Autonomous and adaptive congestion control for machine-type communication in cellular network

Abstract

Machine-type communications have suffered serious congestion, overload, and poor quality of service problems in cellular networks, since the cellular networks are designed for human-to-human communications. Moreover, current solutions just focus on the congestion for single base station and cannot adaptively work in the dynamic and complex conditions. In this article, we provide an autonomous and adaptive attractor-selection-based congestion control scheme for massive access from machine-type communication devices based on the resource separation scheme. First, we introduce a feasible and self-adaptive extended attractor-selection mechanism to decide which base station to be chosen. Simultaneously, an effective estimation algorithm for the traffic load of base stations is also designed to represent the network traffic load without frequent information exchanges among devices or base stations. With the available access resources and estimated traffic load taken into consideration, massive access attempts can receive the decisions via the broadcast and adaptively choose proper stations for alleviation of the congestion and overload. Finally, simulation results show that the proposed attractor-selection-based congestion control scheme achieves better performance in terms of average access delay, collision probability, and throughput of the whole system, adaptively accommodating to unpredictable environments under cellular networks.

Keywords

Massive machine-type communications random-access procedure attractor selection congestion control base station selection

Introduction

Machine-type communications (MTCs) mean information exchanges among miscellaneous objects or between the ubiquitous devices and servers without human interference. It has been regarded as a new type of communication in the next-generation network (NGN), which may widely renew our day-to-day living styles. Plenty of machine-to-machine (M2M) applications have emerged, such as e-health, smart metering, intelligent transportation, and smart grid. Likely in the future, everything around us will be equipped with the ability to connect with the Internet and communicating with each otunicating with each other, constituting the giant network frame which is the so-called Internet of things (IoT).^1,2 The number of connected devices has exceeded the number of people on earth.³ According to the estimation report of the wireless world research forum (WWRF), there will be 7 trillion wireless devices connected to various network for serving billion people in the future.⁴ This massive machine-type communication (mMTC) scenario is also the key use case in future fifth-generation (5G) cellular network. Massive access from a large number of energy-, complexity- and computation-constrained MTC devices need to be handled by 5G network.^5,6

MTC over cellular networks have a large market potential for the sake of their wide applications.⁷ The huge potential of this market will generate prominent revenues which exceeds $300 billion.⁸ The compound annual growth rate (CAGR) would exceed 25% for the MTC devices and corresponding connectivity segments over the next few years.⁹ Apparently, MTC has promising economic and strategic prospects in the future mobile market.¹⁰

Pervasive MTC devices can connect to the network via all kinds of communication technologies, such as ZigBee, Wi-Fi, LoRa, and narrow band IoT (NB-IoT). So far, the cellular network is the most ideal solution for MTC due to its higher capacity, broader coverage, and more flexible radio resource managements, especially the long-term evolution (LTE) infrastructure.⁷ Aiming at providing low power and wide area network (LPWAN) for mMTC devices, the 3rd Generation Partnership Project (3GPP) has carried out the improved standard based on the traditional LTE/LTE-A network. The LTE-Cat 0, LTE-Cat 1, LTE-M, and NB-IoT are simplified with narrower bandwidth, lower data rate, high link budget and so on, which forms the key components of cellular IoT network and cooperatively supports the mMTC scenario under 5G network.^11,12 In this article, we would mainly focus on the access congestion and overload resulted from the typical slotted ALOHA-based random-access procedure (RAP) which is widely used in cellular networks. The research can also be applied to NB-IoT network with slight alterations due to the new design in the access procedure. Maybe the achievable data rate of cellular IoT network is sufficient for almost all the M2M services, but it cannot support the giant amount of simultaneous access attempts, even sacrificing the quality of service (QoS) performance of human-to-human (H2H) communications.¹³ Unlike the traditional voice and data traffic for human-type communications (HTC), there are always infrequent and small-data transmissions in MTC.² Besides, billions of MTC devices would generate a great deal of signaling and data process information under different scenarios, resulting in serious congestion and overload for both the radio access network (RAN) and core network (CN). It is evident that serious congestion and overload from mMTC devices would seriously affect the normal communications among humans, even leading to the network collapse. Therefore, MTC need new, scalable, compatible, and stable solutions for disposal of congestion and overload.

Related work

There have been many leading standardization organisms working on the solution for insuring both the M2M and H2H communications, like the International Telecommunications Union (ITU), the European Telecommunications Standards Institute (ETSI), 3GPP, the Telecommunications Industry Association (TIA), the Chinese Communications Standard Association (CCSA) and the global initiatives such as OneM2M.¹⁴ So far, the key emphasis of this work lies on the MTC improvements without jeopardizing the traditional H2H communications under cellular network, especially dealing with the signaling congestion and overload problem in front of massive access of MTC devices.

There have also been numerous researches focusing on the congestion and overload solutions for M2M services under cellular networks. Dawy et al.¹⁵ introduced the development background of M2M and the common solutions to the network congestion and overload, such as the group-based method and slotted transmission. Soltanmohammadi et al.¹⁶ explored the issues, solutions, and the remaining challenges to enable and improve M2M communication over cellular networks. The comprehensive discussions about the advantages and disadvantages of solutions proposed in recent years are presented in detail. In few previous studies,^17,18 a series of effective methods for network congestion and overload are also summarized and analyzed, like the typical access class barring (ACB), evolved access barring (EAB), back-off scheme, and resource separation scheme (RSS). Zhao et al.¹⁹ proposed a random-access algorithm based on statistics waiting for energy saving. In addition, few authors^20–22 designed and analyzed the distributed queuing–based random-access (DQRA) protocol. Based on a tree-splitting algorithm, devices are organized into contention resolution queue (CRQ) and data transmission queue for collision avoidance. Alavikia and Ghasemi²³ proposed a multiple power level random-access mechanism for M2M communications. Based on the capture effect, collided devices can be decoded by base stations via assigning different levels of power, which implements the multiplexing in the power domain.²⁴ Few authors^25–27 investigated the transmission repetitions in the random channel access (RACH) procedure of NB-IoT and also gave the analysis in terms of successful access probability, average access delay, or throughput. An enhanced access reservation protocol (ARP) with a partial preamble transmission mechanism was proposed to avoid the preamble transmission collisions in NB-IoT.²⁸ The proposed method leveraged the trade-off between mis-detections and collisions and alleviate the congestion puncturing the preamble sequence through the partial preamble transmission mechanism.

However, what the above studies focused on are constrained to solutions of congestion happened in single base station, ignoring the cooperation and dynamic environmental fluctuations among heterogeneous base stations. They put excessive attentions on improving the access mechanisms for MTC devices which are attached to only one base station. All the decisions are determined by only one individual base station without cooperation with others.

The state-of-the-art cellular systems, such as LTE/LTE-advanced networks, are always under a heterogeneous multi-tier network architecture.²⁹ Various cellular base stations are widely deployed for good coverages and high capacity, like macro cell, femto cell, and pico cell, forming an ultra-dense network.³⁰ Massive MTC devices are likely to be served in the highly dynamic heterogeneous wireless environments where multiple base stations are simultaneously available, running various applications. Due to the instability of wireless communications and fierce competitions among mMTC devices and applications for the limited network resources, the characteristics of wireless networks would always dynamically change with time and be hard to keep a stable state. Obviously, it is vital to choose the most suitable wireless network taking into account the conditions of wireless networks. Since the outside conditions of wireless networks have high degree of freedom, deriving that the optimal base station selection solution is likely to suffer from state space explosion and time- and energy-consuming computation.³¹ More efficient, self-adaptive, and robust base station selection solutions are needed in order to smoothly adapt to unstable network conditions, so as to alleviate the congestion and overload with high spectrum efficiency.³²

Researches on the MTC devices under heterogeneous base stations have also attracted lots of attentions. Due to the differences of traffic load and access resources for each base station, cooperation among base stations are needed for congestion and overload control. Especially under RSS, it is more evident, since the radio access resources, like the preamble sequences and physical downlink control channel (PDCH) resources, may be fixed or adjusted dynamically and adaptively.^33–35 Improper base station–selection scheme may aggravate the congestion and overload of some base stations with an extremely low resource efficiency. Lien et al.³⁶ introduced the cooperative access class barring (CACB) scheme for M2M communications and proposed an ACB-based congestion solution. Via the information exchanges among base stations, the ACB parameters can be decided jointly to realize the global stabilization and access load sharing. But frequent data exchanges among base stations are still needed, putting more load and interferences on base stations and devices. Likely, Hsu et al.³⁷ proposed an enhanced cooperative access class barring (ECACB) and traffic-adaptive radio resource management for M2M communications. The number of devices connected to a base station is used to determine the probability that devices can access to the base station. However, MTC devices are always in sleep mode or $RRC_IDLE$ mode. It is improper to regard the number of connected M2M devices as the whole amount of devices in LTE network. Few authors^2,38,39 proposed a reinforcement learning-based base station–selection algorithm. Based on the reinforcement learning algorithm, that is, Q-learning algorithm, M2M devices could choose the appropriate base stations for network access in order to mitigate the serious congestion of each base station. However, such a solution working in a self-organized fashion would lead to frequent message exchanges, which would also put more load and interferences on the MTC devices.

In summary, the above cooperation schemes need frequent information exchanges to support the decision-making. Every node in such schemes needs to maintain the up-to-date information by frequent essential message exchanges from other devices. Even if the task to derive the optimal resource allocation is distributed among the devices, it would generate frequent and large amount of information exchanges among these devices to obtain the latest information of the current status of outside network environments. From a viewpoint of dynamic features of wireless networks and cost, for example, transmission bandwidth, energy consumption, and complexity, such mechanisms are not at all feasible and efficient under this scenario.

Contribution and organization

Therefore, in this article, we propose a robust and self-adaptive attractor-selection-based congestion control (ASCC) mechanism for base station selections. Based on the proposed congestion control mechanism, base stations derive their probabilities to be selected for network access by devices. No data exchange among devices or base stations are needed. Derived results would be broadcast by base stations to mMTC devices under their coverage. Then, after receiving derived access probabilities, devices would probabilistically select their targeted base stations. Ultimately, massive access attempts of MTC devices are separated among several base stations adaptively and robustly. Optimal access allocations would be obtained, mitigating the congestion and promoting the resource efficiency.

In order to accomplish robust and adaptive access attempts allocation in the dynamically changing environment, we characterize the base station–selection scheme via a nonlinear mathematical model based on autonomous and adaptive biological reactions. This model is named as the attractor-selection mechanism (ASM). It is a noise-driven metaheuristic to derive a stable solution of optimization problem in an adaptive way.⁴⁰ Once the current solution is suitable, a basin of attractor corresponding to the solution becomes deep, and the state of whole system statically stays there. When the outside environment changes and the solution becomes inappropriate, the basin of attractor turns unstable and fluctuates. Then the state will choose another suitable solution driven by the outside noise. In order to reflect the dynamic variations of the traffic load for each base station, we also propose a traffic estimation mechanism. Base station can learn about the scale of network attempts via the status of radio access resource utilizations. The degree of congestion for each base station and available access resources would be taken into consideration for the attractor-selection model. Hence, devices are able to dynamically choose the right base station for network access according to the current conditions. The main contributions of this article are summarized as follows:

We present an ASCC mechanism for MTC devices under multiple base stations. By means of choosing the appropriate base stations, massive access attempts would be separated among multiple base stations according to the external conditions. Congestion and overload caused by massive accesses can be alleviated, and the resource efficiency would also be promoted.

We propose an effective estimation method to predict the number of access attempts for base stations. Base stations can learn about the scale of access requirements via the status of radio access resource utilizations. No information exchanges among M2M devices or base stations are needed.

We apply the biology-based attractor-selection model for base station selection⁴¹ due to its self-adaptation to the complex and changeable environments. The network system could adaptively accommodate to external unstable wireless network conditions driven by the system noise. By taking the allocated resources and traffic load of base stations into consideration, congestion and overload of the LTE network would be significantly relieved.

We evaluate the proposed scheme via computer simulations. Both the accuracy of the proposed estimation algorithm and the effectiveness of proposed congestion control scheme are proved with better performance.

The rest of this article is organized as follows. Section “System model” describes the details of system model about the cellular network and RAP. The details about algorithm of ASCC would be introduced in section “ASCC.” In section “Simulation and results,” the proposed estimation method and the results and analyses of the simulation are presented. In the end, section “Conclusion” concludes this article.

System model

In this section, the network model and RAP would be elaborated in detail.

Network model

As shown in Figure 1, the LTE network consists of $N$ number of base stations (or evolved node base station, eNodeB) and $M$ number of MTC devices, respectively. We assume that base stations overlap with each other, enabling mMTC devices covered by multiple base stations. Theoretically, cellular devices can choose any base station for connection establishment and subsequent data transmissions.

Figure 1.

Scenario of MTC devices under multiple base stations.

According to 3GPP specifications, before sending its access attempt to base stations, eNodeB would broadcast the detailed configuration about the RAP, like number of available preamble sequences for contention-based random access and corresponding subframe numbers when devices can send their attempts for network access. Devices can only acquire their transmission opportunities in their authorized available time slots and channels.

If the probabilities of base stations to be selected can be included in the broadcast information, MTC devices can receive them and decide which base station is better to access. Then massive devices can be separately assigned into different base stations, with the congestion status and available resources of each base station taken into consideration. The access resources can be efficiently used and the congestion of the network can also be well mitigated.

RAP

In this subsection, we briefly describe the RAP under the cellular network system. The RACH is mostly initialed by a cellular device before the network connection establishments. There are two categories of RAP as specified in 3GPP standardization: the contention-based RAP and the contention-free RAP. When a device is just turned on or has not obtained or lost the timing synchronization, the contention-based RAP would be needed to establish the network connections. For the contention-free RAP, eNodeBs inform devices of specific configured resource information for network connection establishments, and devices need to stay in $RRC_CONNECTED$ mode. It is often applied for the handover from one base station to another.² As power-constrained M2M devices always stay in sleep mode for energy saving, the connection to eNodeB would always be released after the data transmission. Hence, in this article, we only focus on contention-based RAP, whose details would be introduced in the following as shown in Figure 2, and RAP would mean the contention-based RAP in the following part of this article.

Figure 2.

Contention-based random-access procedure.

First, as shown in Figure 2, devices with network access attempts would randomly choose one preamble sequence from $N_{MTC}$ available ones. $N_{MTC}$ expresses the number of preambles assigned to MTC devices. Afterwards, devices would transmit the selected preamble sequence in Msg1 to the eNodeB. However, when two or more M2M devices simultaneously choose the same preamble sequence, the eNodeB cannot differentiate multiple devices from the same preamble, which would result in access collisions and failures for both or all of the related devices.

Then the eNodeBs would send the random-access response (RAR) message with Msg2 in reply to the received preamble sequence. After receiving the Msg1, the eNodeB would calculate the time spent on the path transmission and include this information in the RAR message. The RAR message conveys at least RA-preamble identifier, timing alignment (TA) information for the time adjustment of next transmission and initial upper limit (UL) grant. If devices cannot receive the RAR message within the RAR time window, the access attempts would be regarded as access failures and retransmitted after a random back-off time period. Meanwhile, devices would increase number of retransmission times by one and promote the transmission power to raise the probability that the preamble is detected by the eNodeB.

Once the Msg2 is received, the device would synchronize its transmission time with the TA information and continue to the next Msg3 stage. If devices cannot receive the RAR messages within the RAR window, they would give up this transmission, perform a random back-off algorithm, and wait for next access opportunity for retransmissions. In the scheduled transmission stage, the radio resouorce control (RRC) connection request message would be sent by devices to the eNodeB with the $C_RNTI$ as an identifier. However, the collided devices also receive the same RAR message and utilize the same UL grant for the RRC connection message transmission. Then multiple transmissions on the same channel simultaneously leads to the collisions with each other and results in the access failures.

Finally, the eNodeB sends resource allocation information during the collision resolution stage. If the eNodeB can decode various RRC connection messages from different devices in previous stage, it broadcasts the identifier (i.e. $C_RNTI$ or the international mobile subscriber identity (IMSI)) as replies. Then the devices would receive the identifier and compare it with its own ID. Only the devices whose IDs are the same as the detected identifiers could complete the RAP. At this moment, the connections would be established ultimately. However, the collided devices have to wait for the next access opportunity for the LTE network system after a random back-off time period. Once the retransmission times exceeded $L_{\max}$ , which denotes the maximum retransmission times, the access attempt would be dropped. The total throughput and access time delay would suffer a huge loss.

The detailed description above is the whole contention-based RAP. Then the connections between M2M devices and eNodeB could be established for subsequent data transmissions.¹⁸ However, the available access resources for MTC devices and traffic load statuses for different base stations may be different from each other.^34,35 Devices randomly choose the base stations for network access, which leads to severer congestion with low resource efficiency. Hence, we need an autonomous and adaptive mechanism for mMTC devices to select proper base stations for congestion alleviations.

ASCC

In order to alleviate the congestion resulted from the mMTC access attempts under dynamic and unstable network conditions, autonomous and adaptive mechanism is urgently needed. In this section, we would introduce the ASM. It originated from autonomous and adaptive behaviors of biological systems which are well known for their robustness and adaptability to various and dynamic environments. The ASM is a mathematical model characterizing the adaptive and robust reactions for Escherichia coli cells in front of the nutrient changes in the outside environments. Via the autonomous and adaptive biology-based mechanism, massive access attempts from MTC devices can be adaptively and robustly distributed to different base stations with the dynamic and unstable environmental conditions taken into account. Consequently, the access congestion and overload can be significantly alleviated, giving guarantees to the QoS requirements of MTC applications and enhancing the utilization efficiency. Here, this biology-originated ASM would be introduced and extended to fit our application scenarios for the congestion control.

Concept of attractor selection

The ASM was proposed in 2006 by Kashiwagi et al.,⁴¹ who present the dynamics of gene expression in E. coli cells in response to outside changing and complex nutrient conditions. It is a metaheuristic optimization method showing what cells should do in order to keep the high cell activity under given nutrient conditions, where some necessary nutrients may decrease or run out.⁴⁰ The attractor in the biology means the gene expression of a cell. Cells would reliably choose the adaptive attractor driven by the gene expression noise with the two mutually inhibitory operons which govern the gene expressions. When one of the necessary nutrients outside becomes scarce, the cell activity would be significantly weakened. Then the mRNA concentration rate would be raised, generating a sequence for synthesis of missing nutrient to make up for the outside nutrient shortages. Cells adaptively accommodate to the external environments by self-regulations. The basic model characterizing the biological reactions of cells to external environments can be expressed as follows⁴¹

\begin{matrix} \frac{d m_{1}}{dt} = \frac{S (A)}{1 + m_{2}^{2}} - D (A) * m_{1} + η_{1} \\ \frac{d m_{2}}{dt} = \frac{S (A)}{1 + m_{1}^{2}} - D (A) * m_{2} + η_{2} \end{matrix}

(1)

where $m_{1}$ and $m_{2}$ are the concentrations of corresponding mRNAs, transcribed from Operon 1 and Operon 2, respectively.⁴¹ Functions $S (A)$ and $D (A)$ separately represent the rate coefficients of synthesis and degradation or dilution. Obviously, $S (A)$ and $D (A)$ is monotonously increasing non-negative functions of cell activity, $A$ . The degree of cellular activity, $A$ , is correlated with the nutrition and growth rate, reflecting the adaptability of a cell to the current outside conditions. The parameter $η_{i} (i \in {1, 2})$ represents the noise in the biological environment, which is the Gaussian white noise.

The attractors of a dynamic system, defined as the above equations shown, has two stable status, where $m_{1} << m_{2}$ or $m_{1} >> m_{2}$ , $(m_{1}, m_{2} \geq 0)$ . Each operon contains a promoter for a specific nutrient and a repressor for another, as well as fluorescence proteins to visualize the concentrations of mRNA.⁴² Assume that there are two kinds of nutrients, $P$ and $Q$ , which can be seen as the gene products of mRNA for growth needs. When the external condition contains both nutrients sufficiently, the cell grows well with high activity. With the nutrient condition changing, for example, lack of nutrient $Q$ , the activity of cells would decrease due to the nutrient shortage. Consequently, the noise would dominate the state $(m_{1}, m_{2})$ instead of gene expression. Driven by the noise, the cell happens to synthesize more nutrient $Q$ , moving toward the appropriate attractor where the cell can compensate for this deficit. Finally, the cell successfully adjusts itself to be accustomed to the external dynamical conditions.

Extended attractor selection for base station selections

In order to apply the original ASM to the higher dimension space for elections among multiple candidate base stations, we introduce the extended attractor-selection model as the following⁴³

\begin{matrix} \frac{d m_{1}}{dt} = \frac{S (A)}{1 + m_{k}^{2} - m_{1}^{2}} - D (A) * m_{1} + η_{1} \\ \frac{d m_{2}}{dt} = \frac{S (A)}{1 + m_{k}^{2} - m_{2}^{2}} - D (A) * m_{2} + η_{2} \\ \dots \dots \dots \dots \\ \frac{d m_{i}}{dt} = \frac{S (A)}{1 + m_{k}^{2} - m_{i}^{2}} - D (A) * m_{i} + η_{i} \\ \dots \dots \dots \dots \\ \frac{d m_{K}}{dt} = \frac{S (A)}{1 + m_{k}^{2} - m_{K}^{2}} - D (A) * m_{K} + η_{K} \end{matrix}

(2)

where $m_{k} = \max {m_{i}, i = 1, 2, 3, \dots, K}$ and $m_{k}$ also satisfies $m_{k} >> m_{i}$ under stable status. The model has $K$ number of candidate base stations to be selected. The term of $m_{k}^{2} - m_{i}^{2}$ , meaning the dissimilarity between states of other candidates and optimal one, can be utilized to represent the inhibitory impact from other candidate networks. Obviously, this can enable the extended model work as same as the original ASM.

In the proposed system model, $m_{i}$ $(m_{i} \geq 0)$ , similar to the concept of the network fitness, represents the dynamic whole system state when choosing the base station $i$ , that is, the access capacity, throughput, and average access delay. It indicates the possibility of selecting the target base station. $A_{i}$ is the activity level of the whole access system, representing the goodness of current base station–selection scheme, and $η_{i}$ is the white Gaussian noise, meaning the outside environmental variations, like the allocated resource changes and fluctuations on the number of access attempts. Just as how cells react to the external environments, the attractor-selection model enables each MTC device to autonomously and adaptively determine its behavior driven by the outside noises. Once the outside environment changes, for example, the allocated preamble sequences reduce, base stations alter their probabilities to be selected to adjust the access allocations for mMTC devices, keeping the high system state value, $m$ . The system can reach the global optimum condition where network congestion and overload can be mitigated with high enhanced resource efficiency.

Through the adaptive and autonomous alternations made by base stations, the whole system state value converge to a stable state. The outside environment changes do affect the access congestion of RAN, that is, the available preambles are kept relatively stable. We can make a hypothesis about the stable state where there are no noises (the noise term, $η_{i} = 0$ , for $i = 1, 2, \dots, K$ ) and no fluctuations $((d m_{i} / dt) = 0)$ . Then the stable equilibrium solution can be derived as below

{\begin{matrix} \frac{d m_{i}}{dt} = 0 \\ η_{i} = 0 \end{matrix} i = 1, 2, \dots, K

(3)

Easily, we can get the solutions as

m_{i} = (\begin{matrix} \frac{- φ (A) - \sqrt{(φ {(A)}^{2} + 4)}}{2} \\ \frac{- φ (A) + \sqrt{φ {(A)}^{2} + 4}}{2} \end{matrix} for i \neq k

(4)

Apparently, the first solution is negative which is not realistic. Hence, we can derive the results of this solution in the following

m_{i} = (\begin{matrix} φ (A) & i = k \\ \frac{\sqrt{φ {(A)}^{2} + 4} - φ (A)}{2} & i \neq k \end{matrix}

(5)

where $φ (A) = (S (A) / D (A))$ for simplicity. We define the coefficient rate, $S (A)$ , as a mathematic polynomial, since the polynomial coefficients can be flexibly and simply tuned for the appropriate $S (A)$ .⁴³ Therefore, the definition of the two coefficient rates can be expressed as follows

{\begin{matrix} S (A) = A \times (α A^{β} + γ) \\ D (A) = A \end{matrix}

(6)

where $α$ and $γ$ are positive real parameters, and $β$ is the positive integer which is not smaller than 2, that is, $β > 2$ . In this article, we applied the setting $α = 5$ , $β = 2$ and $γ = (\sqrt{2} / 2)$ .⁴⁴

As shown in Figure 3, an example with three base station candidates to be chosen is given over 2000 time epochs to elaborate how the extended attractor-selection model works. The parameter setting for this experiment is shown in Table 2 and the access attempts per random-access slot is $48$ , that is, $M = 48$ and $N = 3$ . Assume that there are three base station schemes which are available for MTC devices, that is, Candidate 1, Candidate 2, and Candidate 3. For example, the Candidate 1 means choosing the first base station with higher probability. It can be seen that Candidate 1 is chosen at first and the system-state value keeps high and steady, which demonstrates the goodness of current base station–selection scheme. Simultaneously, the system states of other candidates keeps low with high fluctuations. However, the external environments may go through tremendous changes when $t$ is about $300$ as shown in Figure 3. For example, there are less available access resources or more arrived access attempts. The system state decreases and a new “attractor” solution, Candidate 3, would be searched driven by the outside noise item. Candidate 3 keeps higher and steadier system state than other candidates, which means that choosing Candidate 3 as the target base station could reach a better performance. Hence, in order to keep high system state, Candidate 3 is chosen according to the current conditions. Current base station–selection scheme is better than others. When large changes on the outside conditions happened in about $1900$ , Candidate 2 is chosen as the new attractor which is suitable for the outside environment.

Figure 3.

The state values for different candidates under dynamic conditions.

Derivation of activity

Activity of system-state value, $A (0 \leq A \leq 1)$ , indicates the goodness of current base station–selection scheme. When the current base station–selection scheme is well suitable, the system state steadily stays high at the attractor corresponding to the current base station–selection scheme. In our proposal, the activity $A$ is derived as follows

A = \frac{\sum_{t = 0}^{T - 1} A_{t}^{*}}{T}

(7)

where $A_{0}^{*}$ is the current instant activity, which indicates the instant influence on the whole system state, and $A_{t}^{*}$ is the instant activity at $t$ time intervals ago. $T$ is a constant defining the window of moving average, which is set as $T = 10$ in this article.⁴⁰

The instant activity, $A_{t}^{*}$ , is the goodness of current base station–selection schemes, such as average access delay of devices and throughput. In this article, we employ the traffic load, $p_{s}$ , and allocated access resources, $r$ , as the key condition parameters when choosing the target base stations. The derivation of instant activity can be expressed with the sigmoid function as⁴³

A_{t}^{*} = \frac{1}{1 + \exp (- gh)}

(8)

where $g (g > 0)$ is a gain of sigmoid function and $h$ is the satisfaction of devices when choosing the target base station for network access, indicating the congestion situation. $h$ can be derived as $h = ω_{1} * p_{s} + ω_{2} * r$ , where $ω_{1}$ and $ω_{2}$ are the weight coefficients of the considered traffic load and allocated RACH resources.

The traffic load of target base stations, $p_{s}$ , means the estimated successful access probability for M2M devices. Under RSS, RACH resources for MTC devices would be dynamically allocated in order to minimize the adverse effect on the H2H communications. For simplicity, the allocation of RACH resources is not included in the topic of this article. Allocated RACH resources in RSS, $r$ , can be expressed as the proportion of available preamble sequences assigned to MTC devices. This can be derived as $r = (N_{MTC} / N_{p})$ , where $N_{MTC}$ represents the number of available preambles for MTC devices and $N_{p}$ is on behalf of the total number of preambles in cellular network.

According to preliminary experiments, there is a threshold of activity. When $A > 0.6$ , the base station–selection schemes would stay stable and less congestion would happen. When the activity is smaller than $0.6$ , the system state value decrease and the term of noise would dominate the base station selection. The relationship between satisfaction of devices $h$ and the current instant activity $A_{t}^{*}$ is shown in Figure 4.⁴⁰

Figure 4.

Relationship between the degree of satisfaction and the instant activity.

The activity of whole system status is low when the degree of satisfaction grows from zero. Until $h$ exceeds one certain value, the activity remains low and increasing slowly. However, once $h$ goes beyond that threshold, the instant activity increases exponentially and converge rapidly. Furthermore, when the degree of satisfaction of device is high enough, the activity converges fast. Consequently, device would keep the current choice of target base station even when the degree of satisfaction decreases slightly due to the perturbations of network conditions.

Proposed estimation method of number of access attempts

As the traffic load and available RACH resources are considered for the ASCC scheme, base stations need to learn these two variables in advance. Obviously, the available RACH resources are known, but the traffic load for each base station is unknown. Hence, we propose a feasible and effective estimation mechanism to offer the details about current congestion status in the perspective of RAN. Moreover, the accuracy of this estimation mechanism would also be verified in this part.

In the process of uplink connection establishments, devices randomly select one of available preamble sequences and send it to the target base station in the access slot as described in RAP above. The $n th$ base station can learn about the number of successful devices $M_{s}$ and number of idle preambles $I_{j, n}$ in the $j th$ access slot. Similar to the spirit of Jin et al.,⁴⁵ base stations can estimate the amount of access attempts for the uplink access based on the preamble sequences not transmitted. Let $M_{j, n}$ be the overall number of MTC devices with access attempts in the $j th$ access slot for base station $n$ . Apparently, this can be modeled as a typical “balls and bins” problem.

When $M_{j, n}$ devices contend for preambles for the radio access, the probability of choosing one preamble is $1 / R_{j, n}$ , where $R_{j, n}$ is the available number of preamble sequences in the $j th$ access slot at the $n th$ base station. Since the probability of not selecting one preamble by a device is $(1 - (1 / R_{j, n}))$ , the probability that no devices for the uplink access choose one preamble is $p_{idle} = (1 - (1 / R_{j, n}))^{M_{j, n}}$ . In addition, base stations can also get the measured probability of $p_{idle}$ which is represented as

p_{idle} = \frac{I_{j, n}}{R_{j, n}}

(9)

Hence, via the idle probability of preamble occupations, the estimated number of overall MTC devices for the uplink access in this slot $j$ can be derived as

{\tilde{M}}_{j, n} = \frac{\ln I_{j, n} - \ln R_{j, n}}{\ln (1 - \frac{1}{R_{j, n}})}

(10)

However, this estimation model is of no use when the number of access attempts is large. This is because the constrained number of preamble sequences is not sufficient with respect to the massive access attempts. There would be a situation where all preambles were occupied causing the 10 unable to work. Hence, we propose an improved estimation method for this issue.

When $M_{j, n}$ devices contend for preambles to access the network, the probability that only one device chooses one preamble, $P_{s, j, n}$ can be represented as¹⁸

P_{s, j, n} = \frac{M_{j, n}}{R_{j, n}} * {(1 - \frac{1}{R_{j, n}})}^{M_{j, n} - 1} \approx e^{- \frac{M_{j, n}}{R_{j, n}}}

(11)

The number of access time slots where devices can successfully access the network, which is also the number of success devices, $M_{s, j, n}$ , can be obtained by the mathematic RAP model. Hence, we can get the expression as

M_{s, j, n} = M_{j, n} * e^{- \frac{M_{j, n}}{R_{j, n}}}

(12)

Then we can get the enhanced estimation scheme as

{\tilde{M}}_{j, n} = (\begin{matrix} \frac{\ln I_{j, n} - \ln R_{j, n}}{\ln (1 - \frac{1}{R_{j, n}})}, I_{j, n} > 0 \\ g (M_{s, j, n}), else \end{matrix}

(13)

where $g ({\tilde{M}}_{j, n})$ is the inverse function of equation (12) expressed as follows, deriving the estimated value of overall number of access attempts in the $j th$ access slot for the $n th$ base station. When the number of idle preambles in the $j th$ slot becomes $0$ , the number of access attempts must be larger than the number of available preambles, that is, $M_{j, n} \geq R_{j, n}$ . We can know easily that when $M_{j, n} > R_{j, n}$ , the equation (12) is a monotone decreasing function. Hence, the inverse function of equation (12), ${\tilde{M}}_{j, n} = g (M_{s, j, n})$ , exists as follows

\begin{matrix} {\tilde{M}}_{j, n} = g (M_{s, j, n}) \\ = - R_{j, n} * lambertw (0, - \frac{M_{s, j, n}}{R_{j, n}}) \\ if I_{j, n} = 0 \end{matrix}

(14)

When there are no idle preambles, base stations can obtain the number of access attempts via equation (14). Finally, we can derive the successful access probability indicating the traffic load of the target base stations

p_{s} = \frac{M_{s, j, n}}{{\tilde{M}}_{j, n}}

(15)

Hence, with the proposed estimation method, base stations can learn the traffic load as the process presented in Algorithm 1. As Figure 5 shows, when the real number of access attempts is small, this estimation algorithm matches well. When the access attempts keep increasing, it becomes a little worse, fluctuating slightly around the real values. In short, the proposed estimation algorithm can assess the amount of access attempts with minor deviations. With the traffic load derived, base stations can execute the ASCC scheme with the congestion status and available resources taken into consideration, adaptively and dynamically adjusted to the outside environments. In addition, Table 1 summarizes the variables to be used in this article for clarity.

Algorithm 1: Estimation of access attempts
Initialization: 1: $I_{j, n}$ : number of idle preamble sequences in access slot $j$ for base station $n$ ; 2: ${\tilde{M}}_{j, n}$ : overall number of MTC devices in access slot $j$ for base station $n$ ; 3: $R_{j, n}$ : allocated number of preambles in the $j$ th access slot for the $n$ th base station; 4: $p_{s}$ : the success access probability for devices to complete the network establishment; Algorithm: In the $j$ th access slot, base station $n$ can lean about $I_{j, n}$ 5: for $n = 1 : N$ do 6: if $I_{j, n} > 0$ then 7: Calculate ${\tilde{M}}_{j, n}$ according to 10 8: else 9: Calculate ${\tilde{M}}_{j, n}$ according to 14 10: end if 11: The base station can derive the success probability $p_{s} = \frac{M_{s, j, n}}{{\tilde{M}}_{j, n}}$ 12: return The success probability $p_{s}$ . 13: end for

Algorithm 1: Estimation of access attempts

Initialization:
1:

I_{j, n}

: number of idle preamble sequences in access slot

j

for base station

n

;
2:

{\tilde{M}}_{j, n}

: overall number of MTC devices in access slot

j

for base station

n

;
3:

R_{j, n}

: allocated number of preambles in the

j

th access slot for the

n

th base station;
4:

p_{s}

: the success access probability for devices to complete the network establishment;
Algorithm: In the

j

th access slot, base station

n

can lean about

I_{j, n}

5: for

n = 1 : N

do
6: if

I_{j, n} > 0

then
7: Calculate

{\tilde{M}}_{j, n}

according to 10
8: else
9: Calculate

{\tilde{M}}_{j, n}

according to 14
10: end if
11: The base station can derive the success probability

p_{s} = \frac{M_{s, j, n}}{{\tilde{M}}_{j, n}}

12: return The success probability

p_{s}

.
13: end for

Algorithm 2: Base Station Selection Based on the Extended Attractor-Selection Algorithm
Initialization: 1: $A_{n, j}$ : the network activity when choosing the base station $n$ in the $j$ th access slot; 2: $A_{k}$ : the optimal network activity with the selection of base station $k$ ; 3: $m_{n}$ : the system status when choosing the base station $n$ ; 4: $m_{k}$ : the optimal system status with the selection of base station $k$ ; 5: $p_{n}$ : the probability for choosing the base station $n$ for further transmission; Algorithm: Select a optimal base station $k$ ; 6: if the user has no connections to any base station then 7: for $n = 1$ : $N$ do 8: Calculate $A_{n}$ according to 7 and 8 9: end for 10: The user selects the base station $n$ with $A_{n}$ = $max_{n = 1, 2, \dots, N} {A_{n}}$ 11: else 12: for $ω = 1$ : $N$ do 13: Calculate $A_{n}$ according to 7 and 8 14: Calculate $m_{n}$ according to 5 15: end for 16: $m_{n}$ = arg $max_{n = 1, 2, \dots, N} {m_{n}}$ 17: The user choose the base station $n$ with the probability $p_{n} = \frac{m_{n}}{\sum_{n = 1}^{N} m_{n}}$ 18: end if 19: return The selected station $n$ .

Algorithm 2: Base Station Selection Based on the Extended Attractor-Selection Algorithm

Initialization:
1:

A_{n, j}

: the network activity when choosing the base station

n

in the

j

th access slot;
2:

A_{k}

: the optimal network activity with the selection of base station

k

;
3:

m_{n}

: the system status when choosing the base station

n

;
4:

m_{k}

: the optimal system status with the selection of base station

k

;
5:

p_{n}

: the probability for choosing the base station

n

for further transmission;
Algorithm: Select a optimal base station

k

;
6: if the user has no connections to any base station then
7: for

n = 1

N

do
8: Calculate

A_{n}

according to 7 and 8
9: end for
10: The user selects the base station

n

with

A_{n}

max_{n = 1, 2, \dots, N} {A_{n}}

11: else
12: for

ω = 1

N

do
13: Calculate

A_{n}

according to 7 and 8
14: Calculate

m_{n}

according to 5
15: end for
16:

m_{n}

= arg

max_{n = 1, 2, \dots, N} {m_{n}}

17: The user choose the base station

n

with the probability

p_{n} = \frac{m_{n}}{\sum_{n = 1}^{N} m_{n}}

18: end if
19: return The selected station

n

Figure 5.

Simulation of the estimation method.

Table 1.

Variables used in this article.

Notations	Variables
$N_{MTC}$	Number of preamble sequences for MTC devices
$N$	Number of base stations
$m_{i}$	Concentrations of corresponding mRNAs, the dynamic system state when choosing the base station $i$
$A$	Degree of cellular activity, goodness of current allocation scheme
$η_{i}$	White Gaussian noise, outside environmental fluctuations
$p_{s}$	Successful access probability
$g$	Gain of sigmoid function
$h$	Satisfaction of devices when choosing the target base station
$M_{s}$	Number of successful accessed devices
$M_{j, n}$	Number of devices for the $n th$ base station in slot $j$
$M_{s, j, n}$	Number of successful devices for the $n th$ base station in slot $j$
$\tilde{X}$	Estimated value of $X$
$I_{j, n}$	Number of idle preambles for base station $n$ in slot $j$
$R_{j, n}$	Number of available preambles for base station $n$ in slot $j$
$p_{idle}$	Probability that no devices for the uplink access choose one preamble

MTC: machine-type communication.

Simulation and results

In this section, we would introduce the simulation and analysis of the performances to demonstrate the efficiency and superiority of our proposed ASCC algorithm. We assume that access requests from MTC devices to the network follow Poisson distribution.¹⁸ The system parameters used in the simulation are set based on 3GPP LTE specifications as shown in Table 2. The noise item in the extended ASM is set to follow uniform distribution, that is, $η = rand (0, 1)$ .⁴⁶

Table 2.

Parameters setting.

Parameters	Setting
Number of MTC devices	$0 - 60, 000$
Number of eNodeBs	$3$
Interarrival rate (access requests/second)	$1 / 1000$
Cell bandwidth	$5 MHz$
PRACH configuration	$6$
Preamble format	$1$
Subframe number for access	$3$
Maximum preamble transmission	$10$
RAR window size	$2$
Back-off indicator	$10 ms$

Computer simulations are conducted on top of the MATLAB simulator to verify the effectiveness of the proposed congestion control model. The simulations are developed based on a Monte Carlo approach. We use a computer equipped with Intel Core-5 central processing unit and 8-GB random-access memory. In order to focus on the performance of contention-based RAP, we omit the transmission failure caused by the channel fading and loss. The access failures are all from the collisions of selecting the same preamble sequences. What’s more is that we run the proposed algorithm for the M2M applications for more than 3000 times and get the average values in order to acquire the accurate and reliable results.

We choose the legacy access scheme that devices select the base station with the same probability as the compared scheme in simulations. Massive access attempts from MTC devices are separated equally for different base stations. Moreover, in order to verify the effectiveness of our proposed ASCC scheme, we also run the Q-leaning-based base station–selection scheme as another baseline method for comparisons.³⁸ The proposed ASCC congestion control scheme would be investigated in two perspectives. First, the instant performances with fixed number of access attempts would be simulated in terms of access delay and collision probability. Then the performances under different number of access attempts would be presented to verify the capacity of connecting to mMTC devices.

As shown in the Figure 6(a), we first evaluate the instant performance of the access delay for the proposed congestion control scheme, Q-learning-based scheme and the legacy one. In this scenario, there are $48$ fixed access attempts per random-access slot and $3$ base stations. The access delay is the average time spent by successful devices for connection establishments in the current access slot. Due to the fluctuating external conditions, access delays of devices under three schemes are quite undulant with great fluctuations. However, it can be seen that the access delay of the proposed congestion control scheme always maintains more stable and lower than those of legacy one and Q-learning-based scheme. In contrast, devices with the legacy scheme and Q-learning-based scheme experience larger fluctuations and longer average time delay for network access. Obviously, the Q-learning-based scheme performs better than the legacy scheme, as it takes the delay and throughput of base stations into consideration. Besides, as seen in Figure 6(b), collision probability of the proposed ASCC scheme keeps a significant lower level than the other two schemes. The collision probability of Q-learning-based base station scheme is also lower than the legacy one due to the consideration of the delay and throughput. However, the Q-learning-based scheme requires devices to keep a self-organizing operation style to obtain the necessary information. It only considered the traffic load for base stations, ignoring the available access resources for MTC devices. With the proposed scheme, the traffic load and available access resources would both be considered and utilized for adaptively and robustly choosing optimal base stations for network access. As a result, massive access requirements are suitably assigned to different base stations via the broadcast from base stations. Hence, congestion status can be distinctly alleviated for the whole access system in both the perspectives of access delay and collision probability.

Figure 6.

Simulation results for $M = 48$ and $N = 3$ : (a) access delay and (b) collision probability.

In addition, we evaluate the throughput and average access delay for different numbers of access attempts per second. The throughput here is defined as the number of MTC devices which successfully complete the RACH process per second for the whole system, including all three base stations in this simulation. The average access delay is the delay performance averaged over all devices which execute the RAP. As shown in Figure 7(a), throughput of all three schemes increase when the number of MTC devices increases intially. This is because RACH resources are sufficient when the number of devices is small. The throughput is exactly the number of access attempts and increases with more arrivals. No collisions happened in RAP. For the same reason, the average access delay keeps stable and low at the beginning as shown in Figure 7(b). With more access arriving, collisions would happen during the RAP, and devices need back-off and retransmissions for the completion of connection establishments. The throughput and average access delays would gradually increase as shown in Figure 7. However, when more network requirements arrive, as we can see, the throughput of three schemes begin to decrease. The difference is that the point where they began to decrease is different. The number of access attempts where the throughput begins to reduce is more than the other two schemes. Devices under the legacy access scheme and the Q-learning-based scheme suffer from severe collision due to the improper base station selections. Once the amount of access attempts becomes more, the whole access resources become insufficient with respect to the number of access attempts. Hence, the throughput of three schemes begin to decrease and the average access delays also keep increasing. However, the whole throughput of the proposed ASCC scheme always keeps being higher than the other two schemes and would reach about $35, 000$ per second as shown in Figure 7(a). The average access delay also keeps the lowest level as shown in Figure 7(b). Via the proposed congestion control scheme, devices can adaptively and robustly select the proper base stations driven by external variations. Easily we can derive, the system with proposed ASCC scheme can handle more access attempts from mMTC devices. The ASCC scheme is more suitable to base station selections for the outside environmental changes.

Figure 7.

Simulation results with augment of MTC devices for the proposed mechanism and comparison when $N = 3$ : (a) system throughput and (b) average time delay.

Obviously, the dynamic system reacts adaptively and robustly with the external fluctuating and complex environments. Base stations can derive the accessed probabilities with proposed ASCC mechanism and enable massive access attempts to choose proper base stations, realizing the whole network congestion alleviation. Unlike the Q-learning-based scheme, no information exchanges among devices would be needed, which would cause long delay in the face of massive devices. What’s more is that the proposed ASCC scheme is of low computation complexity, as the access probability calculation load would be derived with explicit equations by base stations. Only during the estimation process when there are no idle preambles, the transcendental equation (16) would be solved by numerical approximations which is negligible with respect to the powerful computation and processing capability of base stations. In summary, the ASCC scheme can enable devices to choose optimal base stations, significantly alleviating the congestion and overload with high resource efficiency. Moreover, it also provides a precious and reliable inspiration for researchers to handle the massive access attempts in 5G network.

Conclusion

Based on the attractor-selection model, this article proposed a solution for signaling congestion and system overload for mMTC access attempts. Simultaneously, an estimation algorithm was proposed for base stations to figure out their traffic load. Then with the traffic load status and available preamble sequences taken into consideration, the ASCC scheme could derive the base station–selection probabilities to be selected without frequent information exchanges among mMTC devices. Then MTC devices would adaptively and robustly select the appropriate base station, and massive access attempts are assigned to different base stations. Hence, the congestion and overload would be significantly mitigated with enhanced resource efficiency. Simulations are also given, which verifies that massive access congestion is significantly alleviated in this proposed scheme. In our future work, we would aim to study the congestion control scheme under bursty traffic.

Footnotes

Handling Editor: James Brusey

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported in part by the National Science and Technology Major Project (2018ZX030110004), in part by the WLAN Achievement Transformation based on the software-defined networks (SDNs) of the Beijing Municipal Commission of Education (201501001), in part by Beijing Municipal Science and Technology Commission (Z171100005217001) and in part by Nation Natural Science Foundation of China (61671073).

ORCID iD

Qi Pan

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