We wrote C programs in Windows 7 to obtain discrete event-driven simu-lation results [6] [7]. Each simusimu-lation instance consists of 100,000 time slots.
We study the case in which the service region is a square and is partitioned intoα = w2 M2M location areas of equal size. LetΛ(i)be the set composed of the indexes of M2M location areas that are adjacent to theith M2M location area. Note that |Λ(i)| ∈ {2, 3, 4}. For a MTC device in a time slot, the mem-ory cost equals the total number of nodes in the parsing tree multiplied by the value of c1. On the other hand, for a MTC device, the total energy cost equals the total number of location updates performed by the MTC device during the simulated time interval multiplied by the value ofc2. For a MTC device in a simulation instance, the total cost is defined to be the sum of the total memory cost and the total energy cost, such like Equation (4.6).
We evaluate the proposed tree pruning algorithm, the LeZi-Update al-gorithm [4], and the naive periodic location update alal-gorithm. When the LeZi-Update is used and it is necessary to prune the parsing tree, except for the root node, all nodes of the parsing tree are deleted. For a MTC device, when the naive periodic location update scheme is used, the memory cost per time slot is zero and the energy cost per location update equals c2, regardless of the mobility pattern. As in many previous works on location update, it is assumed that the wireless channel is characterized byPe, the probability that
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
total cost per MTC device per time slot
10 MTC devices, 16 M2M location areas, γ=20, c1=1, c2=200
Figure 8.1: The total cost of location update schemes, when there are 10 MTC devices
a location update message is not successfully received by the access point/
base station. Unless explicitly stated, Pe = 0 in this chapter.
We use the following DTMC-based mobility model in the C programs.
A MTC device is either static or mobile. The movements of two mobile MTC devices are statistically independent. It is assumed that for each m, {Xk(m)}∞k=0 is a DTMC and X0(m) is an integer-valued random variable that is uniformly distributed in [1, α]. After one time slot, a mobile MTC device either stays in the current M2M location area or moves to one of the adjacent M2M location areas.
To model a variety of mobility patterns, the DTMC-based mobility model has three parameters, ρm, βm, and h. ρm is the probability that the mth mobile device will stay in the current M2M location area after one time slot.
βmis the probability that the mth MTC device moves along a predetermined path/cycle. The function h is used to create the predetermined path/cycle.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
total cost per MTC device per time slot
100 MTC devices, 36 M2M location areas, γ=20, c1=1, c2=200, β=0.95
Periodic location update LeZi−Update Tree Prunning
Figure 8.2: The total cost of location update schemes, when there are 100 MTC devices
In particular, h is a one-to-one mapping from {1, 2, ..., α} to {1, 2, ..., α}such that h(i) ∈ Λ(i), ∀i. In addition, given that the mth mobile device always moves along the predetermined path and it is currently in the ith M2M location area, it will move to theh(i)th M2M location area after one time slot.
For the DTMC {Xk(m)}∞k=0, the corresponding state transition probabilities are set as follows.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
the probability that a MTC device is static
total cost per MTC device per time slot
100 MTC devices, 16 M2M location areas, γ=20, c1=1, c2=200
LeZi−Update Tree Prunning
Figure 8.3: The total cost of location update schemes in heterogeneous net-works
When ρm = 0 and βm = 1, the mobility pattern of the mth MTC device is cyclic. Furthermore, when ρm< 1 and βm= 0,{Xk(m)}∞k=0 corresponds to a symmetric random walk over the graph G.
Letρ,β ∈ [0, 1]be two real numbers. We study homogeneous networks in which (ρm, βm) = (ρ, β), ∀m. In this case, the mobility patterns of all MTC devices are identical. In Figure 8.1, we show the total cost per MTC device per time slot, When M = 10, α = 16, and β∈ {0, 1}. In comparison with the naive periodic location update scheme, the proposed location update scheme could reduce the total cost by at least 32%. When the movement pattern of each MTC device is cyclic, regardless of the value ofρ, the proposed location update scheme outperforms the LeZi-Update algorithm. In particular, the reduction in the total cost ranges from 7% to 28%. When the mobility pattern of each mobile device is cyclic, the proposed location update algorithm could use a small parsing tree to correctly predict the movements of a mobile
5 10 15 20 25 30 35 40 45 50
total cost per MTC device per time slot
10 MTC devices, 16 M2M location areas, c1=1, β=0
c2=200, ρ=0.0
Figure 8.4: The impacts of the maximum number of nodes in a parsing tree device and reduce the frequency of location update. Therefore, in terms of the overall cost, the proposed location update algorithm outperforms the LeZi-Update algorithm. When the movements of each MTC device form a symmetric random walk andρ < 0.6, the proposed location update algorithm is superior to the LeZi-Update algorithm. When the movements of each MTC device form a symmetric random walk and ρ > 0.6, the proposed location update algorithm is slightly inferior to the LeZi-Update algorithm.
In Figure 8.2, we show the total cost per MTC device per time slot, when M = 100, α = 36, and β = 0.95. In this case, regardless of the value of ρ, the proposed location update algorithm outperforms the LeZi-Update algorithm. In comparison with the periodic location update scheme, the proposed location update algorithm could reduce the total cost by at least 50%. In comparison with the LeZi-Update algorithm, the proposed location update algorithm could reduce the total cost by up to 10%.
5 10 15 20 25 30 35 40 102
103
γ
average number of location updates per minute
1000 MTC devices, 16 M2M location areas, c1=1, c2=200, µ=6
LeZi−Update, T=1 minute, Pe=0.0 Tree Prunning, T=1 minute, P
e=0.0 LeZi−Update, T=5 minutes, P
e=0.0 Tree Prunning, T=5 minutes, Pe=0.0 LeZi−Update, T=1 minute, P
e=0.1 Tree Prunning, T=1 minute, P
e=0.1
Figure 8.5: The average number of location updates per minute We also study heterogeneous networks in which there are static MTC devices and mobile MTC devices in the network. In particular, if the mth MTC device is mobile,(ρm, βm) = (0, 1). On the other hand, if themth MTC device is static ρm = 1. In Figure 8.3, we represent the total cost per MTC device per time slots as a function of the probability that a MTC device never moves. When either the proposed location update algorithm or the LeZi-Update algorithm is used, as the fraction of static MTC devices in the network increases, the cost of location update decreases. In comparison with the LeZi-Update algorithm, the proposed location update algorithm could reduce the total cost by up to 27%.
In Figure 8.4, we show the impacts of the maximum number of nodes in the parsing tree on the total cost, when c2 ∈ {200, 10000}and (ρm, βm) = (ρ, 0),∀m. We find that the optimal value of γ depends on the value of ρ and c2. For example, whenc2 = 200, ρ = 0.0, and γ ∈ {5, 10, 20, 30, 40, 50}, the
2 4 6 8 10 12 14 16 18 20 10−1
100
width of a square cell (km)
average number of location updates per minute
real mobility traces, T=1 minute, γ=100, c1=1, c2=200
trace 1, LeZi−Update trace 1, Tree Prunning trace 2, LeZi−Update trace 2, Tree Prunning trace 3, LeZi−Update trace 3, Tree Prunning
Figure 8.6: The impacts of cell size for real mobility traces
total cost is minimized when γ = 30. In contrast, whenc2 = 10000, regardless of the value of ρ, the total cost is a decreasing function of γ. In this case, as the value of γ increases from 40 to 50, the total cost only slightly decreases.
Thus, in practice, γ does not have to be a very large number.
In Figure 8.5, we show the average number of location updates per minute, when there are 1,000 MTC devices in the network and the sensing period is either one minute or five minutes. Let µ be the maximum number of times that a location update message is retransmitted whenever necessary. Re-gardless of the value of (γ, Pe), the proposed location update algorithm out-performs the LeZi-Update algorithm and the naive periodic location update algorithm. When Pe = 0, in comparison with the LeZi-Update algorithm, the proposed location update algorithm could reduce the average number of location updates per time unit by up to 25%.
In Figure 8.6, we show the performance of the location update algorithms, when real mobility traces obtained from [8] are used. For the first mobility traces, in comparison with the naive periodic location update algorithm, the proposed location update algorithm could reduce the average number of location updates per time unit by up to 81%. In comparison with the LeZi-Update algorithm, the proposed location update algorithm could reduce the average number of location updates per time unit by up to 6.39%. For the third mobility trace, in comparison with the LeZi-Update algorithm, the proposed location update algorithm could reduce the average number of location updates per time unit by up to 25.15%.
Chapter 9 Conclusion
In this thesis, we have proposed a novel energy-and-memory efficient loca-tion update scheme for wireless M2M communicaloca-tions. In comparison with periodically registering to the MTC server, it is more efficient for a MTC device to perform location updates only when new nodes are added into the corresponding parsing tree. Based on the theory of random walks over trees, we have proposed optimally pruning the parsing tree to minimize the ex-pected value of the sum of the memory cost and the energy cost for a MTC device. We have found that the proposed scheme could significantly reduce the location update cost.
Future works include jointly optimizing the location update scheme and the paging scheme for wireless M2M communications. Utilizing cloud com-puting technologies for large-scale implementation of the decoding part of the proposed location update algorithm is a promising direction of future research.
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