Abstract
LTE networks consist of tracking areas (TAs) or a group of cells, while several TAs constitute a TA list (TAL). The LTE network adopts TALbased registration, where, if the user equipment (UE) enters a TA that is not in its current TAL, the UE registers the TA to inform the network of its new location. A central policy for TAL allocation, known as a TAbased central policy, was proposed for TALbased registration. Under the central policy, the TA in which the UE registers its location becomes the central TA of the new TAL. This policy can lessen the possibility of the UE quickly exiting the new TAL. However, considering the actual network architecture, it makes TALbased registration a challenge to implement. Thus to mitigate this problem, a cellbased central policy is proposed. This study investigates TALbased registration with cellbased central policy (TbRcc) for LTE networks. TALbased registration with cellbased central policy and singlecell TA (TbRcc1c) is also proposed to reduce the registration cost and make up the optimal TAL. Furthermore, an improved analysis model is presented to reflect the effect of the implicit registration of calls and obtain the exact cost. Comparing the performance of the proposed scheme with those of classical TALbased registration and distancebased registration, the performance of the proposed scheme is shown to improve. The results of this study can help research that addresses the mobility management of nextgeneration networks, as well as LTE networks.
Introduction
In 4G LTE networks, it is necessary to maintain the location of the user equipment (UE), so that incoming calls are connected to the UE. The network keeps track of the location of the UE using a mobility management scheme, which consists of location registration and paging processes. The location registration, also known simply as registration, is a procedure whereby the UE registers its location in the network databases each time it enters a new location. On the other hand, the paging process is a procedure that the network uses to determine the UE’s current cell in the registered location, in order to connect incoming calls to the UE.
The LTE network consists of nonoverlapped tracking areas (TAs), or a group of cells, while several TAs constitute a TA list (TAL). Mobility management entity (MME) is responsible for initiating paging and authenticating the mobile device. Additionally, it retains location information at the TA level for each user and then, during the initial registration process, selects the appropriate gateway [1]. Figure 1 shows that MME connects to the evolved Node Bs (eNBs), whose radio coverage is a cell.
In TALbased registration, the UE registers every time it exits the current TAL to enter a new TAL. If a UE enters a cell that is not in its current TAL, the UE informs MME of its new location, and the MME allocates a new TAL to the UE.
Considering the simple configuration in Fig. 1, if the UE in cell 10 enters cell 13 and the received TA id (TA 4) is not in TAL 1, then the UE registers its new TAL. The MME then allocates TAL 2 to the UE where TAL 2 = {TA 3, TA 4, TA 5}.
Various studies have considered TALbased registration. Chung [2] proposed movementbased TAL forming, based on the assumption that a TA consists of a single cell. Deng et al. [3] proposed to form the TAs as a set of rings, and change adaptively, based on the users’ mobility. Grigoreva et al. [4] proposed the dynamic formation of TALs, based on variable TAL forms, and mobility prediction to reduce signaling. Chen et al. [5] proposed a new green field TA planning model using multiobjective optimization with constraints, which aimed to find a better tradeoff between the two conflicting objectives. In addition, some paging schemes for TALbased mobility management have been proposed [6, 7], and research results on how to apply TALbased registration to not only 4G, but also 5G, have recently been presented [8,9,10]. However, because of their complex procedure, these were difficult to implement. In this situation, it is essential to study how to implement TALbased mobility management to optimize performance on radio channels.
References [6, 7, 11, 12] presented a significant TAL allocation known as central policy. Under this policy, the TA in which the UE registers its location becomes the central TA of the new TAL. This policy can lessen the possibility of the UE quickly exiting the new TAL [6, 7, 11, 12]. This type of central policy is known as a TAbased central policy.
Compared to the traditional static mobility management scheme, such as zonebased registration [13], the TALbased registration can reduce the pingpong effect by adopting the central policy. The performance of the TALbased registration is affected by the allocation of the TAL. Inadequate allocation of TAL may lead to TALbased registration causing side effects. As a result, real implementation of the TALbased registration with TAbased central policy is difficult, since for actual network architecture, gradual increase in the TAL size cannot be guaranteed.
In this study, we consider TALbased registration with central policy. We propose a cellbased central policy to mitigate the problem of the rapid increase in the TAL size in current TAbased central policy. Under the cellbased central policy, the cell in which a UE registers its location becomes the central cell of the new TAL. Under this policy, since the TAL can have any number of TAs, it is possible to implement TALbased registration with cellbased central policy (TbRcc) in actual network architecture. In addition, in this study, we also propose a scheme to further improve the performance of TALbased registration with cellbased central policy and analyze its performance.
The main contributions of this paper are fourfold: (1) The cellbased central policy is proposed to guarantee gradual stepwise increase in the TAL size. (2) TALbased registration with cellbased central policy and singlecell TA (TbRcc1c) is also proposed, in order to reduce the registration cost and make up the optimum TAL. (3) We develop a semiMarkov process model to properly analyze the performance of the proposed scheme. (4) Lastly, comparison of the performance of our scheme with those of classical TALbased registration and distancebased registration shows that the performance of our proposed scheme is better.
The contents of the paper are as follows: Sect. 2 introduces TALbased registration with central policy and proposes TALbased registration with cellbased central policy and singlecell TA (TbRcc1c) to make up the optimal TAL. Section 3 analyzes the signaling cost of the proposed scheme by using semiMarkov process model. Section 4 describes our numerical study to investigate the performance of the proposed scheme. Finally, Sect. 5 concludes the paper.
TALbased registration with cellbased central policy and singlecell TA
First, we introduce TALbased registration with central policy and then propose TALbased registration with cellbased central policy and singlecell TA (TbRcc1c), in order to make up the optimal TAL, and also consider an implicit registration to reduce the total cost of TALbased registration.
TALbased registration and central policy
In TALbased registration, if the UE enters a TA that is not in its TAL, the UE registers its TAL, so as to inform MME of its new location.
Figure 2 shows the 2D hexagonal cell configuration [11, 14] that is considered in this study to analyze its exact performance. A small hexagon represents a cell, and the area marked by bold lines (composed of seven cells) represents a TA. In this 2D hexagonal cell configuration, every cell borders six neighboring cells. Our study also assumes a random walk mobility model [11, 14,15,16]. In this model, the UE enters the six neighboring cells with equal probability (= 1/6).
Considering the TAbased central policy, let N_{C} be the number of cells in a TA and N_{T} be the number of TAs in a TAL.
Figure 2 shows a TAL in a 2D hexagonal cell, where N_{T} = 7. Figure 2b shows that, for example, if a UE exits the current TAL from cell (7, 3), then the UE registers its new TAL, such that its new TA is the central TA of the new TAL. This central policy can avoid the possibility of the UE quickly exiting the TAL.
Figure 2 shows the ring structure of TA that most of the previous studies on TAbased central policy assumed [3, 7, 11, 13]. Under this TAbased central policy, the TAL should have TAs of \(1 + \mathop \sum \nolimits_{i = 1}^{n} 6i\), n = 1, 2, …, in order to set the TA in which a UE registers its location as the central TA of the new TAL. For example, the TAL only has 1, 7, 19, … TAs, and then, the TAL only has 7, 49, 133, … cells. As a result, real implementation of the TALbased registration with TAbased central policy is difficult, since for actual network architecture, gradual increase in the TAL size cannot be guaranteed.
TALbased registration with cellbased central policy
To provide more diverse TAL size, mitigation of the condition of the central TA may be considered. We consider the cell structure of TA in which TA can be composed of any number of cells. For example, in the case of N_{C} = 4, the TAL of N_{T} = 9 can be defined as shown in Fig. 3a, which can be termed TAL with TAbased central policy and fourcell TA. However, even in this case, the most basic TAL of N_{C} = 4 and N_{T} = 1 cannot be defined by the TAbased central policy, since there is no central TA.
Incidentally, in the case of TAL of N_{C} = 4 and N_{T} = 4 as shown in Fig. 3b, even though there is no exact central TA, it seems that cells 1 and 2 approximately correspond to the center of the TAL. Similarly, Fig. 3c shows that in the case of TAL of N_{C} = 4 and N_{T} = 1, even though there is no exact central TA, it seems that cells 1 and 2 approximately correspond to the center of the TAL. If a UE exits cell 2 of the current TAL to enter cell 5, then the UE registers its new TAL such that cells 5 and 2 are the (pseudo) central cells of the new TAL, which can be termed TAL with cellbased central policy and fourcell TA. This is the basic concept of the cellbased (pseudo) central policy. Figure 3b and c shows that cells 1 and 2 are not the exact central cells of the TAL, but are pseudocentral cells of the TAL. However, from now on, we will simply term even this cellbased pseudocentral policy ‘cellbased central policy,’ unless a particular distinction is needed.
In summary, in this study, the cellbased central policy is proposed to mitigate the constraint of the TAbased central policy. Under the cellbased central policy, the cell in which a UE registers its location is the central cell of the new TAL. Figure 4 shows the central cells of the TAL with cellbased central policy for N_{T} = (2 and 4) when N_{C} = 4. Consider, for example, Fig. 4a, in which N_{T} is 2, and N_{C} is 4. In this case, there is no unique central TA, but 2 cells marked as ‘0′ will constitute the central cells of the TAL. Under the cellbased central policy, when a UE exits the current TAL, it registers its new TAL, such that the cell in which it registers is one of the central cells of the new TAL, as shown in Fig. 4a. Similarly, even in the case of TAL of N_{C} = 4 and N_{T} = 4, a UE registers its new TAL such that the cell in which it registers is one of the central cells of the new TAL, as shown in Fig. 4b.
Under this policy, the TAL can have any number of TAs. As a result, it is possible to implement TALbased registration with cellbased central policy for actual network architecture.
Note that TALbased registration with cellbased central policy includes TALbased registration with TAbased central policy. For example, when N_{C} = 7, TALbased registration with TAbased central policy is a special case of TALbased registration with cellbased central policy for N_{T} = 1 + \(\mathop \sum \nolimits_{i = 1}^{n} 6i\), n = 1, 2, …
TALbased registration with cellbased central policy and singlecell TA
Incidentally, what is the optimal N_{C} of TALbased registration with cellbased central policy that offers the minimum total cost? In this section, we suggest that the optimal N_{C} is 1.
For explanation, consider the case of N_{C} = 3, as shown in Fig. 5. Also assume that N_{T} = 3 (the total number of cells in the TAL is 9) shows the minimum total cost. However, in the case of N_{C} = 3, since as the N_{T} increases, the number of cells that make up the entire TAL increases by 3, the actual minimum total cost should be obtained by changing the total number of cells in the TAL from 7 to 11 (natural numbers that are greater than 6, and less than 12).
When the total number of cells in the TAL is either 7 or 11, it would be most appropriate to configure the TAL as N_{C} = 1, N_{T} = 7 or N_{C} = 1, N_{T} = 11, respectively. As a result, we consider that N_{C} = 1, in order to obtain the actual minimum total cost by changing the total number of cells in the TAL from 7 to 11.
Consider Fig. 6 as another example, which shows the possible configurations when N_{C}⋅ N_{T} = 8. Considering the case of N_{C}⋅ N_{T} = 8, there are three possible configurations: (a) N_{C} = 4, N_{T} = 2, (b) N_{C} = 2, N_{T} = 4, and (c) N_{C} = 1, N_{T} = 8.
Figure 6a shows the optimal configuration for N_{C} = 4, N_{T} = 2, and the two shaded cells in the center part are the center cells of this TAL, since they have the same characteristics. Figure 6b shows the optimal configuration for N_{C} = 2, N_{T} = 4, and one shaded cell in the center part is the center cell of this TAL. Finally, Fig. 6c shows the optimal configuration for N_{C} = 1, N_{T} = 8, and the single shaded cell in the center part is the center cell of this TAL. Among them, as shown in Fig. 6c N_{C} = 1, N_{T} = 8 would provide the lowest cost, compared to (a) N_{C} = 4, N_{T} = 2, or (b) N_{C} = 2, N_{T} = 4, since (a), (b), and (c) have (22, 24, and 20) edges, respectively.
Figure 7 shows the total costs for the various TAL structures in Fig. 6, assuming that the calls are generated according to the Poisson processes with the rate λ_{c} = 1, and the staying time in a cell follows a gamma distribution with shape parameter α = 2. It is also assumed that the registration cost for one registration, U, is 10, and the paging cost for the single cell, P, is 1.
Figure 7 shows that the TAL structure (c) N_{C} = 1 has the least cost, compared to any other N_{C}. From the figure, TAL structure (a) N_{C} = 4 has more cost than TAL structure (b) N_{C} = 2, which has more cost than TAL structure (c) N_{C} = 1. Given N_{C}⋅N_{T}, the smaller the N_{C} of a TAL structure, the less the cost. Therefore, the TAL structure adopting N_{C} = 1 has less cost than any other TAL structure adopting N_{C} = (2, 3, 4 and so on) has, since the TAL structure adopting N_{C} = 1 constructs the TAL that has the least registrations.
Therefore, in our study, we assumed N_{C} = 1 to determine the number of cells that make up the optimum TAL. With this assumption, there is no restriction on the number of cells that make up the TAL, and any value is possible.
Figure 8 shows cases of N_{T} = (10 and 14). In Fig. 8a, the upperleft 10 cells constitute TAL of N_{T} = 10 (and N_{C} = 1), in which the two shaded cells in the center part of TAL are center cells. In the figure, there are four kinds of cells: (0, 1, 2, and 3), in which cells with the same number have the same characteristic. If the UE exits the current TAL, then the exited cell and the entered cell (two dotted cells) constitute the center cells of the new TAL, as shown in Fig. 8a. Similarly, in Fig. 8b, the upperleft 14 cells constitute TAL of N_{T} = 14 (and N_{C} = 1), in which the two shaded cells in the center part of the TAL are center cells. In the figure, there are five kinds of cells: (0, 1, 2, 3, and 4), in which cells with the same number have the same characteristic. If the UE exits the current TAL, then the exiting cell and the entered cell (two dotted cells) constitute the center cells of the new TAL, as shown in Fig. 8b.
TALbased registration with implicit registration
Referring to the system requirements [1], if the UE successfully sends a Page Response Message or an Origination Message, the cell can know the UE’s location. This is known as implicit registration (IR) [1, 6, 14]. If a call from or to the UE occurs, the network can identify the UE’s cell by the Page Response Message or the Origination Message, without registration messages. This means that if a network uses a TALbased registration and IR simultaneously, the network can know the UE’s cell without registration process. If IR is adopted, the registration cost of the TALbased registration can be reduced. Therefore, our study considers the TALbased registration with IR, an improved scheme of the original TALbased registration.
Modeling and performance analysis
The following notations are defined to analyze the total cost on radio channels:
C_{P}: Paging cost in one hour.
C_{U}: Location registration cost in one hour.
U: The location registration cost for one registration.
P: The paging cost for one cell.
N_{C}: Number of cells in a TA.
N_{T}: Number of TAs in a TAL.
T_{c}: Interval between two calls (r. v., T_{c} ~ Exp[1/λ_{c}], E(T_{c}) = 1/λ_{c}).
T_{m}: Staying time in a cell (r. v., E(T_{m}) = 1/λ_{m}).
R_{m}: Time between the arrival of the call, and the time when the UE moves out of the cell (r.v.)
\(f_{{\text{m}}}^{*} \left( s \right)\): The Laplace–Stieltjes transform for \(T_{{\text{m}}} \left( { = \mathop \smallint \nolimits_{t = 0}^{\infty } e^{{  {\text{st}}}} f_{{\text{m}}} \left( t \right)dt} \right)\).
We also assume the following to obtain the total cost on radio channels:

When the UE enters a neighboring cell, the probability of selecting one of the neighboring cells is 1/6.

The incoming and outgoing calls are generated with the rates λ_{i} and λ_{o}, respectively, according to the Poisson processes and the staying time in a cell, while T_{m} follows a general distribution with the mean 1/λ_{m}.
Note that by the additional property of the Poisson processes, the incoming calls with the rate λ_{i} and outgoing calls with the rate λ_{o} form total calls with the rate λ_{c} (= λ_{i} + λ_{o}) [17].
SemiMarkov process model
An analytical model for the proposed scheme is presented using 2D random walk mobility and semiMarkov process model. When the values of N_{T} and N_{C} are given, it is also possible to draw the state–transition diagram, and calculate the total cost on radio channels. This paper does not present simulation results, since the mathematical model proposed in this study is so clear that it is not necessary to verify it again by simulation.
An embedded Markov chain model is considered to consider the general cellstaying time and the IR effect of the calls. Assuming N_{C} = 1, a Markov chain model for the consideration of the registration is explained. In our proposed model, the state i is defined as the state in which the UE resides in the cell i.
For example, in the case N_{C} = 1, N_{T} = 4, only three states are necessary to analyze the registration cost, as shown in Fig. 9a:
State 0: The state that UE is in central cells marked as ‘0.’
State 1: The state that UE is in outer cells marked as ‘1.’
State 0′: The state that a call occurred to/from the UE, and the cell changed to central cell.
Note that state 0′ is related to implicit registration. UE in state 0 can enter state 1 with a probability of 1/3P[T_{c} > T_{m}], move to a neighboring state 0 with a probability of 1/6P[T_{c} > T_{m}], or move to a new TAL (and still be in state 0) with a probability of 1/2P[T_{c} > T_{m}]. When a call is generated, the UE in state 0 can transit to state 0′ (in other words, with probability P[T_{c} < T_{m}]). Similarly, the UE in state 1 can enter state 0 with a probability of 1/3P[T_{c} > T_{m}], or move to a new TAL (and be in state 0) with a probability of 2/3P[T_{c} > T_{m}]. When a call is generated, the UE in state 1 can also transit to state 0′ (in other words, with probability P[T_{c} < T_{m}]).
The UE in state 0′ can enter state 1 with a probability of 1/3P[T_{c} > R_{m}], move to a neighboring state 0 with a probability of 1/6P[T_{c} > R_{m}], or move to a new TAL (and to be in state 0) with a probability of 1/2P[T_{c} > R_{m}]. Finally, when a call is generated, the UE in state 0′ can transit to state 0′ (in other words, with a probability of P[T_{c} < R_{m}]).
Figure 9b and c shows that a Markov chain model for other cases can be similarly obtained:
The probability that a UE enters other cells before a call occurs can be calculated as follows [14]:
Now, let us derive m′ = P[T_{c} > R_{m}], which is the probability of a UE, whose state is changed due to the call occurrence, moving to the neighboring cell before another call from/to the UE occurs.
The density function of Rm, f_{r}(t) is from the random observer property [17],
The Laplace–Stieltjes transform for the distribution is as follows:
This gives:
The UE’s staying time in a cell, T_{m}, affects the transition probability. If T_{m} follows a gamma distribution, the mean is 1/λ_{m} and the variance is V. Then, P[T_{c} > T_{m}] is:
In this case, the staying time in state 0′ is different from the staying time in other states. The staying time in state 0′ is the interval from the time a call to/from a UE occurs in a cell, until the time it transits (moves to a neighboring cell, or generates a call again). On the other hand, the staying time in other states, except state 0′, is the interval from the time the UE enters a cell, until the time it transits (moves to a neighboring cell, or generates a call).
It needs to be considered that to evaluate the accurate performance, the staying time in each state is different. First, the staying time in state 0′ can be expressed as:
\(R_{{\text{m}}} , \,{\text{if}} \;T_{{\text{c}}} > R_{{\text{m}}}\).
Its mean can be obtained as follows:
Next, the staying time in other states, except state 0′, can be expressed as:
Its mean τ_{i} (i = 0, 1, 2, …) can be derived as follows:
In order to obtain the steadystate probability \(\tilde{\pi }\), first calculate the steadystate probability π for the usual Markov chain with transition probability P by using the balanced equations, as follows [17]:
Then, considering the different staying time, the final steadystate probability of the semiMarkov process can be obtained as follows [17]:
Total cost on radio channels
The registration and the paging costs constitute the total cost on radio channels.
The registration cost per hour, C_{u}, can be given as follows:
where B is the set of states for the boundary cells in a TAL, and \(p_{{\text{U}}} \left( j \right)\) is the probability that a UE in state j enters a neighboring cell to perform location registration. For example, in Fig. 9a, \(C_{{\text{U}}} = U\lambda_{{\text{m}}} \sum\nolimits_{{{\text{j}} \in {\text{B}}}} {\tilde{\pi }_{{\text{j}}} \cdot p_{{\text{U}}} \left( j \right) = U\lambda_{{\text{m}}} \left[ {\left( \frac{1}{2} \right)\left( {\tilde{\pi }_{0} + \tilde{\pi }_{0^{\prime}} } \right) + \left( \frac{2}{3} \right)\tilde{\pi }_{1} } \right]}\), since B = {0, 1, 0′}, \(p_{{\text{U}}} \left( 0 \right)\) = \(p_{{\text{U}}} \left( {0^{\prime}} \right)\) = 1/2, and \(p_{{\text{U}}} \left( 1 \right)\) = 2/3.
Assuming the mobile network adopts simultaneous paging [14, 15] the paging cost per hour is as follows:
Finally, the total cost on radio channels may be obtained, as follows:
Numerical results
To obtain the numerical results for TALbased registration with cellbased central policy and singlecell TA, the following assumptions are made [14, 15, 18]:
U = 10, P = 1, λ_{m} = 5, λ_{c} = λ_{i} + λ_{o} = 1 + 1 = 2.
Both incoming call and outgoing call are generated according to the Poisson processes with the rates λ_{i} and λ_{o}, respectively. The staying time in a cell follows a gamma distribution with mean 1/λ_{m}.
Performance of TALbased registration with cellbased central policy and singlecell TA
Figure 10 shows the total costs for various numbers of TAs in a TAL. Generally, as the number of TAs in a TAL increases, the registration cost decreases due to the infrequency of the registrations; however, because of the large paging area, the paging cost increases. Finally, in this case, the optimal number of TAs in a TAL that minimizes the total cost is 7:
The optimal number of TAs in a TAL that results in the minimal total cost can be obtained for any other situation. Figure 11 shows the total costs and the optimal number of TAs in a TAL for various E(T_{m}). Generally, the lower the E(T_{m}), the greater the total cost. This is because of the increase in the location registrations. As a result, as E(T_{m}) decreases, the optimal number of TAs in a TAL increases, since the location area (TAL) must be large to reduce location registrations.
Figure 12 shows the total costs and the optimal number of TAs in a TAL for various calltomobility (CMR) ratios. CMR is defined as λ_{c}/λ_{m}, i.e., the higher the CMR, the more the call generation compared to cell entrance. Consequently, the higher the CMR, the greater the paging cost due to increase in paging. Therefore, as CMR increases, the optimal number of TAs in a TAL decreases, since the location area (TAL) must be small to reduce paging cost. In the examples, the optimal number of TAs in a TAL is 7, which when CMR = 1, minimizes the total cost. On the other hand, when CMR = 1.15, the optimal number of TAs in a TAL is 5; and when CMR = 1.35, the optimal number of TAs in a TAL is 4:
Through many numerical results for various circumstances, the proposed TALbased registration with cellbased central policy yields better performance than the TALbased registration with TAbased central policy in every case.
Effect of implicit registration
Figure 13 shows the effect of implicit registration in total costs. In general, if implicit registration is implemented, the registration cost decreases. Figure 13 shows that when CMR = 1 and implicit registration is not implemented, the optimal number of TAs in a TAL would be 5, and the total cost is 9.106. On the other hand, if implicit registration is implemented, the optimal number of TAs in a TAL would be 7, and the total cost is 6.023. In this case, because of the effect of implicit registration, total cost decreases by 33.9%.
Comparison with distancebased registration
Figure 14 shows the total costs of various numbers of TAs in a TAL for singlecell TA (N_{C} = 1), compared to distancebased registration (DBR) that shows good performance [14, 15, 18]. Note that DBR is a special case of TALbased registration with singlecell TA. In these circumstances, TALbased registration with singlecell TA reached a minimum value of 8.536 at 5 TAs, while DBR had a minimum value of 8.779 at 7 TAs (i.e., distance threshold = 2). In Fig. 14, it is evident that TALbased registration with singlecell TA is superior to DBR in every case.
Conclusion
This study investigated TALbased registration with central policy for LTE networks. This policy can lessen the possibility of the UE quickly exiting the new TAL. However, considering the actual network architecture, it makes TALbased registration a challenge to implement. Thus, a cellbased central policy was proposed to mitigate this challenge. TALbased registration with cellbased central policy and singlecell TA (TbRcc1c) was also proposed to reduce the registration cost and make up the optimal TAL.
Furthermore, an improved analytical model for the proposed scheme was proposed that uses 2D random walk mobility and semiMarkov process model to consider the effect of implicit registration of calls and obtain exact cost. Finally, comparison of the performance of TbRcc1c with those of the classical TALbased registration and distancebased registration shows that the performance of the proposed scheme is improved.
Finally, the TALbased registration with cellbased central policy is shown to be superior to TALbased registration with TAbased central policy in every case, and that TALbased registration with singlecell TA is superior to distancebased registration (DBR), which is known to show good performance.
Under the proposed policy, the TAL can have any number of TAs; as a result, it is possible to easily implement the proposed TbRcc1c in any real network architecture. The results of this study can be used in research on the mobility management of nextgeneration networks [8,9,10], as well as LTE networks. In further study, the 5Grelated matters will be investigated to implement the proposed method in 5G network.
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Acknowledgements
This research was supported by Research Base Construction Fund Support Program funded by Jeonbuk National University in 2020. This research was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2016R1D1A1B01014615), and by the Ministry of Science, ICT and Future Planning (2017R1E1A1A03070134).
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Jang, HS., Baek, J.H. Optimal TALbased registration with cellbased central policy in mobile cellular networks: a semiMarkov process approach. J Supercomput (2021). https://doi.org/10.1007/s11227021036248
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Keywords
 2D random walk model
 Mobility management
 Location registration
 TALbased registration
 Central policy
 SemiMarkov process