=Paper=
{{Paper
|id=Vol-3422/Paper13
|storemode=property
|title=The Risks Assessment of Delivery Failures for Application-to-Person SMS Market
|pdfUrl=https://ceur-ws.org/Vol-3422/Paper13.pdf
|volume=Vol-3422
|authors=Mykhailo Odarchenko,Serhii Zavhorodnii,Roman Odarchenko,Maksym Zaliskyi
|dblpUrl=https://dblp.org/rec/conf/citrisk/OdarchenkoZOZ22
}}
==The Risks Assessment of Delivery Failures for Application-to-Person SMS Market==
https://ceur-ws.org/Vol-3422/Paper13.pdf
The Risks Assessment of Delivery Failures for Application-to-
Person SMS Market
Mykhailo Odarchenko1, Serhii Zavhorodnii1, Roman Odarchenko1 and Maksym Zaliskyi1
1National Aviation University, Lubomyr Huzar Ave., 1, Kyiv, 03058, Ukraine
Abstract
Despite the widespread development of communication technologies, SMS messages remains widely
used by mobile subscribers, mobile operators, and enterprises. Nowadays, Application-to-Person SMS
is actively developing to deliver content of different kind to mobile phone from enterprises, banks,
mobile operators, and also valid for Mobile Internet of Things. Due to the action of various random
factors, SMS messages may not be delivered, which can lead to mobile subscribers dissatisfaction and
reduce the level of trust in the communication service operator. This paper concentrates on the
analysis and assessment of delivery failures risks for application-to-person SMS market. The main
attention is paid to the mathematical model building for statistical data on messages transmitting by
communication service provider. The cumulative probabilities of successful messages delivery are
described using exponential and hyperbolic models. The unknown coefficients of models are
estimated based on iterative procedure. Model correction during iteration is possible due to the
optimization paraboloid usage. The proposed methodology gives the possibility to create online
decision-making platform with predictive capability for fast and accurate estimation of delivery
failures risk.
Keywords 1
Risks assessment, Short Message Service, SMS completion failure ratio, mathematical model building,
exponential model, hyperbolic model
1. Introduction
The short message/messaging service (SMS) is in use for almost 30 years now. It has been first
sent on December 3, 1992, using a personal computer and it was addressed to a mobile phone
[1]. Since then, SMS has become one of the most used communication channels worldwide. It
became possible due to simplicity, availability and accessibility of the SMS. Hence the age, SMS
remains widely used by mobile subscribers, mobile operators, and enterprises. Forecasts show
that only Application-to-Person (A2P) SMS market was valued at 64.42 Billion USD in 2021
and it is expected to reach 84.18 Billion USD by 2029, exhibiting the compound annual growth
rate of 3.43% during the forecast period. According to the GSMA Mobile Economy 2020
CITRisk’2022: 3rd International Workshop on Computational & Information Technologies for Risk-Informed Systems, January
12, 2023, Neubiberg, Germany
EMAIL: odarchenko.m.s@gmail.com (M. Odarchenko); zavgorodniys67@ukr.net (S. Zavhorodnii); odarchenko.r.s@ukr.net
(R. Odarchenko); maximus2812@ukr.net (M. Zaliskyi)
ORCID: 0000-0002-7714-3558 (M. Odarchenko); 0000-0003-2451-5108 (S. Zavhorodnii); 0000-0002-7130-1375 (R. Odarchenko);
0000-0002-1535-4384 (M. Zaliskyi)
© 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
research, there were over 6.1 billion unique mobile subscribers in 2021, with smartphones
accounting for 60% of connections [2].
Range of SMS use cases continues to expand. It started with:
1. Point-to-Point (P2P) SMS: providing means of sending messages to and from mobile
phones.
2. Application-to-Person (A2P) SMS: used to deliver content of different kind to mobile
phone from enterprises, banks, mobile operators, and others, and also valid for Mobile Internet
of Things (MIoT).
3. Technical enabler: Over The Air (OTA) messaging used for Universal Mobile
Telecommunications System (UMTS) Subscriber Identity Module provisioning, Internet
Protocol (IP) session wake-up [3].
Another important function of SMS is being a part of emergency communications. Short
Message Service or SMS messages can be sent to a mobile terminal without special options
needing to be set on the handset. SMS is widely known and accepted, and messages can contain
detailed instructions for citizens on required actions to take. Under normal conditions, delivery
can be almost instantaneous, but a large number of messages require considerable time.
Since the mobile terminal acknowledges successful reception of the SMS, the retry
mechanism guarantees a very high rate of successful delivery. Severe network congestion may
lead to a delayed delivery. SMS in itself is not location specific. However, there are technical
means to detect where mobile handsets are located, but not necessarily in a timely manner.
Active probing generates a lot of traffic on the signaling channels and passive probing requires
expensive equipment to probe each Radio Access Network (RAN) node [4].
2. Related works
The analysis of literature in the field of SMS-based communication channels showed that
sufficient attention is paid to scientific research of these channels effectiveness and possibilities
of such technologies utilization in various branches of human society.
The SMS is a very cheap, at the same time highly reliable way to use the communication
channel, and can be used on all mobile terminals [5]. Almost 100% of the population worldwide
uses the mobile phone and is able to send and receive short text messages. Benefits of using
short text messages encourages their adoption in business and industry.
When using SMS messages, information security methods can also be applied [6]. The
security of messages and the use of additional encryption methods make it possible and
promising to use SMS for banking purposes [7]. Moreover, additional SMS sending can improve
the quality of steganography when sending encrypted voice messages [8].
The branches of SMS utilization are different. Paper [9] presents a web-based SMS
management system whose main function is to enable non-technical users to perform SMS study
reconfiguration. The presented system has been tested for the purposes of medicine and health
monitoring, as well as ensuring child development monitoring.
Paper [10] concentrates on SMS-based system as supporting tool of global position system
for tracking a moving target. Using SMS for such purpose provides suitable response time and
acceptable accuracy for location tracking.
The possibilities of SMS usage for user authentication throughout the internet are discussed
in [11]. The authors analyzed the scenario for successful information delivery, techniques of
encryption to eliminate the events of user account hijacking.
Due to the action of various random factors, SMS messages may not be delivered, which may
lead to mobile subscribers dissatisfaction and reduce the level of trust in the communication
service operator [12]. Various methods to improve the quality of SMS delivery can be applied.
Paper [13] deals with the analysis of SMS behaviors and estimation of efficiency in form of
delivery failures. To reduce the delivery delay, authors proposed to implement timeout timer.
Paper [14] discusses the robust SMS platform based sliding window and technique of load
balancing. The proposed methodology, which provides high efficiency, is used for aviation
information service application system with ability to meet strong requirements for aviation
safety providing [15]. Paper [16] presents the method for extending the coverage area for SMS
communication based on Long Range (LoRa) networks.
To analyze the efficiency of SMS transmitting, the statistical methods are usually used. Paper
[17] focuses on mathematical background for cost analysis while SMS retransmission using real
data example. Another example of statistical analysis of real data on mobile banking services is
considered in [18].
To carry out statistical analysis of data on SMS delivery can be used methods and technique
from related fields of study, for example spline-approximation technique that discussed in [19],
methods of diagnostic variable model building considered that considered in [20], sequential
methods of diagnostic variable estimation proposed in [21] and others.
This paper concentrates on the analysis and assessment of delivery failures risks for
application-to-person SMS market. The main attention is paid to the mathematical model
building to estimate the SMS completion failure ratio. The initial information for mathematical
model building is statistical reports on messages transmitting by communication service
provider.
3. Materials and methods
3.1. Key parameters for defining reliability of SMS service
Provided the wide range of SMS use cases and it being essential part of GSM suite, quality of
service is regulated by standard set by The European Telecommunication Standard Institute
(ETSI) in its latest technical specification ETSI TS 102 250-2 v.2.7.1 (2019-11) “Speech and
multimedia Transmission Quality (STQ); QoS aspects for popular services in mobile networks;
Part 2: Definition of Quality of Service parameters and their computation”. Parameter overview
chart with trigger points is shown in Figure 1.
Figure 1: SMS parameter overview with trigger points
The following set of parameters for evaluation of quality of service is defined [22]:
1. SMS Service Non-Accessibility [%] – denotes the probability that the end-user cannot
access the short message service when requested while it is offered by display of the network
indicator on the User Equipment (UE).
2. SMS Access Delay [s] – denotes the time period between sending a short message to the
network and receiving a send confirmation from the network at the originating side.
3. SMS Completion Failure Ratio [%] – corresponds to the ratio of unsuccessfully received
and sent messages from one UE to another UE, excluding duplicate received and corrupted
messages.
4. SMS End-to-End Delivery Time [s] – corresponds to the time period between sending a
short message to the network and receiving the very same short message at another UE.
5. SMS Receive Confirmation Failure Ratio [%] – denotes the probability that the receive
confirmation for a sent attempt is not received by the originating UE although requested.
6. SMS Receive Confirmation Time [s] – corresponds to the time period between sending a
short message to the network and receiving the receive confirmation for this message from the
network.
7. SMS Consumed Confirmation Failure Ratio [%] – denotes the probability that the
consumed confirmation for a sent attempt is not received by the originating UE although
requested.
8. SMS Consumed Confirmation Time [s] – corresponds to the time period between sending a
short message to the network and receiving the consumed confirmation from the network.
As P2P SMS usage declines over past decade [23], and usage of A2P SMS, MIoT and OTA
SMS is expanding such parameters as SMS Completion Failure Ratio, SMS End-to-End
Delivery Time, SMS Receive Confirmation Time become the key parameters as it affect the
mobile terminated (MT) SMS.
The transaction flow for MT SMS scenario shown in Figure 2.
Figure 2: MT SMS transaction flow
SMS Completion Failure Ratio is calculated by following equation [22]:
unsuccessfully received SMS
SMS Complition Failure [%] = × 100 .
all SMS service attempts
SMS End-to-End Delivery Time is calculated by following equation:
SMS End-to-End Delivery Time [s] = t B , receive − t A, send [s].
SMS Receive Confirmation Time is calculated by following equation:
SMS Receive Confirmation Time [s] = t B , receive confirmation − t A,send [s].
These parameters can be affected on different stages of message delivery: congestion in the
SMS system (between SMS originator and Mobile operator network), congestion in signaling
links in mobile operator’s network or in the interworking connections (connection between
mobile operators), service non-availability in certain geographical areas.
The risk of delivery failures for A2P SMS Market can be considered as SMS Completion
Failure Ratio. Let this risk is q , then p = 1 − q is the probability of correct delivery of SMS.
3.2. Mathematical model building for SMS delivery parameter
Consider the real data example of SMS delivery performance.
Table 1 presents statistical data showing SMS MT sent across all operators in country A in
the period of time 15/10/22-31/10/22 by one of Communication Platform As A Service
(CPAAS) providers.
Table 1
SMS MT delivery statistics between 15/10/2022 and 31/10/2022
SMS MT Delivery parameter Number of SMS MT
Total 2492766
Delivered 2196792
Expired 159584
Undeliverable 136390
Delivered within 10s 1811373
Delivered within 30s 248302
Delivered within 1m 36723
Delivered within 5m 55041
Delivered within 15m 11394
Delivered within 30m 6490
Delivered within 1h 7329
Delivered within 3h 6616
Delivered within 6h 3450
Delivered within 12h 2931
Delivered within 24h 3870
Delivered within 48h 3273
Data from Table 1 show that in this case 82.46% of all delivered SMS MT are delivered within
10 seconds, which is acceptable value.
Observed data can be considered as time series with discrete time and measurements in time
moment t = {10, 30, 60, 300, 900,1800, 3600,10800, 21600, 43200, 86400,172800} [s]. To build the
mathematical model for such time series can be used general approximation techniques, for
example described in [24]. The quantity of delivered messages decreases over time. The range of
change for this quantity is significant.
To represent the data better, logarithmic scale for quantity and time is more preferable for
visual analysis. In addition, the natural logarithms for cumulative quantity of delivered SMS can
also be used. To estimate the risk of delivery failures, the current statistical probabilities of
successful delivery 𝑝𝑝𝑖𝑖 and corresponding cumulative probabilities 𝑝𝑝𝛴𝛴𝛴𝛴 are calculated.
Figure 3 shows the initial dependencies for observed data presented in Table 1.
a b
c d
Figure 3: Observed time series: a – dependence of delivered messages quantity on time;
b – dependence of statistical probabilities of successful delivery on time; c – dependence of cumulative
quantity of delivered messages on time; d – dependence of cumulative probabilities of successful
delivery on time
Visual analysis of dependencies presented in Figure 3 makes it possible to conclude that
cumulative curves are more suitable for risk assesment of delivery failures.
Consider two alternative models for risk assessment.
1. Exponential model.
This model is determined according to following equation:
f (t ) = a − ae − bt , (1)
where a and b are model coefficients need to be estimated.
It should be pointed out that in case of cumulative probabilities data analysis the estimate of
model coefficient a is suitable for assessing the probability of correct delivery of SMS. So the
risk of delivery failures can be found as q = 1 − a .
The general approach to estimate the model coefficient is usage of ordinary least squares
method after making assumption about normal distribution of errors. In this case, it is necessary
to solve the system of equation
N N
∑
i =1
f i ( e − bt i
− 1 ) − a ∑i =1
(e − bt i − 1) 2 = 0,
N N N
f t e − bt i − a t e − bt i + a t e − 2bt i = 0.
∑
i =1
i i ∑i =1
i ∑
i =1
i
The solution of such system of equation is complicated problem.
Consider alternative approach. At the first iteration, we can calculate the unknown
coefficients making assumption that exponential curve (1) contains first and last sample of initial
dataset. In this case, it is necessary to solve the system of equation
f1 = a (1 − e ),
− bt1
f N = a (1 − e ).
− bt N
After mathematical simplification, we can get
f1
a= .
1 − e −bt1
The model coefficient b can be found as non-zero solution of equation
f1 f
− 1 + e − bt1 − 1 e − bt N = 0.
fN fN
To solve this equation, one of the numerical method can be used.
The second iteration is associated with minimizing the standard error of the model. For this
purpose, optimization paraboloid can be implemented. The general methodology of mentioned
optimization is discussed in [24].
To estimate the risk of delivery failures using complete statistical data, we need to analyze
data observed within two days. The using of exponential model (1) building technique gives the
ability to construct online decision-making platform with predictive capability for fast estimation
of delivery failures risk. For example, we can measure the data within 5 minutes duration and for
corresponding data estimate the model coefficients with subsequent recalculation of one of these
coefficients into the risks of delivery failures. The flowchart of corresponding method is shown
in Figure 4.
Data collection within
short time duration
Mathematical model
correction based on
optimization paraboloid
Cumulative probabilities
calculation
Prediction of risk of
delivery failures
Mathematical model
building for the first
iteration
Figure 4: The flowchart of risk assessment of delivery failures
Consider the example of model building for data shown in figure 3d. The first iteration gives the
following estimates of model coefficients: a = 0.881 and b = 0.756 . The mathematical model of
cumulative probabilities will be
pΣ (ln t ) = 0.881 − 0.881e −0.756 ln t . (2)
To correct the mathematical model, we considered 25 options of model coefficients (five
possible values of each coefficient) and calculated standard deviations. The results of
computation are presented in Table 2.
Table 2
The results of standard deviations computation
S(a, b) b = 0.656 b = 0.706 b = 0.756 b = 0.806 b = 0.856
a = 0.861 0.03308 0.02535 0.0197 0.01639 0.01551
a = 0.871 0.02489 0.0164 0.009999 0.007296 0.009344
a = 0.881 0.01918 0.01099 0.006288 0.008203 0.01285
a = 0.891 0.01843 0.01409 0.01438 0.01763 0.02177
a = 0.901 0.02312 0.02241 0.02454 0.028 0.03183
The data from Table 2 was approximated using paraboloid and ordinary least squares method.
The calculation gives the following model of paraboloid:
S (a, b) = 26.079 − 55.695a + 30.091a 2 − 4.173b + 0.591b 2 + 3.692ab .
The minimum of paraboloid determines the best model coefficients: aopt = 0.877 and
bopt = 0.791 . Therefore, model (2) after correction takes the optimal form:
pΣ opt (ln t ) = 0.877 − 0.877e −0.791ln t . (3)
The result of approximation using model (3) is shown in Figure 5.
Figure 5: Exponential model for cumulative probabilities of successful delivery
So the risk of delivery failures for model (3) is q = 1 − aopt = 0.123 .
2. Hyperbolic model.
This model is determined according to following equation:
at ,
f (t ) = (4)
1 + bt
where a and b are model coefficients need to be estimated.
To determine the risk of delivery failures, we can analyze cumulative probabilities similar to
the model (1). But in this case, the risk of delivery failures can be approximately found as
q ≈ 1− a b .
The exact values of model coefficients are solutions of the system of two equations obtained
after using ordinary least squares method:
N f i ti N
ti
2
∑ − a∑ = 0,
i =1 (1 + bt i )
2
i =1 1 + bt i
N 2 3
f i ti N
ti
∑
(1 + bt )2 − a ∑ = 0.
i =1 (1 + bt i )
3
i =1 i
To simplify estimation of model coefficients, we can use approach described for model (1).
Therefore, at the first iteration, we assume that hyperbolic curve (4) contains first and last
sample of initial dataset. In this case, it is necessary to solve the system of equation
f1 (1 + bt1 ) = at1 ,
f N (1 + bt N ) = at N .
After mathematical simplification, we can get
f1 f N (t1 − t N ) t f −t f
a= and b = 1 N N 1 .
t1t N ( f1 − f N ) t1t N ( f1 − f N )
At the second iteration, model is corrected using optimization paraboloid.
Consider the example of hyperbolic model building for data shown in figure 3d. After the
first iteration, the initial estimates of model coefficients were obtained: a = 1.455 and b = 1.568 .
Then the model (4) will be
1.455 ln t
pΣ (ln t ) = . (5)
1 + 1.568 ln t
At the second iteration, the mathematical model correction was carried out for 25 options of
model coefficients (five possible values of each coefficient) based on standard deviations
calculation. The results of computation are presented in Table 3.
Table 3
The results of standard deviations computation
S(a, b) b = 1.508 b = 1.538 b = 1.568 b = 1.598 b = 1.628
a = 1.395 0.0277 0.04147 0.05606 0.0706 0.08485
a = 1.425 0.01738 0.02504 0.03828 0.05257 0.06689
a = 1.455 0.02475 0.01682 0.02262 0.03524 0.04922
a = 1.485 0.04123 0.02622 0.01675 0.02044 0.03234
a = 1.515 0.05969 0.04291 0.02779 0.01711 0.01856
The standard deviations can be determined as dependence on model coefficients using ordinary
least squares method:
S (a, b) = −0.974 − 0.782a + 4.112a 2 + 2.044b + 2.758b 2 − 7.256ab .
The minimum of paraboloid determines the best model coefficients: aopt = 1.444 and
bopt = 1.529 . Therefore, model (5) after correction takes the optimal form:
1.444 ln t
pΣ (ln t ) = . (6)
1 + 1.529 ln t
The result of approximation using model (6) is shown in Figure 6.
Figure 6: Hyperbolic model for cumulative probabilities of successful delivery
So the risk of delivery failures for model (6) is q = 0.104 .
4. Results and discussions
This section presents numerical examples of risk assessment for two datasets of SMS MT
delivery. The initial data are shown in Table 4.
Table 4
SMS MT delivery statistics between 31/10/22 and 06/11/22 (dataset 1) and between 07/11/22
and 13/11/22 (dataset 2)
SMS MT Delivery Number of SMS Cumulative Number of SMS Cumulative
parameter MT (dataset 1) probability MT (dataset 2) probability
Total 1020320 – 890677 –
Delivered 902546 – 788318 –
Delivered within 10s 740181 0.725 657701 0.738
Delivered within 30s 101664 0.825 73300 0.821
Delivered within 1m 12892 0.838 12076 0.834
Delivered within 5m 22822 0.86 22637 0.86
Delivered within 15m 7920 0.868 6999 0.868
Delivered within 30m 3222 0.871 2562 0.87
Delivered within 1h 3942 0.875 3429 0.874
Delivered within 3h 3152 0.878 3017 0.878
Delivered within 6h 1739 0.88 1427 0.879
Delivered within 12h 1458 0.881 1452 0.881
Delivered within 24h 1930 0.883 1927 0.883
Delivered within 48h 1624 0.885 1791 0.885
Data analysis for the first and second datasets gives possibility to conclude that in both cases real
value for delivery failures risk is q = 0.115 .
Consider the results of risk assessment using proposed methodology and exponential model
(1). To make decision about risk value, we use only four values of datasets measured within 5
minutes of observation.
At the first iteration, the following models for two datasets were obtained:
pΣ (ln t / dataset1) = 0.870 − 0.870e −0.779 ln t and pΣ (ln t / dataset 2) = 0.867 − 0.867e −0.828 ln t .
The second iteration gives corrected results:
pΣ opt (ln t / dataset1) = 0.872 − 0.872e −0.797 ln t and pΣ opt (ln t / dataset 2) = 0.866 − 0.866e −0.838 ln t .
The results of approximation using exponential model for the first and second datasets are
shown in Figure 7.
a b
Figure 7: Exponential model for the first (a) and second (b) datasets
The estimates for failures delivery risk for the first and second datasets are 0.128 and 0.134,
respectively. Figure 7 shows good coincidence of data with exponential model and sufficient
accuracy of risk assessment in the task of long-term forecasting. At the same time, the
exponential model gives slightly increased risk estimates.
Consider the results of risk assessment using proposed methodology and hyperbolic model
(4) for data collected within 5 minutes of observation. At the first iteration, the following models
for two datasets were obtained:
1.2 ln t 1.356 ln t
pΣ (ln t / dataset1) = and pΣ (ln t / dataset 2) = .
1 + 1.22 ln t 1 + 1.402 ln t
The second iteration gives corrected models:
1.147 ln t 1.327 ln t
pΣ opt (ln t / dataset1) = and pΣ opt (ln t / dataset 2) = .
1 + 1.202 ln t 1 + 1.392 ln t
The estimates for failures delivery risk for the first and second datasets are 0.111 and 0.1. The
hyperbolic model has sufficient accuracy and gives slightly decreased risk estimates.
To increase the accuracy of risks assessment, it is desirable to organize data collecting with
high enough sampling frequency within 5 minutes observation.
5. Conclusion
The SMS remains widely used in human communication, business and industry because of low
cost, simplicity of use, adaptability to all mobile phones. Analysis has shown that A2P SMS-
based communication market is still growing. Due to the action of various random factors, SMS
messages may not be delivered, which can lead to mobile subscribers dissatisfaction and reduce
the level of trust in the communication service operator. At the same time, different applications
face the problem of increasing the efficiency of SMS transmitting in terms of improvement for
SMS completion failure ratio.
Analysis of main parameters for evaluation of quality of service gives possibility to choose
the risk of SMS delivery failure as the main efficiency measure having influence of consumers’
satisfaction and services costs.
This paper concentrates on the analysis and assessment of delivery failures risks for A2P
SMS market. The main attention is paid to the mathematical model building to estimate the SMS
completion failure ratio. The initial data for model building are SMS MT delivery statistics. For
convenience, these data are converted to the cumulative probabilities of successful delivery.
The cumulative probabilities of successful messages delivery are described using exponential
and hyperbolic models. The unknown coefficients of models are estimated based on iterative
procedure. At the first iteration, initial values of model coefficients are estimated making
assumption about model curve containing two samples of observed dataset. At the second
iteration, model is corrected using optimization paraboloid technique. The final models are used
to assess the risk of SMS delivery failures.
The proposed methodology gives the possibility to create online decision-making platform
with predictive capability for fast and accurate estimation of delivery failures risk.
The future research directions are associated with:
– substantiation of the structure for efficiency support system of SMS communication
channel based on risks forecasting of SMS delivery failures;
– costs analysis due to SMS unsuccessful delivery;
– implementation of artificial intelligence method for optimization of SMS communication
channel.
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