Estimation Based Adaptive ACB Scheme for M2M Communications Hongliang He, Pinyi Ren, Qinghe Du, and Li Sun School of Electronic and Information Engineering, Xi’an Jiaotong University, China
[email protected] {pyren,duqinghe,lisun}@mail.xjtu.edu.cn
Abstract. It is a critical challenge to support massive access of devices in a short period in machine-to-machine (M2M) communications. In this paper, we propose a estimation based adaptive Access Class Barring (ACB) scheme to improve the scalability of M2M networks. First, we propose a simple estimation scheme to estimate the network loads. Then we obtain two functions which are the relationship of ACB’s barring factor (the parameter of access probability) and network loads to maximize the system throughput. According to the estimation and the obtained functions, eNB changes ACB barring factor dynamically to adapt to the network load conditions. At the same time, we summarize the boundedness of the adaptive scheme. Finally, simulation results illustrate that our scheme can increase the system throughput and reduce access delay obviously. Keywords: M2M · Adaptive ACB · Throughput · Delay
1
Introduction
The Internet of Things (IoT) is expected to provide ubiquitous connectivity among machines and it recognized as a revolution in our daily life [1]. Machineto-machine communication, also called machine-type communication (MTC) in the Third Generation Partnership (3GPP) standards, is one of the most important applications of IoT [2, 6]. For M2M communication, generally a large number of devices need to transmit small data and they will access the physical random access channel (PRACH) randomly [7], it is a difficult task to enable M2M communications when a huge number of devices access the network simultaneously for it will results in heavy congestion and delay [8], which is different from the traditional human-to-human (H2H) communications and other communications [3, 4]. The M2M overload problem is considered as a foremost problem. One of solutions is the scheduling which eNB can allocate the resources, such as preambles, to the specified devices. But it involves a large signaling overhead [5]. Other solutions are random access oriented. In 3GPP [9], a network coordinated random access scheme called as the Access Class Barring (ACB) is adopted. However,
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Estimation Based Adaptive ACB Scheme
p
p p MTC User
MTC User MTC User
Active device
Idle device
Fig. 1. Random access scenario
ACB cannot adjust the access probability (one of parameters of ACB) adaptively in each slot. According to the delay characteristic of different M2M devices, Extended Access Barring (EAB) is proposed to enhance the ACB scheme. In [14], authors proposed a cooperative ACB scheme to balance the traffic of different cells. In [10], a fast adaptive slotted ALOHA scheme is studied. In [11], the authors studied the group based massive access management. In [12], an adaptive medium access control mechanism for cellular based machine-to-machine (M2M) communication is proposed. Similarly, dynamic Access Class Barring for M2M communications in LTE networks is considered in [13]. One of the reasons that M2M networks occur congestion is the eNB (the base station of LTE) cannot know the network traffic exactly. In this paper, first, we propose a simple estimation scheme to estimate the network loads. Then we get two dynamic adjustment functions, which are the relationship of ACB’s access probability and network loads, to maximize the system throughput. Simulation results illustrate that two functions can achieve the same performance and it shows that our scheme significantly outperforms the traditional ACB scheme in terms of not only throughput but also average delay. Finally, we summarize the boundedness of the adaptive ACB scheme. The remainder of the paper is organized as follow. In Section 2, we present the system model. Section 3 describes the estimation scheme. In section 4, we analysis the metrics of adaptive ACB scheme. In section 5, simulation results are presented to evaluate the performance of the proposed scheme. The paper is concluded in Section 6.
2
System Model
Consider a random access M2M communication scenario, which is shown in Fig. 1. One eNB and a great quantity of M2M devices in the cell. We assume the M2M devices are uniformly distributed. There are two status to every M2M device, idle or active.
Estimation Based Adaptive ACB Scheme for M2M Communications
2.1
3
Access Class Barring
In each slot i (i = 0, 1, 2, . . . , L), the eNB broadcasts an ACB barring factor p (0 ≤ p ≤ 1), the M2M device which is activated generates a random number q (0 ≤ q ≤ 1). If q is less than p, the active device pass through the ACB check, and it will apply for the preamble. Otherwise, the device will be barred for a period of random time [15] Tbarring = (θ + α × rand) × T,
(1)
and it need to repeat the ACB check in next slot, where rand is a random number uniformly range from interval [0, 1), T is another parameter of ACB scheme (it is a constant in this paper), θ = 0.7, α = 0.6. 2.2
Random access procedure
The contention-based random access (RA) procedure is consisted by a fourmessage handshake [2]. After an active M2M device passed the ACB check, it randomly selects a preamble to transmit an access requests in message-1. Then the eNB transmits a Random Access Response (RAR) in message-2. In message3, when the M2M device receives a response to the selected preamble, if more than one devices select the same preamble in the same RA slot, a collision will occur and the collision devices will retransmit in the next slot. In message-4, based on the reception of a Connection Request, the eNB transmits a Connection Resolution message as an answer to message-3. Noticing that in this process the eNB can obtain the number of preamble collisions and successes, but it does not know how many devices ask for the preambles. So it does not know the situation of congestion. 2.3
The device activation model
In proposal [16], we know the model that the devices arrive in a period of time denoted as Ts with probability g(t) and follow a beta distribution with parameters x = 3, y = 4 tx−1 (Ts − t)y−1 , (2) g(t) = x+y−1 B(x, y) Ts where B(x, y) is the beta function. Define Ai is the number of device arrivals (i.e. network loads) in slot i, it is the sum of three-type devices: the number of active devices in slot i, it obeys beta distribution as described in formula (2); the number of devices collided in last slot i − 1, which will re-access the network in slot i; the number of devices did not pass the ACB check in some previous slots, which need to re-access the network in slot i. The number of devices which apply for the preambles as Bi and it is by Ai after ACB check. In each slot, the available preambles are K. Denote G as the preambles that only one device to apply and it is equal to the number of preamble successes; C as the preambles that two or more than two devices to apply and it is equal to the number of preamble collisions; I as the preambles that no devices to apply and it is equal to the number of idle preambles.
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Estimation Based Adaptive ACB Scheme
3
The estimation of network loads
In this section, we propose a simple scheme to estimate the number of devices which apply for the preambles in current slot (i.e. B, without loss of generality, we omit the subscript i). Then according to the barring factor, we can estimate the number of device arrivals A (i.e. the network loads of current slot), because of A and B have the following relationship B = Ap.
(3)
According to A, the eNB can change the ACB barring factor dynamically and it will be described in next section. If B devices request to K preambles with equal probability 1/K. The probability that one preamble is selected by exactly one device is B−1 B 1 1 , Ps = 1− 1 K K
(4)
where K is the number of preambles in one slot, Ps is the probability of one preamble success. So we can get the distribution of the number of preamble successes G as K P (G = g) = (Ps )g (1 − Ps )K−g . (5) g This is a binomial distribution, so the expectation is B−1 ¯ = E(G) = KPs = B 1 − 1 G . K
(6)
The probability that one preamble is selected by none of devices is 1 B Pnone = 1 − . K So we can get the distribution of the number of idle preambles I as K P (I = e) = (Pnone )e (1 − Pnone )K−e . e
(7)
(8)
This is also a binomial distribution, so the expectation is
So we can know that
1 B I¯ = E(I) = KPnone = K 1 − . K
(9)
I¯ K −1 ¯ = B , G
(10)
and B=
¯ (K − 1)G . ¯ I
(11)
Estimation Based Adaptive ACB Scheme for M2M Communications
5
From section 2 we have known that eNB can obtain the number of preamble collisions and successes, so we can estimate B as ˆ = (K − 1)G . B I
(12)
Then
ˆ B Aˆ = . (13) p where p is the ACB barring factor. Estimate the traffic load is to adjust the network parameters (e.g p) dynamically and the next work in our paper is to find the optimal adaptive function.
4 4.1
Parameters Analysis Analysis of the adaptive ACB scheme
There are Ai devices arrive in slot i, so we can get the probability a i Pr Bi = bi Ai = ai = pbi (1 − pi )ai −bi . bi i
(14)
where pi is the ACB barring factor in slot i. We only consider that Ai ≥ 1, and the expectation of Bi is EBi Bi Ai = Ai · pi . (15) From the law of total expectation, we can obtain that ! EBi (Bi ) = EAi EBi Bi Ai = EAi (Ai · pi ).
(16)
Devices which arrive in slot i, select all K preambles with equal probability pi /K. So the probability that one preamble is selected by exactly one device as pi ai −1 ai pi . (17) 1− Pone = K 1 K Ai =ai So if there are Gi preambles to succeed, the probability of Gi is K Pr Gi = gi Ai = ai = P gi (1 − Pone )K−gi . gi one Obviously, this is a binomial distribution, the conditional expectation is EGi Gi Ai = K · Pone a =A . i
i
According to the law of total expectation, ! ! pi Ai −1 . EGi (Gi ) = EAi EGi Gi Ai = EAi Ai · pi 1 − K
(18)
(19)
(20)
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Estimation Based Adaptive ACB Scheme
We know that the number of device successes are equal to the number of preamble successes, so the number of device collisions can be described as Fi = Bi −Gi , ! pi Ai −1 EFi (Fi ) = EBi (Bi ) − EGi (Gi ) = EAi Ai · pi 1 − 1 − . (21) K
4.2
Analysis of Metrics
In this paper, we consider the following two performance metrics: – Throughput ratio: Throughput is defined as the expected number of M2M devices which access the network successfully in a period of time Ts , which is equal to the total number of preamble successes. In this paper, we prefer to consider the ratio of throughput and the total number of active devices in Ts , and we call it throughput ratio or access success probability. – Average access delay: The delay of one device is the time from device sending the request to preamble until access to the M2M network successfully. So the average access delay can be defined as the ratio that the sum of each active device’s delay to the total number of active devices in time Ts . Equation (20) shows the number of device successes in each slot, so the throughput ratio can be formulated as L
λ = Psuc =
1X EG (Gi ), N i=1 i
(22)
L is the total number of slots, N is total number of active devices in Ts . In adaptive ACB scheme, the delay is caused by two reasons, the ACB barring and the collision. From formula (21), we obtain the collision devices’ number in slot i as EFi (Fi ) = EBi (Bi ) − EGi (Gi ) which will repeat the ACB check in slot i + 1, so the delay caused by collision in slot i can be denoted as τ1,i = EBi (Bi ) − EGi (Gi ) l, (23) l is the length of each slot. So the total delay caused by collision is τ1 =
∞ ∞ X X τ1,i = EBi (Bi ) − EGi (Gi ) l. i=1
(24)
i=1
From formula (1), we know that devices locate in slot i can only go to the slot [i + θT /l, i + (α + θ)T /l) after ACB check (rand = 0, rand = 1 respectively). The average number of devices from slot i go to the slot [i + θT /l, i + (α + θ)T /l) is EAi (Ai ) − EBi (Bi ) (the number that devices pass through ACB are Bi , so the number that devices do not pass through are Ai − Bi ), devices that uniformly
Estimation Based Adaptive ACB Scheme for M2M Communications
7
drop in each slot in [i + θT /l, i + (α + θ)T /l) are (l/αT ) EAi (Ai ) − EBi (Bi ) . so the delay brought by ACB check in slot i is i+(α+θ)T /l
τ2,i =
X v=i+θT /l
l EAv (Av ) − EBv (Bv ) (v − i)l. αT
(25)
Then the total delay brought by ACB check is ∞ ∞ i+(α+θ)T X X X /l l τ2 = τ2,i = EAv (Av ) − EBv (Bv ) (v − i)l. αT i=1 i=1
(26)
v=i+θT /l
so we can obtain the average delay as τ = (τ1 + τ2 )/N . 4.3
The proposed adaptive scheme
From formulas (20) and (22), we know that the throughput ratio is related with Ai and pi . We hope that if eNB broadcasts a constant pi , the loads Ai in the network is optimal or if eNB knows the network loads Ai it can broadcast a optimal barring factor pi . We should notice that if the throughput in each slot is maximum, the system throughput will be maximized. So we can consider the maximal throughput from two aspects. First, taking the derivative of λ with respect to Ai , pi pi Ai −1 ∂λ 1 + Ai · log 1 − , = pi 1 − ∂Ai K K
(27)
the base of logarithm is e. It can prove that when Ai ≤ −1/log(1 − pi /K), ∂λ/∂Ai ≥ 0, so Ai is the bigger the better and the maximum Ai is K when pi = 1 under this condition. When Ai > K, the maximum of throughput ratio is got when ∂λ/∂Ai = 0 and we can obtain that Ai =
−1 , (1 − pKi )
and pi = K(1 − e
− A1
(28)
).
(29)
1 Ai < K pi Ai ≥ K.
(30)
i
So the control function is ?
pi1 =
and we call it method 1. Second, taking the derivative of λ with respect to pi , we can get that pi Ai −1 pi pi −1 ∂λ 1 − (Ai − 1) 1 − . (31) = Ai 1 − ∂pi K K K
8
Estimation Based Adaptive ACB Scheme
1
traditional ACB method 1 method 2
Throughput ratio
0.98
0.96
0.94
0.92
0.9
0.88 0.5
1
1.5
2
Total number of active devices
2.5
3 4
x 10
Fig. 2. The comparison of throughput ratio
It can prove that when Ai < K, ∂λ/∂Ai ≥ 0, and the optimal pi is 1. When Ai > K, the maximum of throughput ratio is got when ∂λ/∂pi = 0 and we can obtain that K pi = . (32) Ai So the control function is ?
pi2 =
1 Ai < K pi Ai ≥ K.
(33)
and we call it method 2. Intuitively, if Ai and pi exist strong corresponding relationship, the two different methods will bring similar effect. In fact, it can be proved that when 0 ≤ pi ≤ 1, the two optimal functions is almost the same, and our simulation results also show it.
4.4
The boundedness of the adaptive ACB scheme
First, it is hard to change the network parameters in current slot, so the eNB can just change the parameters in next slot. It brings some errors. Second, the estimation will brings errors too. These two type of errors will affect the performance of the adaptive scheme. Third, from the formula (30) and (33), we can find that the dynamic scheme can only adjust the traffic when Ai > K, when Ai < K it can not help and the access depends on the random access. It maybe brings the waste of preambles, and it can be further improved, which is our future work.
Estimation Based Adaptive ACB Scheme for M2M Communications
9
1.8 1.6 1.4
traditional ACB method 1 method 2
Delay(s)
1.2 1 0.8 0.6 0.4 0.2 0 0.5
1
1.5
2
2.5
Total number of active devices
3 4
x 10
Fig. 3. The comparison of delay
5
Simulation Results
To evaluate the performance of the proposed scheme, we adopt simulation parameters in [16]. Consider a Ts = 10 seconds randomization period and the RACH be configured to occur every 5 ms (PRACH configuration index is 6, a slot is 5 ms), there are 54 preambles in each slot. This means there are 200 RACH opportunities per second and a total of 10800 preambles per second. N range from 5000 to 30000. The mitigation of congestion can be measured by two main metrics, the system throughput and the access delay, we analysis the metrics by simulation and they are showed as follow. In order to compare, we set the traditional ACB’s barring factor as 0.8 and the barring is 4, it can be proved by simulation which can obtain the best throughput. From Fig. 2, we can know that the throughput ratio of two optimal adaptive functions are almost the same and they are higher than the traditional ACB obviously. From Fig. 3, we can observe that the delay improvement achieved by two optimal functions as compared to the traditional ACB. In addition, the delay also illustrate two optimal adaptive functions have the same performance. It shows that the system throughput and the access delay improved obviously by using the adaptive ACB scheme, which benefits from the combine of estimation scheme and the optimal adaptive functions. Simulation results illustrate the proposed scheme can really alleviate the congestion of M2M network.
6
Conclusion
The ability of traditional ACB to alleviate the congestion problem of M2M network is limited. In this paper, we propose an estimation based adaptive ACB
10
Estimation Based Adaptive ACB Scheme
scheme to solve the problem. Combining the simple estimation of the network loads and the adaptive barring factor method, our scheme improves the system throughput and decreases the access delay significantly.
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