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THE CONSTRUCTION AND ANALYSIS OF GENERALIZED MODEL OF RESOURCE SHARING FOR LTE TECHNOLOGY WITH FUNCTIONALITY OF NB-IOT
Sergey N. Stepanov,
MTUCI, Moscow, Russia, stpnvsrg@gmail.com
Mikhail S. Stepanov,
MTUCI, Moscow, Russia, mihstep@yandex.ru
Elena E. Malikova,
MTUCI, Moscow, Russia
Ariunaa Tsogbadrakh,
Ulan Bator, Mongolia
Juvent Ndayikunda,
Bujumbura, Burundi, juvndayi@mail.ru
DOI 10.24411/2072-8735-2018-10204
This work was supported by the Russian Foundation for Basic Research, project no. 16-29- 09497ofi-m.
Keywords: multiservice models, resource sharing, finite number of sources, performance measures, system of state equations.
The model of resource sharing for 3GPP LTE technology with functionality of standardized NarrowBand IoT (NB-IoT) technology is constructed. Two types of traffic are considered. One comes from wireless video surveillance cameras. The flows of corresponding requests follow Poisson model if number of requests sources is large or Engset model if number of requests sources is small. Another type of traffic comes from machine-type communications of different kinds of smart meters. The flow of corresponding requests follows Poisson model with batch arrivals and possibility of waiting if all resource units are occupied. The number of waiting positions and maximum allowed time of waiting are restricted. The time of servicing of all types of requests has exponential distribution with parameter depending on the type of the flow. Using the model the definitions of main performance measures are given with help of values of probabilities of model's stationary states. They are include the ratio of lost requests, the mean value of resource units occupied by requests of each type considered in the model, the mean value of the file transfer time, the mean value of waiting time for requests of machine- type communications. As a particular cases the model include cases when only traffic from video surveillance cameras is considered and only traffic of machine-type communications is considered. The system of state equations that relates the probabilities of model's stationary states is derived. The model can be used for study the scenarios of resource sharing between LTE and NB-IoT traffic flows.
Information about authors:
Sergey N. Stepanov, professor, doctor of science, MTUCI, head of the chair of communication networks and commutation systems, Moscow, Russia Mikhail S. Stepanov, docent, Cand. Tech. Sciences, MTUCI, the chair of communication networks and commutation systems, Moscow, Russia Elena E. Malikova, docent, Cand. Tech. Sciences, MTUCI, the chair of communication networks and commutation systems, Moscow, Russia Ariunaa Tsogbadrakh, PhD student, MTUCI, the chair of communication networks and commutation systems, Ulan Bator, Mongolia Juvent Ndayikunda, PhD student, MTUCI, the chair of communication networks and commutation systems, Bujumbura, Burundi
Для цитирования:
Степанов С.Н., Степанов М.С., Маликова Е.Е., Цогбадрах А., Ндайикунда Ж. Построение и анализ обобщенной модели разделения ресурса для LTE технологий с функциональностью NB-IoT // T-Comm: Телекоммуникации и транспорт. 2018. Том 12. №12. С. 71-77.
For citation:
Stepanov S.N., Stepanov M.S., Malikova E.E., Tsogbadrakh A., Ndayikunda Ju. (2018). The construction and analysis of generalized model of resource sharing for LTE technology with functionality of NB-IoT. T-Comm, vol. 12, no.12, pр. 71-77.
1. introduction
The main trend in the development of information systems is necessity of processing different kinds of data from numerous distributed sources that are include the low-cost and low-traffic smart meters and massive video surveillance systems deployed for security and safety purposes [1-4J. The surveillance cameras use much more transmission resources then smart meters. Large amount of smart meters and surveillance cameras may be deployed in places where wired connectivity is not feasible due to technical or economic reasons. The existing wireless technologies are not capable to support requirements of servicing traffic streams that can be produced by massive video surveillance systems.
This problem has been recently recognized by 3GPP with the ratification of a dedicated in-band deployment mode in LTE Rel. 13 that allows to share the radio spectrum when serving traffic of large-scale video surveillance cameras with sensor traffic by using the NB-IoT technology, It is necessary to emphasis that by introducing the hardware and software possibilities of sharing the radio resources between LTE and NB-IoT technologies, 3GPP does not provide specific recommendations on how these resources should be shared. The formulated problems can be solved by elaborating the model that takes into account the peculiarities of collection and processing oftraffic streams that eomcs from LTE-devices and NB-IoT-devices. This task will be considered in the following parts of the paper. In Section 2 the mathematical description of the model will be presented. In Section 3 the main performance measures will formulated. In Sections 4 the system of state equations that relates the model's sta-tionaiy probabilities is outlined. Conclusions are drown in the last section. The process of requests forming by LTE-devices and ofNB-IoT-devices is shown on the Figure 1.
LTE-tit vices: vjdw cameras
Base M№n with Tu rationality of LTEJNB-loT
LTE-devices
targe gro uptofLTE-
V J
TD« tijieli arrival traffic of H&ajt-
»T...C» w4*
Radio resources
TE
1 NE 40
'Ihps- smart meters and actuators
Dynamic-or static Slicing} resource a I location
of NB-IoT-device sessions. Let us denote by v the total number of resource units (channels) and by c denote the transmission speed provided by one channel. The value of c usually equals to the minimum transmission speed requirement of coming request for servicing. Let us denote by Q| he set of flow numbers that
include llows originated from large population of LTE-devices. Because of this assumption the changing of their number doesn't influence greatly the intensity of requests coming. In this case we can use the poissonian model when describing the process of requests coming. Let us denote for this type of flows by A* the intensity of requests arriving, k £ fi| ■
Let us denote by the set of flow numbers that include
flows originated from LTE-devices requiring a large amount of cell transmission capacity. Usually this are requests for services based on transmission of video traffic of improved quality. Number of LTE-devices of this sort comparatively small. In this case Engset model is used to describe the requests coming. Let us denote for this type of flow by fik the parameter of exponentially distributed time between successive requests arrival and by Sh denote the number of users, k € i12 ■
Let us define the common characteristics of requests from LTE-devices coming and servicing. Let us denote by ak the parameter of exponentially distributed service time, by £>* we denote the number of resource units used for servicing of one request and by at we denote the intensity of offered traffic expressed in potential number of connections called erlangs, k=\,2,...,n. it is easy to check that for Engset model of re-SkPk
Ok+ßk
and for Erlang model of requests
Data analytics centers
Tig. 1. Considered system main features
2. Mathematical description of the model
The volume of available radio resources of LTE cell in uplink direction is measured in terms of its smallest granularity. We call it channel or resource unit. Total number of channels is a linear function of the number of resource blocks. There are some number of LTE-devices and NB-IoT-devices located in the cell and connected to the corresponding base station. The LTE-devices and NB-IoT-devices are sources of transmission sessions [4]. To construct the model the approaches derived in [5-1OJ will be used.
In the model we consider n flows of requests for serving of LTE-device sessions and one flow of requests for servicing
quests coming ak
coming ak = ^
Requests for servicing from NB-IoT-devices arrive in groups (batches). We also assume that arrival of the groups follows the Poisson law of intensity Xd. With the probability fjt j = l,„.(g,the arriving group has g<v + w requests,
where w is the number of waiting positions for requests from NB-IoT-devices. The arriving group of j requests is taken for servicing entirely if j <v — i, where i is the number of resource units used to serve the requests of LTE-devices. If / >v —/, then (v— i) requests are accepted for servicing, the rest (j + i— v) requests are accepted for waiting entirely if j + i — v:<'W. If j+i— v> w then w requests are accepted for waiting, the rest (j + i — v— w) requests are lost without resuming. The volume of transmitted file has exponential distribution with mean value of F bits. The time of servicing of one request from NB-IoT-devices by one channel has exponential distribution with parameter f,td =-j. The maximum allowed
waiting time is restricted by random time having exponential distribution with parameter equals to a. The mathematical model of conjoint servicing of requests from LTE and NB-loT devices is shown on the Figure 2.
Let us denote by 4 (/) the number of requests of A'-th flow of LTE-devices being on servicing at time t and by d(t) we denote the number of requests of NB-IoT-devices being on servicing at
time I. The dynamic of a model stales changing is described by multidimensional Markov process with components
rif)=ijl(t)r...,ia(t),d(f]i},
defined 011 the finite set of model's states S. Let us denote by ft, ¿2,..., i„,d) the state of the process under consideration, and by S denote the set of all possible states.
The vector (i\,i2,-.,i„,d) belongs to S when /1,i„,d varies as follows
ft = 0,l,..„min
Si,
i„ — 0,1,..-,min
Sn,
/2 =0,1,...,min j27
(l)
d — 0,t,...,v+ vv —i'A -... — i„b„.
In (1) the value sk = QO, if k G ii]. Let us denote by p(i],i2>—J„,d) the value of stationary probability of state (¡I,/;,...,/,„£/) € S. It can be interpreted as portion of time the model stays in the slate (iltilt...,i„,d). This interpretation gives the possibility to use the values of p(/|,i2,...,/„,£/) for estimation of model's main performance measures.
The process ol conjoint servicing of П Howsoi requests from LTE-devices and one Лом from NB-loT
Channel resource of uplink line expressed as V channel units
Лк, ьк, 1/ak
О- Д, bk> 1/ak А, Ьк, 1/ak
■
With probability ft the ^ comtng group has j
requests from NB-loTdevices
ID
Ш
w
Waiting requests can leavethe queue because the restriction Dn maximum a (lowed waiting time
Waiting places tor requests from NB'loT. devices
Fig 2. Mathematical model of conjoint servicing of requests from LTE and NB-loT devices in LTE cell with functionality of NB-loT
3. Performance measures
The model performance measures are depending on the type of the requests and can be defined by summing probabilities p{ii,i2,...,i„,d) over corresponding subsets of 5. Let us start with definition of performance measures for requests coming from LTE-devices. The type of definition depends on the model used for flow description. Let us suppose that k € and denote
for the state (ii,i2,...,i„,d) by 1 the total number of resource units occupied by requests from LTE-devices i — i{bt +... +i„b„. Because PASTA property the portion nk of lost requests of jt-th flow equals to the portion of time when existent amount of free channels is insufficient for excepting of a call of A-th flow. We have the following definition of the characteristic
((/|,:j.....:„,ri)6S[/+d+6j>v}
Let us suppose that k £ fi 2 - The portion 7TCtk of lost requests of A-th flow formed by finite group of LTE-devices because of absence the necessary amount of free channels is defined as ratio of the intensity of lost requests to the intensity of coming requests
Y^ p{i\,h,-J„,d){sk -ik)fik _ {('|A.....i„.iJ)6S|/+rJ+6t>v}_
J2 p(A>k,--m>>>d) )fik {«a.....
The portion 71 uk of time when necessary amount of free
channels is insufficient for excepting of a call of A-th How is obtained alter summing probabilities of states having such property
Vt,k — Y! p(h,i2,-,i,„d) ■
{(il .¡2 ,...,i„,d)€$\i+d+bk >v}
The intensity A ^ of coming requests of A-th flow formed by finite group of LTE-devices is defined as follows
A* - ^ p(iui2,-J„,d)(sk - ik)pk ■
.....i„,d)eS}
The portion 7T^k of lost traffic of A-th flow formed by finite
group of subscribers because of absence the necessary amount of free channels is defined as ratio of the blocked traffic to the intensity of coming traffic
Ok ~yk
m,k
Ok
For any k = 1,2.....n the mean number mk of resource
units occupied by servicing the requests of A-th flow and the mean number yof requests of A-ih flow being on servicing are defined by relations
m = p(h,i2,...,in,d)ikbk\
{(¿1.6.....
Wk= Y p{i\,k,...,i,„d)ik ■
{(¿N¿3.....
Let us introduce the definitions of performance measures for requests coming from NB-1oT-devices. The mean number bj of requests in one group is defined by relation
Ki. i =■
1
Khi
bd=EfjJ-
The portion 71 j \ of requests lost because at the moment of
request coming the available number of free resource units and waiting positions is insufficient for excepting of a request is defined by relation
£ i>(u.....u-HE/^tM ■
The portion nd 2 of requests lost after the excess of maximum allowed wailing time is defined by relation.
1 ■»
— ¿2 p(i\,il,-,in,d)(i + d-v)<7 •
'hA/ [{(ft./j.....si ,rf)es|j
The portion Ttj requests lost by all reasons considered in the model is defined by relation
% = + ^d.l ■
The mean number v t of requests being on serv ice is defined by the following expression
ys- p$lyh,-Jn,d)d +
{((,./;.....(„ .d Ki I i¥d<V.d >0}
{((,./;.....i,,rf)E5|f+i/>v}
The mean number yw of requests being on waiting is defined by relation
y* = p{h,h,~,i»,4){i + d~v)-
{(/j,/2.....J„.i/)ti| :+</>!'}
The mean number _>'</ of requests being in the system on servicing or waiting is defined by formula
M = >'.v + yw ■
The mean time of file transfer is defined hy relation
T - y<I
Let us derive the conservation law for LTE-device traffic. Let us suppose that k G i^i then:
Jtk =Akxk+ykak. (2)
Let us suppose that k € fi; then A * = A k7ic.k + ykak. (3)
Now derive the conservation law for NB-toT-device traffic
Aibj = AjttdMi + y/Zd + ■ (4)
Obtained relations are proved by multiplication of equations of (5) with p(i\,/2,...,in,d) in the left part consequently by i],i2t—Jntd and summing up the obtained expressions over {/i,/?,...,/„,£/) € S . Another possibility to prove (2)-(4) is to use the Little Formula.
4. The system of state equations
Let us denote for the state (/¡,¡2,...,/„,d) € S by i the total number of resource units occupied on transmission of traffic originated by LTE-devices i — itbt + ... + i„b„. Let us derive the
system of stale equations. By using the indicator function we represent all equations of the system of state equations in one relation. It will be shown latter that this is very convenient for realizing the iterative procedures of solving the corresponding system.
It is necessary to equate the intensity of transition r(t) out of the arbitrary model's state (i{,i2,...,i„,d) to the intensity of transition r(t) into the state (/,,i2,...,i„,d) . In the model considered the following events can change its state: the coming of new requests for servicing from LTE- and NB-loT-devices, finishing of servicing for requests accepted for service and leaving of waiting positions after expiring of maximum allowed waiting time. Let us consider these events and write the intensities of events that change the model's states.
The coming of request of i-th flow for servicing of traffic of LTE-devices for poissonian model (intensity Ak > changes the state (/[,/'2,...J„,d) with probability one if there is necessary amount of free resources to accept a call. Necessary condition of this event is inequality / 4- d + bk < v. In this case with intensity P(i\,i2,...,i„,d)A.k the model state changes from
(h,h,-,'n,d) to (/1,/,,.„,/* +1,...,i,„d).
The coming of request offc-th flow for servicing of traffic of LTE-devices for Engset model (intensity (sk — ik)f3k) changes the stale (i\,i2,...,i„,d) with probability one if there is necessary amount of free resources to accept a call. Necessary condition of this event is inequality / + d + bk < v. In this case with intensify P(hth,—,in,d)(S)t - ik ) fik model state changes from (iui2,...J„,d) to (/',,i2,...,ik + \,...,i„,d).
The coming of request for servicing of traffic of NB-IoT-devices for batch poissonian model (intensity Xj) changes the state (i],ilt...,i„id) with probability one if ihere is necessary amount of free resources to accept a call. Necessary condition of this event is inequality i + i/ + l < y. In this case with intensity P(i[,i2,---Jn,d)/lil the model state changes from (iui2,...,i„,d) to (i],i2,.,.,i„,d + 1).
The coming of request for servicing of traffic of NB-loTdevices for batch poissonian model (intensity ) changes the state (iui2,...,i„,d) with probability one if there are no free resources to accept a call (necessary condition of this event is inequality i + d + \ > v) hut there are free waiting positions (necessary condition of this event is inequality i + d — v < h> )■ In this case with intensity P(il,i2,...,i„,d)Aj the model state changes from (i],i1,..„it,,d) to (/,,i2,..,,i„,d + 1).
The finishing of service of request of fc-th flow for transition of traffic LTE-device (intensity ikak) change the slate (iui2,...,i„,d) with probability one if there is at least one request of ¿-til flow on service i.e. ik >0. In this case with intensity »h ,<-,in»d)ikOCk the model state changes from (/,,/,,...,/„,d) 10 (iui2,...,ik - l,...,i„,d).
The finishing of service of request for transition of traffic NB-IoT-device (intensity da,/) change the state (/,,/;,...,;',,,(.7)
with probability one if there is at least one request of A-th flow on service and queue is empty i.e. £f>0,/ + c/<v.ln this case
with intensity PHiti1,...,i„,d)dalj the model state changes from (iui2,...,i„,d) to (iui2,,..,ik%£.,i„Td — 1).
The finishing of service of request for transition of traffic NB-loT-device (intensity (v — i)ati) change the state {i\,i2,,..,in,d) with probability one if there is at least one request of A-th flow on service and queue is not empty i.e. d > 0, / + d > v. In this case with intensity
P(l\,i'2.,...,in,d)(v— ¡y&d the model slate changes from (iuilt...X,d) to (iui2,.„,ik,...,i,„d-\).
The finishing of waiting of request for transition of traffic NB-loT-device (intensity (; -f- d — v)<r) change the stale
(/],/:,,..,i„,d) with probability one if there is at least one requests on waiting (necessary condition of this event is inequality i + d>v). In this case with intensity P(i\,i2i--dii,d)(i + d— v)cr the model state changes from (/„fe,...,/„,</) to (it,i2,...,ik,...,i„,d - 1).
The sum of these intensities over A from 1 to n gives the left part of the system of state equations. Lei us find the expression for the right part. The coming of request of A-th How for serv icing of traffic of LTE-deviees for poissonian model (intensity Ak) changes the state (i[J2,...Jk — 1,...,i„,d) with probability one if there is at least one call on service i.e. ik >0. In this case with intensity P{iui2,...,ik — 1,...,/„,d)Ak the model state changes from(i'[,i'2,,..,/t — \,...,i„,d) to (j],i2,...J„,d).
The coming of request of A-th flow for servicing of traffic of LTE-devices for Engset model (intensity (sk —ik + \)pk) changes the stale »*2»«>»** ~ l,--->'«><i) with probability one if there is at least one call on service i.e. ik > 0 and / + d < v. In this case with intensity P(i},i2,...,ik - l,...,i„,d)(sk —ik + \)(ik the model state changes from {iui2,%.,ik - \,...,i„,d) to (/,,/2,...,i„,d).
The coming of request for servicing of batch traffic of NB-IoT-devices changes the model state into (iili2,...J„,d) depending on the batch size and has the following intensity d g Y^Pi'uk^J^d-T)^ f,+l(i+d>v,d-v+i = w) Y, fj /=i [ j=I+\
The finishing of servicing of one request originated from LTE-devices and describing by Poisson model changes the model state into (ij,/2,...,i„,<ii) with following intensity P(i\,i2,...,(* + \,...,i„,d)(ik + X x(l(i + d + bk < v) + I(i + d + bk >v,i + bk < v)).
The finishing of servicing of one request originated from LTE-devices and describing by Engset model changes the model state into (/,, 1*2,,i„,d) with following intensity
P(iui2,..Jk +1.....4,¿0(4 +\)ak(I(i + d + bk <v,ik + l<i't) +
+/(/ + d+bk>vjk+\<sk,i + bk< v)).
The finishing of servicing or w aiting of one request originated from NB-ioT-devices changes the model state into (i[,i2,...,i„,d) with following intensity P(ii d +1 i(d +1 )a,jl(i + d +1 < v) +
-K(v-i)aci + (i+d +1 -v)&)I(i + d + \ > v,i + d + \ - v< w)).
After equating left and right parts we obtain system of state equations. The possibility of realizing of all events in the system is described by indicator function. The system of state equations can be written as follows
PihJi.....i„,d)
^T(V0' + At <v + ikakI(it >0))+ (5)
*<ES>1
+ V ((St - ik )ßk Iii + bk < v) + ikakI(ik > 0)) + k€ £12
(/(i 4 rf + l<v)4/(i+rf fl>v,/ fi/-V< №>) + +ad (dl(d > 0,/ + d < v) 4-(v-i)I(d >0,i + d>v)) +
+(/ + d - v)<j/(/ -1- d - v > 0)
= J2 .....~1.....> 0,i+d <v) +
+ J2 Pih*h,~,it -1.....imd)(sk-ik +\)ßkI(ik > 0,/ + (/<!')+
k&l2
d
+X>'ui2,-Jn,d-l)A/ fl+I(i+d>V,d-V+i=w) Y/i
1=]
j=l+\
+Y2p('id2,..-,ik+l.-J,nd)(ik+\)ak(/{i + d + bk<v) +
ieiii
+/(/ + d + bk > v, i + bk < v)) +
+\)ak(I(i+d+hk <vjk +1 <sk) +
k&h
+I{i+d+bk>v, ik +\<sk,i+bk <v)) +
+P{iui2,...j„,d+\t{d+\)ad!{i+d+\<v)+
-K(v-i)ad +(i+d + \- v)cr)I(i + d+\>wi + d+\-v<w)).
Values P{iui2,.„,in,d) satisfy the normalizing condition
Cfi.it.....J,
5. Numerical examples
The model constructed can be used for analyzing the dependence of main performance measures on the model's input parameters in particular on increasing the value of input traffic. Let us choose the following fixed values of input parameters: v— 100 channel units (c.u.), /? —2; = c.u.; b2 — 20 c.u.; w= ¡0; F = 1 Mbit; a2 = 1; c = 1 Mbit;
CC,i = C/F — 1. Batch arrival is defined by the following parameters: g —19; fj = Vg,j = . The mean number b,/ of NB-IoT requests in one group if de lined from relation blt — j\ + f2l +...+ fgg = 10. The value of o is defined by
relation o = 1. The values of intensities or,, a2, GCj, a are expressed in number of corresponding events in time unit.
7TT
To simplify the choose of parameters as a unit of time was taken the mean time of service of one request from LTE-device. The input traffic will be characterized by p the potential load coming on one channel.
Figure 3 shows the results of calculation 7r[, —nc2t 71 j
with increasing of p in interval from 0 to 1. The characteristics are calculated by solving the system of state equations. As can be anticipated the value of losses increases with increase of p. The losses of requests from LTE-devices increases much faster then losses of requests from NB-loT-devices. This is because the requests from LTE-devices needs more channels for servicing then requests from NB-loT-devices. The advantages in occupying resource for requests from NB-loT-devices can be also seen on dependence of , m2,tn^ with increasing of p in interval from 0 to 1 shown on Figure 4.
0.5 0.45 0.4 0.3S 0.3 0.25 0.2 0.15 0.1 0.05 0
le transfer time, the mean value of waiting time for requests of machine-type communications. As a particular cases the model include cases when only traffic from video surveillance cameras is considered and only traffic of machine-type communications is considered. The system of state equations that relates the probabilities of model's stationary states is derived. By using the indicator function all equations of the system state equations are written in one relation. This result is very convenient for realizing the iterative procedures of solving the corresponding system. The model can be used for study the scenarios of resource sharing between LTE and NB-IoT traffic Hows.
35
30
25
20
15
ID
mi
m,
0,!
0,2 0,3 0,4 0.5 The Iliad of channel.
Fig. 4. The dependence of
0,6 0,7 0,B 0,9
on p
O 0.1 0.2 0.3 0.« 0.5 0.6 0.7 O.B 0.9 1
The load of channel, p
Fig. 3. The dependence of x2 nti on p
The requests with small requirements for resource displace from service requests with large requirements for resource. The negative consequences of such behavior of performance measures can be eliminate by dividing the set of resources into two groups with separate service of LTE-device traffic and NB-IoT-deviee traffic. The size of the separate groups can be found with help of model constructed.
Conclusion
The model of resource sharing for 3GPP LTE technology with functionality of standardized NarrowBand loT (NB-IoT) technology is constructed. Two types of traffic are considered. One type conies from wireless video surveillance cameras. The llows of corresponding requests from LTE-devices follow Poisson model if number of requests sources is large or Hngset model if number of requests sources is small. Another type of traffic comes from machine-type communications of different kinds of smart meters. The flow of corresponding requests from NB-IoT-devices follows Poisson model with batch arrivals and possibility of waiting if all resource units are occupied. The number of waiting positions and maximum allowed time of waiting are restricted by some numbers.
The time of servicing of all types of requests has exponential distribution with parameter depending on the type of the flow, hi the framework of the constructed model the definitions of main performance measures are given with help of values of probabilities of model's stationary stales. They are include the ratio of lost requests, the mean value of resource units occupied by requests of each type considered in the model, the mean value of the
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9. Siepanov S.N., Romanov A.M. (2014). Real-Time traffic service modeling specialties of a finite user group and data traffic with a dynamically changeable transmission speed on access lines. T-Comm. Vol. 8. No. 12, pp. 91-93. (inRussian)
10. Stepanov S.N., Romanov A.M., Osia D.L. (2015). Construction and analysing ofdaia transmission model on access line with finite number of subscribers. T-Comm. Vol. 9, No,9, pp. 29-34. (in Russian)
ПОСТРОЕНИЕ И АНАЛИЗ ОБОБЩЕННОЙ МОДЕЛИ РАЗДЕЛЕНИЯ РЕСУРСА ДЛЯ LTE ТЕХНОЛОГИЙ С ФУНКЦИОНАЛЬНОСТЬЮ NB-IOT
Степанов Сергей Николаевич, Московский Университет Связи и Информатики (МТУСИ), Москва, Россия, stpnvsrg@gmail.com Степанов Михаил Сергеевич, Московский Университет Связи и Информатики (МТУСИ), Москва, Россия Маликова Елена Егоровна, Московский Университет Связи и Информатики (МТУСИ), Москва, Россия
Цогбадрах Ариунаа, Улан-Батор, Монголия Ндайикунда Жувен, Бурунди
Аннотация
Построена модель распределения ресурса для сети беспроводной связи стандарта LTE с функциональностью NB-IoT. В модели рассматривается процесс поступления и обслуживания двух типов трафика. Один поток образован камерами слежения. Поступление соответствующих запросов следует пуассоновской модели, если предполагается, что число источников нагрузки велико, или модели Энгсета, если предполагается, что число источников нагрузки мало. Другой поток образован передачей информации разного рода датчиков. Появление запросов этого типа описывается пуассоновской моделью с групповым поступлением и возможностью ожидания для запросов, получивших отказ. Число мест ожидания и максимально возможное время, ограничивающее пребывание заявки на ожидании, ограничены. С использованием модели сформулированы определения для основных характеристик качества обслуживания поступающих запросов. Среди них: доля потерянных запросов, средний объем ресурса, занятый на обслуживания каждого из рассмотренных типов трафика, среднее время передачи файлов, составляющих групповой трафик. Частными случаями анализируемой системы являются модели, в которых рассматривается процесс поступления и обслуживания только трафика видеокамер или только групповой трафик датчиков. Построена система уравнений статистического равновесия, связывающая значения стационарных вероятностей модели. Разработанная модель и средства ее анализа могут быть использованы для исследования сценариев распределения ресурса между трафиком различных коммуникационных приложений, обслуживаемым с использованием технологий LTE и NB-IoT.
Ключевые слова: мультисервисные модели, совместное использование ресурса, конечное число источников нагрузки, характеристики качества обслуживания, система уравнений равновесия.
Литература
1. Голышко А.В., Степанов С.Н., Тихвинский В.О., Тереньтьев С.В. Экспертно-аналитическая система для исследования инновационных решений на телекоммуникационном рынке // Электросвязь. № 7. 2007. С. 32-36.
2. Степанов С.Н. Основы телетрафика мультисервисных сетей. М.: Эко-Трендз, 2010. 392 с.
3. Степанов С.Н. Теория телетрафика: концепции, модели, приложения. М.: Горячая линия-Телеком, 2015. 868 с.
4. Begishev V., Petrov V., Samuylov A., Moltchanov D., Andreev S., Koucheryavy Y., Samouylov K. Resource Allocation and Sharing for Heterogeneous Data Collection over Conventional 3GPP LTE and Emerging NB-IoT Technologies // Computer Communications. 2018. Vol. 120. No 2, pp. 93-101.
5. Степанов С.Н., Степанов М.С. Планирование ресурса передачи при совместном обслуживании мультисервисного трафика реального времени и эластичного трафика данных // Автоматика и телемеханика. 2017. № 11. С. 79-93.
6. Stepanov S.N., Stepanov M.S. The Model and Algorithms for Estimation the Performance Measures of Access Node Serving the Mixture of Real Time and Elastic Data. In: Vishnevskiy V., Kozyrev D. (eds) Distributed Computer and Communication Networks. DCCN 2018. Communications in Computer and Information Science (CCIS), vol 919, pp. 264-275. Springer, Cham.
7. Степанов С.Н., Степанов М.С. Планирование ресурса передачи информации соединительных линий мультисервисных иерархических сетей доступа // Автоматика и телемеханика. 2018. № 8. C. 66-80.
8. Васильев А.П., Степанов С.Н. Построение и анализ математической модели с динамическим распределением канального ресурса при групповом поступление запросов на передачу данных // T-Comm: Телекоммуникации и транспорт. 2016. Т. 10. № 11. С. 55-59.
9. Степанов С.Н., Романов А.М. Моделирование особенностей обслуживания трафика реального времени от конечных групп пользователей и трафика данных с динамически изменяемой скоростью передачи на линиях доступа // T-Comm: Телекоммуникации и транспорт. 2014. Том 8. № 12. С. 91-93.
10. Степанов С.Н., Романов А.М., Осия Д.Л. Построение и анализ модели передачи данных на линии доступа от конечной группы абонентов // T-Comm: Телекоммуникации и транспорт. 2015. Т. 9. № 9. С. 29-34.
Информация об авторах
Степанов Сергей Николаевич, Московский Университет Связи и Информатики (МТУСИ), заведущий кафедрой сети связи и системы коммутации, д.т.н., Москва, Россия
Степанов Михаил Сергеевич, Московский Университет Связи и Информатики (МТУСИ), к.т.н., доцент кафедры сетей связи и систем коммутации, Москва, Россия
Маликова Елена Егоровна, Московский Университет Связи и Информатики (МТУСИ), к.т.н., доцент кафедры сетей связи и систем коммутации, Москва, Россия
Цогбадрах Ариунаа, Московский Университет Связи и Информатики (МТУСИ), кафедра сети связи и системы коммутации, аспирант, Улан-Батор, Монголия
Ндайикунда Жувен, Московский Университет Связи и Информатики (МТУСИ), кафедра сети связи и системы коммутации, аспирант, Бурунди
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