=Paper=
{{Paper
|id=Vol-2407/paper-09-038
|storemode=property
|title=
Three algorithms for traffic limitation in emergencies
|pdfUrl=https://ceur-ws.org/Vol-2407/paper-09-038.pdf
|volume=Vol-2407
|authors=Andrey K. Levakov,Nikolai A. Sokolov
|dblpUrl=https://dblp.org/rec/conf/ittmm/LevakovS19
}}
==
Three algorithms for traffic limitation in emergencies
==
https://ceur-ws.org/Vol-2407/paper-09-038.pdf
84
UDC 621.391
Three algorithms for traffic limitation in emergencies
Andrey K. Levakov* , Nikolai A. Sokolov†
*
Department of Technical Director
Center Macro-regional Branch (Center MRF) of PJSC Rostelecom
“Comcity”, household 6, build. 1, Kievskoe shosse 22km, Moscow, 108811
†
Department of Network Planning
Saint-Petersburg branch of Central science research telecommunication institute
Warshavskaya 11, St. Petersburg, 196128, Russia
Email: levakov1966@list.ru, sokolov@niits.ru
Three algorithms for traffic limitation arising in case of significant congestion which are
caused by emergencies of different nature are considered. The first algorithm is based on
the introduction of a pause between the moments of call arrival from each source. Each call
represents the attempt to establish a connection from a fixed or mobile phone. The second
algorithm is based on restriction of the communication session duration. With regard to
telephone communication, session is considered as the conversation time. The third algorithm
provides for the sorting of calls and the possibility of separating the number of servers into
two groups taking into account the nature of specific emergencies. In this case, servers
are terminals in the emergency call center. The effectiveness of the proposed algorithms
in emergencies is analyzed. Some examples of practical implementation of the proposed
solutions are given. In conclusion, the directions of further work are formulated. Mainly, these
directions are based on interdisciplinary research in relation to the operation of a multiservice
network in emergencies.
Key words and phrases: teletraffic system, call, pauses between demands, limitation
of holding time, calls sorting, effectiveness of the algorithm.
Copyright © 2019 for the individual papers by the papers’ authors. Copying permitted for private and
academic purposes. This volume is published and copyrighted by its editors.
In: K. E. Samouylov, L. A. Sevastianov, D. S. Kulyabov (eds.): Selected Papers of the IX Conference
“Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems”,
Moscow, Russia, 19-Apr-2019, published at http://ceur-ws.org
Levakov A. K., Sokolov N. A. 85
1. Introduction
The teletraffic theory studies telecommunications networks and their elements as
stochastic systems [1, 2]. The available research papers and articles on teletraffic theory
rarely consider whether it is possible to change the nature of the incoming request flow
and their service time deliberately and divide the service units into several groups. The
studies are mainly focused on the request service processes and choice of the appropriate
algorithms. This approach is reasonable when the majority of requests are generated to
satisfy the communication and information needs [3] of the telecommunication networks’
users. However, it is an entirely different case when the requests come largely in response
to extraordinary events, such as, for example, emergency situations [4].
In emergencies, certain elements of telecommunications networks often experience a
considerable overload, which can be decreased in different ways. Among them, three
algorithms are of ultimate importance because they allow increasing the portion of
requests processed successfully.
This article describes a teletraffic system that technically allows implementing three
changes. First, we can modify the nature of the incoming flow by introducing pauses
between requests created by each load source. Second, the request service time can be
restricted. Third, the requests that arrive at first responders can be sorted [5] by the
probable cause, which also helps to increase the portion of requests processed successfully.
The proposed algorithms have been successfully tested for processing of requests
created by fixed or mobile networks’ subscribers. The corresponding examples are given
at the end hereof.
2. Mathematical model of a teletraffic system
The model under study can be represented as a black box [6] with the defined
processes 𝐴(𝑡), 𝐵(𝑡), 𝐶(𝑡), 𝐷(𝑡) and 𝑃 (𝑡) (see Fig. 1). The black box notion is typically
used to simplify the research of complex systems. Representing a complex system
as a black box does not require a profound understanding of its operating principles.
Normally, it is sufficient to study the system input and output process and controls.
A(t) B(t) D(t)
C(t) P(t)
Figure 1. Teletraffic system modeled as a black box
Process 𝐴(𝑡) at the queuing system input relates to the request flow, which is one of
the most important notions in the teletraffic theory. A request refers to any element
that should be processed. In this article, a request means an attempt to establish a
connection from a fixed or mobile phone. The word “service” is used as a generic term
for a set of actions to establish a connection between the voice communication terminals.
Process 𝐵(𝑡) is assumed to describe servicing. In some cases, a request cannot be
processed; then it leaves the teletraffic system. Process 𝑃 (𝑡) reflects such events. The
successfully processed requests form a flow, which process 𝐷(𝑡) represents. This request
flow is commonly referred to as an incoming flow. Process 𝐶(𝑡) represents the black box
control functions. Together with other management operations, this process provides for
the functions implemented with the three algorithms mentioned above.
The mathematical model is also defined using the modified Kendall’s notation [7].
Generally, the model under study can be represented as follows:
86 ITTMM—2019
𝐺𝐼/𝐺𝐼/𝑉 /𝑟/𝑓0 (1)
Symbol 𝐺𝐼 indicates that two distributions (duration of intervals between the request
arrival time and their service time) are subject to any probability law; the number of
service units is equal to 𝑉 ; the number of waiting places in a queue amounts to 𝑟; the
requests are processed on a first-served basis without priorities.
With the following simplifications, we observed a number of regularities: the request
flow follows a Poisson law and the service time distribution follows an exponential law.
In some applications, it is appropriate to consider that there are no waiting places in the
queue (𝑟 = 0). In the modified Kendall’s notation, such an idealized (simplified) model
is denoted as follows:
𝑀/𝑀/𝑉 /𝑟/𝑓0 (2)
To analyze both models, it is generally appropriate to use the simulation method.
In most cases, getting the required dependencies for model (2) is based on the known
analytical relations [1, 2].
3. Introducing pauses between call attempts in telecommunication
networks
In the teletraffic theory, load intensity 𝑌 [2, 8] is defined as the product of 𝑛 (total
number of the connected terminals), 𝜆 (average intensity of requests from one terminal
per unit of time) and ℎ (mathematical expectation of the time the network resources
are occupied):
𝑌 = 𝑛𝜆ℎ (3)
The loss probability defined by the Erlang formula is often denoted as follows:
𝐸(𝑌, 𝑉 ). It is convenient to represent the value of the pause duration 𝜏 as a fraction of
the mean value of occupation time ℎ. This fraction is share is denoted by letter 𝜗. It is
appropriate to denote the corresponding request loss probability as follows: 𝐸(𝑌, 𝑉, 𝜗).
If the network is overloaded during an emergency situation, value 𝑌 often exceeds
value 𝑉 by several times. To get the quantitative estimations, we first consider the case
when 𝑉 = 30 for three levels of 𝑌 that define the following probability values 𝐸(𝑌, 𝑉 ):
∙ 𝐸(𝑌 = 3𝑉, 𝑉 = 30) ≈ 0.67;
∙ 𝐸(𝑌 = 6𝑉, 𝑉 = 30) ≈ 0.83;
∙ 𝐸(𝑌 = 9𝑉, 𝑉 = 30) ≈ 0.89.
Fig. 2 shows functions 𝐸(𝑌, 𝑉, 𝜗) for different duration values of the pause between
the call attempts. We chose to use the logarithmic scale for the ordinate axis. It is evident
that introducing comparatively short pauses between the connection attempts reduces
the number of lost calls considerably. For example, to maintain the loss probability level
below 0.01 even when 𝑌 = 9𝑉 , it is sufficient to introduce pauses that last about 3% of
an average conversation time.
Unfortunately, we have to introduce longer pauses for small values 𝑉 . In particular,
simulation results for 𝑉 = 3 showed that if 𝑌 = 9𝑉 , then the loss probability level stays
below 0.01 when the pause lasts at least 50% of an average conversation time.
The model analysis (1) revealed that the behavior of the functions shown in Fig. 2
does not change [9, 10] when the nature of distributions 𝐴(𝑡) and 𝐵(𝑡) changes. However,
choosing a proper value 𝜏 becomes a more complicated task. To solve it, we should
follow a procedure that involves periodic traffic monitoring of value Y, awareness of the
maximum allowed traffic intensity 𝑌𝑀 𝐴𝑋 , preventive selection of the pause duration
change limits – 𝜏𝑚𝑖𝑛 and 𝜏𝑚𝑎𝑥 , respectively. Modern switching systems and call centers
allow estimating value 𝑌 in real time. We can assume that value 𝜏𝑚𝑖𝑛 is equal to zero.
Threshold 𝜏𝑚𝑎𝑥 is estimated giving due consideration to psychological factors of users’
Levakov A. K., Sokolov N. A. 87
0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
1 ϑ
0.1
Y=3V
0.01
0.001
Y=6V
0.001
Y=9V
E(Y,V,ϑ)
Figure 2. Changes in the request loss probability with the introduced pauses
behavior in emergency situations [11, 12]. The preliminary studies indicated that most
users perceive value 𝜏𝑚𝑎𝑥 = 30𝑠 as an acceptable waiting time.
Fig. 3 shows how value 𝜏 (with some simplifications) is selected based on a set of
comparatively simple calculations. This procedure does not seem difficult to implement
in modern telecommunication equipment.
Periodic traffic No Yes
Y>YMAX τ = (τmin+τmax)/2
monitoring
No Yes
Y>YMAX τmin = τ
Figure 3. Pause duration 𝜏 selection procedure
To improve the public perception of the proposed suggested algorithm, telecommu-
nications networks’ users should be provided with explanations. This task has two
essential aspects. First, the public should be informed about possible changes in call
processing via various mass media. Second, so-called voice prompts during emergency
situations can help users gain a better understanding of the connection establishment
mechanism. Namely, the following phrase can be used as a prompt: “You can make
another call attempt in 30 seconds.”
4. Restriction of the communication session duration
According to formula (3), the load intensity can be decreased by restricting the
maximum conversation time ℎ𝑚𝑎𝑥 by a predefined threshold 𝑋. Value 𝑋 and threshold
𝜏𝑚𝑎𝑥 are selected giving due consideration to psychological factors of users’ behavior
88 ITTMM—2019
in emergency situations [11, 12]. According to a number of experts, the initial value 𝑋
can be set to 2 minutes. In addition, a voice prompt should be used, for example: “The
conversation time is limited to 2 minutes.”
The conversation time restriction should be the first measure implemented before
pauses between the call attempts are introduced. Thus, both algorithms can be reason-
ably considered to form a joint solution for restricting the load intensity in emergency
situations (see Fig. 4). To simplify the example, we assume that the duration of the
pause between the call attempts increases only once, which makes it longer by summand
𝛿𝜏 .
Periodic traffic No Yes Introduction of the
Y>YMAX
monitoring restriction: hmax≤X
No Yes Introduction of the
Y>YMAX
pause with duration τ
No Yes Pause duration
Y>YMAX
increase by Δτ
Figure 4. Algorithm to limit the load intensity in emergency situations
Formula (3) gives grounds for the following statement: the load decrease efficiency
is defined by the relation of values ℎ and 𝑋. On the other hand, we should bear in
mind that if the maximum conversation time is decreased noticeably, the number of the
repeated call attempts will grow [1].
5. Sorting the calls in the emergency call center
At present and in the near future, telecommunications are the main information
exchange channel between users and first responders. The first responders’ workplaces
are located in a specialized center, which is normally connected to the 112 emergency
telephone system [5, 14]. In a large-scale emergency situation, the number of incoming
calls to first responders increases dramatically. Most of the calls are related to the same
event and contain almost identical information.
To minimize the number of such calls, voice prompts should inform the users that
the first responders are aware of the emergency situation and taking measures. The
conducted studies proved that such a solution could reduce the number of calls induced
by the emergency situation by at least 40% [15]. To solve this task, we need to define
a certain area 𝑆𝐸𝑆 , which has the lasting effects of the emergency situation. Fig. 5
pictures this area as an ellipsis within the first responders’ service area 𝑆0 . It is evident
that 𝑆0 > 𝑆𝐸𝑆 in most cases; however, the following two inequalities can be true for
the load intensity values 𝑌0 and 𝑌𝐸𝑆 : 𝑌0 ≥ 𝑌𝐸𝑆 and 𝑌𝐸𝑆 ≥ 𝑌0 . The right part of
Fig. 5 shows the queue of r calls that arrived from two areas, 𝑆𝐸𝑆 and (𝑆0 − 𝑆𝐸𝑆 ).
The software in the emergency call center is represented as a queue management unit,
which sorts the calls in such a way so that the service procedure is close to the so-called
Levakov A. K., Sokolov N. A. 89
Sources
of traffic
S0 Y0
Queue with a length of r calls
Terminals of operators in
emergency service centre
1
SE ... ...
r i 1 2
YE .
.
.
Management system of V
queue to operators
Figure 5. Sorting the calls in the emergency call center during an emergency
situation
egalitarian algorithms [16,17]. The "egalitarity" (equality, derived from French "égalité")
is determined by the equivalence of the call loss probability or waiting time values.
The right part of Fig. 5 shows the queue of r calls that arrived from two areas, 𝑆𝐸𝑆
and (𝑆0 − 𝑆𝐸𝑆 ). The software in the emergency call center is represented as a queue
management unit, which sorts the calls in such a way so that the service procedure is
close to the so-called egalitarian algorithms [16, 17]. The egalitarity (equality, derived
from French “égalité”) is determined by the equivalence of the call loss probability or
waiting time values.
The key research findings that allow us to define the call sorting rules are given in [13].
This article examines another call sorting aspect based on dividing 𝑉 first responders’
workplaces (service units in terms of the teletraffic theory) into two groups, 𝑉0 and 𝑉𝐸𝑆 .
According to the teletraffic theory [2], when the load characteristics 𝑌0 and 𝑌𝐸𝑆 are
identical, dividing the service units into two or more groups results in 𝑉0 + 𝑉𝐸𝑆 > 𝑉 .
Let us assume that a group of first responders has been specially trained to process
the calls typical for a certain emergency situation. When the situation occurs, the first
responders are capable to process calls from area 𝑆𝐸𝑆 faster. This is possible because
value 𝑌𝐸𝑆 decreases with the decrease of factor ℎ in formula (3).
To illustrate this statement, let us consider a numeric example with the following
initial conditions:
∙ The emergency call center receives over 500 requests per hour.
∙ Half of the calls arrive from area 𝑆𝐸𝑆 .
∙ The average request processing time is 3 minutes.
∙ The allowed call loss probability is set to 0.01.
∙ The average request processing time for this emergency situation can be reduced
to 1.5 minutes if a trained group of first responders is involved.
To simplify the calculations, we assume that 𝑟 = 0. Then, we use the first Erlang
formula to estimate the loss probability [1, 2]. To comply with the allowed call loss
probability standard without the preventive training of first responders on how to address
specific issues of a particular emergency situation, 36 workplaces should be created.
With the assumptions made, when two groups of first responders are created, 𝑉0 = 21
and 𝑉𝐸𝑆 = 13. It means that the total number of workplaces can be decreased to 34.
Thus, call sorting helps in addressing a range of topical issues related to call processing
in emergency situations. It should be emphasized that training of first responders should
become an ongoing process considering the changes in the nature of certain emergency
situations and the new information technology developments aimed at increasing security.
90 ITTMM—2019
6. Examples of practical applications of the proposed algorithms
The proposed algorithms have been tested during the development and implementa-
tion of the 112 emergency telephone system equipment in the Russian Federation by
PROTEI company. Based on the conducted research, the “Traffic Limitation Mechanism
in Emergencies” study was contributed to the 13th Study Group of the Standardization
Sector of the International Telecommunication Union [18].
The emergency situation effects can be efficiently minimized based on the inter-
disciplinary research results [19]. For this reason, several stakeholders have approved
the practical guidelines on the implementation of the proposed solutions, which gives
hope of getting a synergistic effect [4]. In particular, the rational use of the emergency
notification system resources reduces the volume of traffic that arrives at the emergency
call center. However, the opposite process can also take place: less informative messages
in the emergency notification systems can lead to mass panic, which, in turn, stimulates
the snowballing growth of traffic in the telecommunications networks.
In emergency situations, traffic can be successfully limited with the efficient feedback
communication between all the participants in the information and communication
sector, such as research centers, equipment designers, design institutes, construction
companies, maintenance companies, and information resource providers. The feedback
communication can be arranged using the key principles of dia$par [20], which creates a
cybernetic model of real-life objects and processes. This model is called a digital twin
and allows analyzing the results of the emergency situation consequence liquidation (in
terms of the telecommunications networks’ stability) and reproducing various scenarios
of changes in the multiservice traffic.
7. Conclusions
The three algorithms that limit traffic in emergency situations, which we examined
herein, have proven to be efficient. It is important that the proposed solutions can
be implemented with comparatively simple modifications in the telecommunication
equipment software.
The mentioned algorithms have been adapted to process the voice traffic. In the
future, the share of other types of traffic sent as SMS, MMS and otherwise will grow. It
means that the traffic will become more and more multiservice, which will require the
new algorithms to be developed or the existing ones to be modified.
The suggestions on how to minimize the redundant information on the Internet
nowadays are given in [21], for example. According to the authors of the article, such an
approach is extremely important in emergency situations when decision-makers should
never be distracted from the essence of the task they are to solve. The use of neural
networks [22] and other artificial intelligence techniques [23] is the principal direction of
future developments in the traffic limitation algorithms.
References
1. S. N. Stepanov, Teletraffic theory: concepts, models, applications, Goryachaya
Liniya – Telecom, 2015, 867 p.
2. Y. N. Kornyshev, A. P. Pshenichnikov, A. D. Kharkevich, Teletraffic theory, Radio
i Svyaz’, 1996, 272 p.
3. Maslow A. G, Motivation and personality, Eurasia, 2001, 478 p.
4. A. K. Levakov, Features of the next generation network in emergency situations,
IRIAS, 2012, 108 p.
5. B. S. Goldstein, A. K. Levakov, N. A. Sokolov, Access to the call center "112",
Vestnik Svyazi, 2012, no.1, p. 5-8.
6. M. Bunge, A General Black Box Theory, Philosophy of Science, Vol. 30, No. 4, 1963,
pp. 346-358.
Levakov A. K., Sokolov N. A. 91
7. N. A. Sokolov, The tasks of telecommunication network planning, Tehnika svyazi,
2012, 432 p.
8. ITU-D. Teletraffic Engineering Handbook (edited by V. B. Iversen), Geneva, 2003,
321 p.
9. A. K. Levakov, The results of the simulation of the NGN network with a significant
increase in traffic. Part I, Telecommunications, 2012, no.7, pp. 32-34.
10. A. K. Levakov, The results of the simulation of the NGN network with a significant
increase in traffic. Part II, Telecommunications, 2012, no.8, pp. 24-25.
11. T. N. Gurenkova, I. N. Eliseeva, T. Yu. Kuznetsova, O. L. Makarova, T. Y. Mata-
fonova, M. V. Pavlova, Y. S. Shoigu, Psychology of extreme situations, Akademiya,
2009, 320 p.
12. B. V. Boev, V. S. Yastrebov, Prediction of mass panic processes in man-made
accidents and disasters, Journal of Neurology and Psychiatry, 2009, no.11, p. 81-88.
13. A. K. Levakov, Sorting calls with increasing load in the "System-112", Vestnik
Svyazi, 2013, no.1, p. 26-29.
14. COCOM 18-03. Working Document "Implementation of the European emergency
number 112 - Results of the eleventh data-gathering round", Brussels, 2018, 11 p.
15. A. K. Levakov, M. V. Kabanov, N. V. Pinchuk, N. A. Sokolov, Evaluation of
methods to reduce telephone traffic generated by the reaction of subscribers to the
event, Vestnik Svyazi, 2015, no.2, p. 12-15.
16. A. Demers, S. Keshav, S. Shenker, Analysis and simulation of a fair queuing
algorithm, ACM SIGCOMM Computer Communication Review, 1989, Volume 19
(4), pp. 1-12.
17. S. F. Yashkov, A. S. Yashkova, Egalitarian division of the processor, Information
processes, 2006, Volume 6, No. 4, p. 396-444.
18. http://www.itu.int/md/meetingdoc.asp?lang=en&parent=T13-SG13-140707-C&
PageLB=100 (accessed on 11 February 2019).
19. N. N. Moiseev, Selected Works. In 2 volumes. Volume 2. Interdisciplinary research
of global problems. Publicism and social issues, Taydeks Ko, 2003, 264 p.
20. https://diasparbusiness.com/cis-ru/what-is-diaspar (accessed on 11 February
2019).
21. A. K. Levakov, N. A. Sokolov, The concept of "modified reality", Vestnik Svyazi,
2018, no.11, p. 3-6.
22. C. C. Aggarwal, Neural Networks and Deep Learning, Springer, 2018, 497 p.
23. D. L. Poole, A. K. Mackworth, Artificial Intelligence: Foundations of Computational
Agents, Cambridge University Press, 2018, 820 p.