Parameters of the Сarrier Sense Multiple Access Protocol with Conflicts Resolving at the Physical Layer Текст научной статьи по специальности «Медицинские технологии»

Visnyk N'l'UU KP1 Seriia Radiolekhnika tiadioaparat.obuduuannia, "2019, Iss. 79, pp. 55—59

Y^K 519.2, 621.39

Parameters of the Carrier Sense Multiple Access Protocol with Conflicts Resolving at the Physical Layer

Yerokhin V. F., Poliakova A. S., Sboiev R. Yu., Hoi V. D.

National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" E-mail: Roman.sboycv&gmaU. com

At present., the global growth of communication needs makes us more efficient in using of the frequency spectrum. The development of communication systems requires an increase of throughputs, but the frequency spectrum is limited, which will not allow to increase the channel width or the number of channels. Assuming that at one frequency there is an opportunity to transmit several mutual interference signals at one time, the problem of the separation of these signals arises. But, complexity of demodulation procedures has significantly increased compared to the classical. It is necessary, therefore, to determine whether this complexity increasing will be justified. To answer this question, it is necessary to find out how the throughput of the random multiple access system increases, where the frequency resource multiple reusing is possible. For research was chosen the carrier sense multiple access protocol, which have become widespread in packet networks for their successful combination of relative simplicity of access algorithms and fairly high efficiency. The purpose of the research is to determine the main characteristics of the various carrier sense multiple access protocols with collision detection and with additional assumption about conflicts resolving at the physical layer. The parameters of the carrier sense multiple access protocols with collision detection and with additional assumption about conflicts resolving at the physical layer are obtained. It is shown that in comparison with the classical protocol, the assumption about paired conflicts resolving at the physical layer gives the significant increasing of the throughput in the communication systems with such access protocols. The comparison results are given. The obtained results allow to confirm the expediency of implementation in demodulators of the perspective receiving devices algorithms of conflicts resolving at the physical layer as being characterized by relatively small complexity.

Key words: CSMA CD: conflicts resolvconflict.s resolving on the physical layer: multiuser detection theory-queuing system: source of recurring calls

DOI: 10.20535/RADAP.2019.79.55-59

Introduction

With the rapid development of telecommunication networks and the continuous increase of their traffic. There is an urgent need to consider about reusing of a frequency resource by complicating demodulators that will be able to receive two or even more interfering signals1.

For specialized radio networks in Ukraine fixed bands are allocated2, which are identified and controlled by radio frequency distribution services. At the same time, the number of subscribers of such networks and the intensity of information exchange in them gradually increase. The solution of the problem of frequency resource deficit can be based on its reusing for example, by the methods of the multiuser detection theory fl 7]. However, algorithms for opti-

1https://news.finance.ua/ua/news/-/431277/

-https://www.kmu.gov.ua/ua/npas/39517235 https://zakon.rada.gov.ua/laws/show/1208-2005-%D0%BF

riial demodulation of mutually interferingsignals are characterized by rapid increasing of complexity its exponential dependence on the number of mutually interferingsignals thatnmst be separated. Even when mutually non-orthogonal signals are 2-3. the appropriate algorithms are nontrivial (see. for example. [3 10]). Therefore, apractical interest is the question of how much the parameters of a random multiple access protocol will improve with confiictsresolving between radio signals in receiver demodulators. that is, at the physical layer. Snch parameters firstlyare their throughput and the average time before the successful transmitting [7.12].

The purpose of the article is to summarize the obtained results about the throughput of the widely nsed CSMA-CD protocol [7.11.12]. and to calculate the average time before the successful transmittingwith an

56

Yerokhin V. F., Poliakova A. S., Sboiev 11. Yu., llol V. D.

additional assumption about conflicts resolving at the physical layer (CRPL). Were selected examples that expected for the possibility of technical implementation in the near future - the CRFL multiplicity 2 and 3.

1 Throughput of the CSMA-CD protocol with CRPL

The CSMA-CD protocol functions as follows. Requirements for the simplest flow with the parameter A enter the service system. The servicing of each requirement is a two-stage exponentially distributed with a parameter on the first and at the second stage. The description of the service in the analyzed queuing system (QS) in the form of a two-stage procedure is due to the fact that at a certain random interval of time, initially, the transmission of messages to all users should be allowed. At the end of this random time interval, depending on the number of processed (identified) applications at the first stage, there arises either their reset to the source of recurring calls (SRC) with intensity x (if there was an unresolved conflict) or successful non-conflict service in the second stage. Thus, the task of the first stage is to "collect" a certain number of applications for further servicing, and the task of the second - useful service. In real communications networks, this can be interpreted as the generation by terminals of some autonomous signal of a prohibition of transmission after the first phase to the end of the second (non-conflict) phase -autonomously for each terminal, that IS, clS ci procedure for detecting all terminals by the fact that the channel is occupied with the allowable number of signals (in the examples, considered one, two or three) or as a procedure for detecting an unresolved conflict at the first stage, but which arose as a result of decentralized management. The simplest (Poisson) flow is considered as it has stationary properties and no aftereffect.

The stationary equations obtained in previous papers have the form:

— when serving only single applications of exponentially distributed duration [12]:

+ ^ + 2£2 + 2£fc2 - 2k) +

+ 4£2 k + C3 + 2i2k2 = 0. (1)

Here and then

e = A, k = * =

^2

Nazarov's proposed asymptotic method of QS analysis is determined not by the system load, but by the intensity of the repetition of a single call when this intensity approaches zero. The network performance thus reaches the maximum value, that is, asymptotic analysis in this case allows to determine the limiting

(by productivity) capabilities of access protocols and to obtain analytical expressions that determine the dependencies for their basic numerical characteristics.

Also, using previously obtained results in this ell*© el of research and for a description of obtaining stationary equations, see [11]:

— when it is solving paired conflicts between applications of non-coincident random duration [11]:

Çz2 + (9fc£ - 12fc2 + 9fc2C + 2£2)z+

+ r + 9fc£2 + 9fc2C2 = 0; (2)

— when it is solving pairs of conflicts between applications of coincident random duration [11]:

2 + (9£fc - 12fc2 + 3£fc2 + 2£2)z+

+ r + 9£2 k + 3£2 k2 = 0; (3)

— when it is solving triple conflicts between applications of non-coincidentrandom duration:

Çz2 + (16£fc - 36fc2 + 22^k2 + 2£2)z+

+ £3 + 16£ 2k + 22£2 k2 = 0; (4)

— when it is solving triple conflicts between applications of coincident random duration:

iz2 + (16ffc - 36fc2 + 12£fc2+

+ 2£2)z + C3 + 16C 2k + 12£2 k2 =0. (5)

For clarity, the results of the throughput analysis using the equations (l)-(5) are shown in Fig. 1.

Fig. 1. Throughputs of CSMA-CD protocols

The obtained dependencies testify to the following. If the CRPL is multiplied by 2, then on the condition that their exponentially distributed non-coincident times of service requests in the second stage, the throughput is asymptotically reaching 1.33, and if, at the same time, they are random but coincide with the duration it is reaching 2 (it doubles).

When successful simultaneous servicing of three applications is possible, this also gives a further

noticeable increase in throughput. When serving at the second stage of applications with non-coincident random duration, the throughput reaches 1.63, while when processing applications of coincident random duration it is reaching 3 (increases asymptotically three times as compared with [10]).

2 The average time before the start of successful servicing

The average time before the start of successful servicing can be determined by the number of repeated unsuccessful attempts. Attempting to get to the second stage of service will be successful only if the first stage reveals the number of applications (which then enters the second, stage of service without conflicts), which does not exceed the possibilities of resolving conflicts at the physical layer. Otherwise, after the first stage, all applications are sent to the source of repeated calls.

The appropriate expressions have the form: — when it is serving only individual applications:

T =(-1 + -M ,;

VMi M2/

(6)

— when it is solving pairs of conflicts between applications of non-coincidence durations:

T = + + —)x;

(7)

— when it is solving pairs of conflicts between applications of the coincidence duration:

T =

(2/ii + /12) X;

(8)

— when it is solving triple conflicts between applications of non-coincidence durations:

Fig. 2. Dependence of the average time before the successful transmitting from the intensities of applications servicing

The payment for an increasing the throughput at the CRPL is a significant growth of the average time before the successful transmitting in the analysed protocols when reached their throughputs. For example, even with k = 5 and solving conflicts of multiplicity 2, the average time before the successful transmitting is increased by 2.79 times, if the duration of the servicing of both applications coincide, and by 4 times, if not coincide.

Depending on the average time before the successful servicing from the intensity of the incoming stream (at k = 10) shown at graphic Fig. . The comparison of these graphics shows that when applying the protocols with the implementation of the CRPL procedures it is necessary to significantly shorter time before the successful transmitting with the served load equal to the protocol throughput without the CRPL. For example, with the CRPL the servicing of paired applications of non-coincidence durations is less than 2.9 times and 9.8 times - at their coinciding durations, and at CRPL multiplicity of 3 - in 7.6 and 18.7 times in accordance (see vertical dotted line at the Fig. 3). If, however, compare the average time before the start of the successful servicing of the CSMA-CD with the same condition, but without the CRPL, with this parameter in other protocols, we obtain an increasing of the throughput with the CRPL multiplicity of 2 in 1.3 and 1.8 times, and at multiplicity of 3 in 1.65 and 2.58 times - (see the horizontal dotted line in Fig. 4).

t=(-L + -L + _L + -1) ,; (9)

\3^i 3^2 2^2 M2/

— when it is solving triple conflicts between applications of the coincidence duration:

T =

(3/i i + /12) X'

(10)

The results of calculations by the formulas (6)-(10) at the edge of existence of stationary equations (l)-(5) are presented at the graphic of Fig. 2.

Fig. 3. Dependence of the average time before the successful transmitting from the intensity of the incoming stream of applications

58

•Т CSMA-CD triple con on the phy [ M'ith mismatc iqts resolving ijal layer 1 hedj '.CSMA-CD with coincident I ¡pair conflids resolving I 1 on the physical layer 1 1 ■l

CSMA-CD with mismatched

pair conflicts resolving on the physical layer , 1 / /1 / / / / / / 1 / / V / / / / /l / / / / SMA-CD with coincii lent

CSMA-CD --—' 1 triple conflicts resolvit on the physical layer s

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 .4 1.5 1.6 1.7 1.8 1.9 2 2.1

Fig. 4. Comparison of the served load of the CSMA-CD protocols with the CRPL with the classical CSMA-CD protocol

Conclusions

1. Resolving conflicts at the physical layer significantly improves the throughput of the CSMA-CD protocol: in 1.33 ^ 2 times, with the successful resolving conflicts of multiplicity 2 and 1.63 ^ 3 times when solving conflicts of multiplicity 3. When really achievable values k e (5 ^ 50) such an increase ranges from 1.38 to 2.2 when it is solving conflicts of multiplicity 2 and in the range from 1.72 to 3.46 when it is solving conflicts of multiplicity 3 in accordance, depending on the coincidence or non-coincidence of the servicing time of applications at the second stage.

2. The average time before the successful transmitting, assuming the CRPL and the incoming stream intensities equal to the throughput of the analyzed protocols, increases significantly - in 1.8 ^ 5.67 times, depending on the multiplicity of resolving conflicts and the coincidence or non-coincidence of the servicing durations. At the same time, when the average time before the successful servicing is limited by the throughputs of the CSMA-CD protocols without the RCFR, the served load of the protocols with the CRPS increases in 1.3 ^ 2.58 times, depending on the above-mentioned factors.

3. Comparison of the throughputs and the average time before the successful servicing of CSMA-CD protocols proves the expediency of implementing CRPL even with minimal multiplicities of 2-3. The task of resolving conflicts with multiplicity greater than 2-3 exponentially complicates the demodulator circuits, and further increases the throughput (except when the duration of all the second phase applications is coincident).

References

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Yerokhin V. F., Poliakova A. S., Sboiev R. Yu., Hoi V. D.

[3] Ageev D.V. (1935) Osnovyi teorii lineynoy selektsii, Nauchno-tehnicheskiy sbornik, Iss. 10, pp. 8-28.

[4] Borisov Yu. and Penin P. (1967) Osnovyi mnogokanalnoy peredachi informal,sii, Moskva, Svyaz, 435 s.

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[8] Klyuev V.F. (2015) Issledovanie optimal'nykh kogerentnykh demodulyatorov AM i ChM signalov [The study of optimal coherent demodulators AM and FM signals], Nizhniy Novgorod, 20 p.

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[11] Sboyev R.Yu., Polyakova A.S. and Yerokhin V.F. (2018) Asymptotic analysis of the random multiple access protocol "Nonpersistent CSMA-CD" with pairwise conflicts resolving at the physical layer, Problemy teplekomunikatsii, 3p.

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Параметри протокол1в МДКН-ВК при розв'язанш конфлж-шв на ф1зичному

piBHi

брохлнВ. Ф., Полякова А. С., Сбоев Р. Ю., Голь В. Д.

На тепер1шшй час глобальне зростання потреб у зв'язку змушуе нас бшьш ефективно використовува-ти частотний спектр. Розвиток систем зв'язку потре-буе збшьшення пропускних спроможностей, при цьому частотний спектр обмежений, що не дозволить збшь-шувати ширину каналу чи i'x кЬтьшсть. Якщо зробити припущення, що на однш частот! ¡снуе можливкть пере-давати одразу декшька взаемозаважаючих сигнашв, то виникае задача роздшення цих сигнашв. Очевидно, що складшсть процедур демодулягщ суттево зросте в nopiB-нянш з класичними. Тому необх1дно з'ясувати, чи буде виправданим таке зростання складность Щоб вущовкти на це питания, необх1дно визначити - як збЬтьшиться пропускна спроможшсть деяко! системи зв'язку з ви-падковим множинним доступом, де можливе кратне повторне використання частотного ресурсу. Для дос.ш-дження оберемо протоколи множинного доступу з контролем несдвно!, що набули широкого поширення в паке-тних мережах за i'x вдале поеднання в1дносно1 простота

алгоритмов доступу та досить впсоко! ефектпвноста. Метою до&шдження е визначення основних характеристик р!зновид1в протокол!в множинного доступу з контролем неавно! та виявленням конфлштав за додаткових припущень про розв'язання конфлштав на ф!зпчному р!вш. Були одержан! параметри протокол!в множинного доступу з контролем неавно! та виявленням конфль кт!в за додаткових припущень про 1х розв'язання на ф!зпчному р!вш. Показано, що в пор!внянш з класи-чнпм протоколом за припущення про розв'язання пар-них конфлшлв на ф!зпчному р!вш суттево шдвищуе-ться иропускна спроможшсть системи зв'язку з таким протоколом доступу. Наведеш результата пор1вняння. Одержан! результата дозволяють стверджувати про до-цшьшсть впровадження в демодулятори перспективних приймальних пристрош алгоритм!в розв'язання копфль ктав на ф1зичпому р!вш як таких, що характеризуються в1дпоспо невеликою складшстю.

Ключовг слова: випадковий множпннпй доступ; МДКН-ВК; розв'язання копфлштав на ф!зичпому р!в-ш; теор!я багатокористувацького детектування; системи масового обслуговування

Параметры протоколов МДКН-ВК при разрешении конфликтов на физическом уровне

ЕрохинВ. Ф., Полякова А. С., Сбоев Р. Ю., Голь В. Д.

В статье представлены уравнения стационарности протоколов множественного доступа с контролем несущей и обнаружением конфликтов при дополнительном предположении о разрешении конфликтов на физическом уровне. Наведены результаты сравнения нескольких протоколов по пропускной способности и среднего времени до начала успешной передачи. Полученные результаты позволяют утверждать о целесообразности внедрения в демодуляторы перспективных приемных устройств алгоритмов решения конфликтов на физическом уровне с относительно небольшой сложностью.

Ключевые слова: случайный множественный доступ; МДКН-ВК; разрешение конфликтов на физическом уровне; теория многопользовательского детектирования; системы массового обслуживания