major components here include an advanced spacecraft with a
specialized toolkit and robotic arms just like humans for capturing, interacting with, and
manipulating a client, software for managing semi-autonomous servicing tasks, and an
advanced sensor suite for careful rendezvous and proximity operations. In case when any
satellite developing a snag is discovered, the servicing spacecraft is made to approach it,
grab it, pull it close, and repair or exchange the faulty part with a toolkit it is carrying. If a
satellite runs out of the fuel, similar technology is used to refuel it.
In past, it was not possible to repair all satellites in orbit. It was mandatory to build them
accordingly so that they can be serviced. Like for example when all three-rubidium clock
of IRNSS 1A satellite failed, then it was pushed to graveyard. The satellite was launched
by Indian space and research organization (ISRO) as the rst in the queue of India’s own
regional navigation system, NAVIC. But today the technology has matured and can repair
all satellites on orbit. The Servicer designed SSL is compatible with most government and
commercial spacecraft that are currently in orbit, even those not designed to be serviced in
space.
1.5. STAGE 2: (OPTIONAL)
If the satellite is not working properly even after the maintenance done at the compulsory
vacation, the satellite may go for an extended optional vacation. Luckily, the propelled
apply autonomy installed new satellite overhauling undertakings are planned to lessen the
quantity of satellites confronting this sort of inopportune retirement. Overhauling rocket
can x, reposition, and refuel satellites utilizing automated arms, and will in the long run
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have the option to collect satellites altogether in space. Satellite overhauling could wipe out
the requirement for governments and organizations to contribute millions — and once in
while billions — into structuring, building, and propelling a substitution satellite each time
xes or fuel are required. Overhauling would likewise serve a national security job, the
same number of government satellites hand-o basic data that shouldn’t be disturbed. The
innovation even can possibly enable people to achieve Mars.
Graphic 2. Satellite service.
Source: own elaboration.
1.6. RENEGING
Likewise, because of restlessness clients may leave the framework subsequent to joining the
line. This procedure of reneging happens during mandatory excursion with parameter γ.
The clients/clients are holding up at the less than desirable end to get any sort of valuable
data which are to be sent by the transponders at the uplink stations. Be that as it may,
the procedure of gathering, might be postponed a ton during the movement of necessary
support.
Consequently, the client may become irritated and they are not willing to remain back in
the line. Thus, they will look for some other downlink station to show signs of improvement
gathering of sign on schedule. Henceforth reneging happens.
1.7. FEEDBACK SERVICE
Furthermore, if the client is disappointed with the administration, they can decide on an
input administration with likelihood p.
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Criticism administration is essential, if the sign sent by the transponder isn’t appropriately
gotten by the end clients. Henceforth the undesired or undesirable sign got at the recipient
may nourished back again to get the unadulterated type of sign. i.e. signal without clamor.
So as to keep away from this sort of loud ag, we have to avert our framework with
considerably more prociency.
So as to give high throughput, the inertness ought to be low. There were a few stages
which are recorded underneath, to diminish the input administrations. A large number of
these arrangements hazard creating more otsam and jetsam from impacts, and all future
costly and disputable. Another methodology is to forestall space crashes in any case through
better trac control. Today, satellite administrators don’t have exact orbital parameters
for dierent satellites that may represent a danger of impact. Just a couple of nations —
primarily the United States, and somewhat China, Europe, and Russia — approach exact
following information, and that data is stayed quiet, in case it uncovers insights concerning
the advanced instrumentation used to assemble it.
Military organizers have since quite a while ago discussed the requirement for “space
situational mindfulness”, and the military tracks satellites for its very own motivations. But
the inexorably jam-packed nature of close earth circles, in addition to the risk presented
by crash otsam and jetsam, has driven numerous to contend that we need comparable
following abilities for the regular citizen area. The shabby method to do this is to make
a portion of the military information open; the costly way is manufacturing a dierent,
absolutely regular citizen following framework. The parts utilized for the uplink and
downlink correspondence ought to be very much prepared with no harms. The gear used
for this sort of correspondence ought to be kept up appropriately, with a wide range of
approval procedures to give productive sign at the less than desirable end.
2. METHODOLOGY OF SOLVING THE ABOVE QUEUING ISSUE
2.1. METHODOLOGY
The above queuing issue is solved by supplementary variable technique of queuing theory.
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First, we outline the administering conditions for the lining issue engaged with satellite
correspondence concentrate in area 4 by utilizing the boundaries like help rendered, short
excursion, long get-away, delay in getting into upkeep work, reneging, input administration
and phases of administration. Here help is rendered into two phases which make the
framework to work out in a simplicity way.
As a subsequent advance, we process out the underlying limit states of the issue characterized.
Next by the utilization of dierent advantageous factors, we infer the likelihood creating
capacity of the line size of the satellite correspondence lining issue. In continuation, length
of the line, number of clients (attempts to be completed) in the framework, holding up time
of the clients in the line just as in the framework are inferred.
2.2. BENEFITS
All the deductions are defended by methods for numerical outline and graphical
depiction. In light of that, examination have been made in the numerical investigation
and the investigation is done in the examination report. Having a profound report on
the examination, one can get limiting the defer procedure in getting into the excursion
method in the Satellite. Additionally, framework support work is required whether for
shorter length or longer span could be anticipated. This investigation assists with doing the
dierent components in correspondence issue in an exact way. This prompts the length of
the line to be negligible in the framework. Use factor would be made to a maximal. Satellite
correspondence framework attempts to a maximal level.
3. ASSUMPTIONS UNDER LYING THE MODEL
Customers arrive in groups to the Queuing system (In the process of communication).
Clients arrive in batches to the system modelling supermarkets with mean arrival rate λ> 0.
λek (k = 1 to n) be the rst order probability that a batch of r customers arrive at the system.
Here, 0 ≤ ek ≤1 and ek =1
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For the rst stage of service, is the conditional probability of completion of
completion of rst stage of service. The probability distribution function of the rst stage
of service and its corresponding density function are given by .Hence
Similarly for all the other parameters Delay process , Compulsory vacation
Stage 2 process we have the following functions respectively:
4. STEADY STATE CONDITIONS OVERSEEING THE FRAMEWORK
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
The following boundary conditions are used to solve the above equations.
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(10)
(11)
(12)
(13)
5. DISTRIBUTION OF THE QUEUE LENGTH AT ANY POINT OF
TIME
Multiply (1) by zn and sum over n from 1 to ∞ and add it to (2) results in the following
equation
(14)
(15)
(16)
(17)
Similarly,
(18)
(19)
(20)
(21)
Now integrating (14) from 0 to x, it gives
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(22)
Integrating the above by parts,
(23)
Where is the Laplace Stieltje’s transform of the service time.
Again multiply (22) by and integrating,
(24)
Similarly, from the other parameters, we have
(25)
(26)
(27)
(28)
(29)
(30)
Using (28) and (30) in (18) we get,
(31)
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To nd the probability making limit of the line gauge paying little mind to the state of the
structure.
Let Pq (z) be the probability generating function of the Queue size.
Then adding (23), (25), (27) and (29), we get
Hence,
(32)
6. RESULTS
The idle time Q is determined by using the normalization condition
Using L’Hopital’s rule, we get
Also
From Q, the utilization factor ρ can be determined.
Let Lq a chance to demonstrate the reliable state typical number of customers in the line.
By then
Where N(z) and D(z) are the numerator and denominator of (32).
Since Pq (z)= =1, we utilize two-fold separation and get
(33)
Where primes mean subordinates with respect to z and after a course of action of logarithmic
enhancement, we get length of the queue Lq in closed frame.
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Substituting for N '(1), N ''(1),D'(1), D'' (1) from (34) – (37) in (33), we obtain Lq in closed form.
Further the mean waiting time of a customer in the queue as well as in the system and
the number of customers waiting in the system can be found using Little’s formula
L= Lq+ ρ
7. NUMERICAL JUSTIFICATION OF THE MODEL
Assume that service time follows exponential distribution in particular and based on this
condition, the numerical justication is elaborated below:
The values are collected accordingly: λ = 2, θ1= 5, r = 0.5, γ = 0.6
Table 1. Variation of θ1=3,5,7,9,11.
QρLq L WqW
0.2770 0.7230 4.8008 5.5238 2.4004 2.7619
0.3817 0.6183 1.7827 2.4010 0.8914 1.2005
(34)
(35)
(36)
(37)
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0.4346 0.5654 1.1901 1.7555 0.5951 0.8778
0.4667 0.5333 0.9656 1.4989 0.4828 0.7495
0.5019 0.4981 0.7789 1.2770 0.3895 0.6385
Source: own elaboration.
Graphic 3. Variation of θ1.
Source: own elaboration.
Table 2. Variation of θ2=5,6,7,8,9.
QPLq L WqW
0.2770 0.7230 4.8008 5.5238 2.4004 2.7619
0.2850 0.7150 4.1952 4.9102 2.0976 2.4551
0.2906 0.7094 3.9202 4.6296 1.9601 2.3148
0.2948 0.7052 3.6871 4.3923 1.8436 2.1962
0.2980 0.7020 3.5179 4.2199 1.7590 2.1100
Source: own elaboration.
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Graphic 4. Variation of θ2.
Source: own elaboration.
8. NUMERICAL ANALYSIS
From Table1, it is identied that, if the process of completion of work in the rst stage
increases, it leads to a decrease in the length of the queue and also in the other performance
measures. As the work gets completed sooner, the server idle time Q increases. Table 2 gives
the fact that, as the probability of completion of vacation increase, it leads to an absence of
a long queue in the communication process. It results in the decrease in waiting time of the
process to be carried out in the queue as well as in the system. The results are as expected.
9. CONCLUSIONS
The Queuing procedure happening in the satellite communication procedure has been
well analyzed in this paper. The Queuing problem is solved by means of supplementary
variable method. The corresponding Queue execution measures are determined. The
numerical illustration and the graphical picture well scrutinized the Queuing problem in
satellite communication process. As a future work, obstruction can be brought into various
stages. Furthermore, the possibility of Bernoulli move away could be added as it expects
an obvious part taking everything together the coating structure. Equivalent examination
of execution methods with this model can be appeared by including the parts of kept
worthiness, balking in dierent stages, Priority alliance, set up time and multi move away
from strategy. The system of need can be utilized in the above model and as a remarkable
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case this model can be diminished from that as of late arranged model. Retrial cooperation
can be considered in this model.
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