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.
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].
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.
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. 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. SMS End-to-End Delivery Time is calculated by following equation:
SMS End-to-End Delivery Time [s] = tB, receive − tA,send [s].
SMS Receive Confirmation Time is calculated by following equation:
SMS Receive Confirmation Time [s] = tB,receiveconfirmation − 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.
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. 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 and corresponding cumulative probabilities are calculated.
Figure 3 shows the initial dependencies for observed data presented in Table 1. 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 ,
(
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 ∑ fi (e−bti − 1) − a∑ (e−bti − 1)2 = 0, i=1 i=1 N N N ∑ fitie−bti − a∑tie−bti + a∑tie−2bti = 0.
i=1 i=1 i=1 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 (
After mathematical simplification, we can get
a = 1 − fe1−bt1 .
The model coefficient b can be found as non-zero solution of equation f1 − 1 + e−bt1 − f1 e−btN = 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 (
Data collection within
short time duration Cumulative probabilities
calculation Mathematical model building for the first iteration
Mathematical model correction based on optimization paraboloid
Prediction of risk 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−0.756ln t .
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. 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 + 30.091a2 − 4.173b + 0.591b2 + 3.692ab .
The minimum of paraboloid determines the best model coefficients: aopt = 0.877 and
bopt = 0.791. Therefore, model (
pΣopt (ln t) = 0.877 − 0.877e−0.791lnt .
The result of approximation using model (
The exact values of model coefficients are solutions of the system of two equations obtained after using ordinary least squares method: ∑N fiti − a ∑N ti 2 i=1 1 + bti i=1 (1 + bti )2 = 0, ∑N fiti 2 − a ∑N ti3 i=1 (1 + bti )2 i=1 (1 + bti )3
To simplify estimation of model coefficients, we can use approach described for model (
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 (
1 + 1.568ln 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.
The standard deviations can be determined as dependence on model coefficients using ordinary
least squares method:
bopt = 1.529 . Therefore, model (
This section presents numerical examples of risk assessment for two datasets of SMS MT delivery. The initial data are shown in Table 4.
Total
Delivered pΣopt (ln t / dataset1) = 0.872 − 0.872e−0.797lnt and pΣopt (ln t / dataset2) = 0.866 − 0.866e−0.838lnt .
The results of approximation using exponential model for the first and second datasets are shown in Figure 7.
a Figure 7: Exponential model for the first (a) and second (b) datasets b 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 pΣ (ln t / dataset1) = 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
(
. . pΣ opt (ln t / dataset1) =
and pΣopt (ln t / dataset2) = 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.
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 SMSbased 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. [15] I.V.Ostroumov, N.S.Kuzmenko, Configuration Analysis of European Navigational Aids Network, 2021 Integrated Communications Navigation and Surveillance Conference (ICNS), Dulles, USA, April 19-23, 2021, pp. 1–9. DOI:10.1109/ICNS52807.2021.9441576 [16] F.Giménez, C.Zerbini, G.Riva, Extending SMS Service Coverage in Rural Areas by using LoRa Communication Technology, IEEE Latin America Transactions, 18 (02), 2020, рр.214–222. DOI:10.1109/TLA.2020.9085273 [17] S.-I.Sou, Y.-B.Lin, C.-L.Luo, Cost Analysis of Short Message Retransmissions, IEEE
Transactions on Mobile Computing, 9 (