# Mobility Management Scheme with Mobility Prediction in Wireless Communication Networks

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## Abstract

**:**

## 1. Introduction

## 2. Registration Scheme with Flexible TAL Forming

- (1)
- The UE predicts the movement direction based on the accumulated past data “every time the UE performs location registration (or leaves the current location area)” and configures the location area accordingly, (The UE moves to the center cell(s) of new location area with probability q).
- (2)
- When moving between cells in the location area, it moves according to the random walk model (that is, the probability of selecting one of the 6 surrounding cells is the same).

## 3. Modeling and Performance Analysis

_{U}: The location registration cost in an hour

_{P}: The paging cost in an hour

_{c}: The interarrival time between two calls (r.v., T

_{c}~ Exp[λ

_{c}], E(T

_{c}) = 1/λ

_{c})

_{m}: The time spent in a cell (r.v., E(T

_{m}) = 1/λ

_{m})

_{m}(=${\int}_{t=0}^{\infty}{\mathit{e}}^{-st}{f}_{m}\left(t\right)dt$)

_{m}: The remaing time from the call occurrence to the time the UE moves out of the cell (r.v.)

_{in}and outgoing calls with mean 1/λ

_{out}from total calls with mean 1/λ

_{c}= 1/(λ

_{in}+ λ

_{out}).

- ○
- State S
_{1}: The state that UE is in the initial cell, where the user requires registration and forms new TAL. In an urban case, due to random walk assumption, the state S_{1}changes to S_{3}after the user moves to the center cell (cell 3). For the rural case, if the user moves to cell 2 or cell 3, the S_{1}changes to S_{4}. On the other hand, when the user moves into outer cells which are not included in the same TAL, the state S_{1}does not change and another registration is requested. - ○
- State S
_{2}: The state that UE is in central cells (cell 3 in urban area, and cell 2 or 3 in rural area) depicted as S_{2}. - ○
- State S
_{3}: The state that UE is in outer cells. - ○
- State S
_{4}: The state that UE is in two outer cells (cell 1 or 5) in the rural environment. - ○
- State S
_{5}: The state that UE is bottom and top cells (cell 7 or 9) in the rural case. - ○
- State S
_{0}: The state that a call occurs to/from the UE and the cell is changed to central cell. Note that state S_{0}is related to implicit registration [4,7,25]. That is, when an incoming or outgoing call to/from the UE occurs, the UE’s location can be updated without additional registration cost.

#### 3.1. Urban Environment

_{1}) can enter cell 3 (state S

_{2}) with a probability of qm or enter any one of the remaining 5 cells with a probability of (1 − q)m/5. If it enters one of 3 neighboring cells that are not in the current TAL, it will register its location (state S

_{1}).

_{1}) enters a neighboring cell (state S

_{2}or state S

_{3}), the state of the UE becomes state S

_{0}. Such a state transition occurs with a probability of 1 − m = P[T

_{c}≤ T

_{m}]. Note that, in this case, cell is not changed. However, a new TAL is set up (by implicit registration) and the cell becomes cell 1 in Figure 1.

_{c}> R

_{m}].

_{c}> R

_{m}], let us consider R

_{m}. The density function of R

_{m}, f

_{r}(t) is from a random observer property [20,21]:

**P**

_{urban}as follows:

#### 3.2. Rural Environment

_{1}) can enter cell 2 or cell 3 (state S

_{2}) with a probability of qm or enter any one of the remaining four cells with a probability of (1 − q)m/4. If it enters one of the two neighboring cells that are not in the current TAL, it will register its location (state S

_{1}).

_{1}) enters a neighboring cell (state S

_{2}or state S

_{3}), the state of the UE becomes state S

_{0}. Such a state transition occurs with a probability of 1 − m = P[T

_{c}≤ T

_{m}]. Note that in this case, cell is not changed. However, a new TAL is set up (by implicit registration) and the cell becomes cell 1 in Figure 1.

**P**

_{rural}for a rural environment as follows:

#### 3.3. Semi-Markov Process Model

_{0}is different from the time spent in other states. The time spent in state S

_{0}is the interval from the call occurrence to/from a UE in a cell to the time it moves to a neighboring cell or when a call occurs again. On the other hand, the time spent in other states except for state S

_{0}is the interval from the time the UE enters a cell to the time it moves to a neighboring cell or when a call occurs.

_{0}can be expressed as follows:

_{0}can be expressed as follows:

_{i}(i = 1, 2, …, 5) can be obtained as follows:

**P**(

**P**

_{urban}or

**P**

_{rural}) using the following balanced equations:

## 4. Simulation

- (i)
- Every UE turns on the power in cell number 1.
- (ii)
- The call arrival time (incoming or outgoing) to the UE follows an exponential distribution with a mean of 1/λ
_{c}(T_{c}~ Exp[λ_{c}]). - (iii)
- The time spent in a cell follows a gamma distribution with a mean of 1/λ
_{m}[25] (T_{m}~ Gamma(α, β), E(T_{m}) = αβ = 1/λ_{m}). - (iv)
- If the call occurrence time is less than the time spent in a cell, the UE does not require registration as the system knows the UE’s location without any additional registration cost.
- (v)
- Otherwise, when the call arrival time is greater than or equal to the time in a cell, the UE moves to the direction with a probability of q. Note that the moving direction is randomly chosen among six directions. The number of registrations can be updated whenever the UE crosses the new TA.
- (vi)
- If the call arrival time is less than equal to the sum of time spent in a cell, the simulation procedure of the UE stops.
- (vii)
- Finally, the paging cost (number of paged cells) is evaluated. Note that the paging cost is 7 in an urban environment and 10 in a rural environment.

## 5. Numerical Results

_{c}= λ

_{in}+ λ

_{out}= 0.5 + 0.5 = 1.0

_{in}and 1/λ

_{out}, respectively. The time spent in a cell followed a gamma distribution with parameters 1 and 1/λ

_{m}.

_{c}= 7 (urban case). From the numerical results, it was observed that the number of registrations decreased as the moving probability, q, to the predicted direction increased, and the number of registrations decreased as CMR increased. Above all, it was observed that analytical and simulation results were very close. It could be concluded that the semi-Markov process model gave accurate results since differences between analytical results and simulation results were less than 1.42% on average. Therefore, subsequent numerical results were obtained using the semi-Markov process model. Therefore, subsequent mathematical results were obtained using the semi-Markov process model.

_{c}= 7 when q ≥ 0.75, although the registration cost of the proposed scheme with random walk mobility (q = 1/6) was higher compared to the performance of the DBR.

_{c}= 10 at q ≥ 0.85.

- (i)
- The number of registrations (or registration cost) decreased as the CMR increased because the UE resided longer in a cell with less registrations required.
- (ii)
- (iii)
- If CMR < 1 corresponding to current small cell configurations was considered, the registration scheme with our flexible TAL forming outperformed the typical DBR and the original TAL-based scheme.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**TAL forming scheme depending on UE’s moving direction prediction. (

**a**) Urban area (small sector, 60°); (

**b**) Rural area (big sector, 120°).

**Figure 2.**State transition diagram for an urban environment (small sector, 60°). (

**a**) State of a small sector (60°). (

**b**) State transition diagram of a small sector.

**Figure 3.**State transition diagram for rural environment (big sector, 120°). (

**a**) State of a big sector (120°). (

**b**) State transition diagram of a big sector.

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**MDPI and ACS Style**

Jang, H.-S.; Baek, J.-H.
Mobility Management Scheme with Mobility Prediction in Wireless Communication Networks. *Appl. Sci.* **2022**, *12*, 1252.
https://doi.org/10.3390/app12031252

**AMA Style**

Jang H-S, Baek J-H.
Mobility Management Scheme with Mobility Prediction in Wireless Communication Networks. *Applied Sciences*. 2022; 12(3):1252.
https://doi.org/10.3390/app12031252

**Chicago/Turabian Style**

Jang, Hee-Seon, and Jang-Hyun Baek.
2022. "Mobility Management Scheme with Mobility Prediction in Wireless Communication Networks" *Applied Sciences* 12, no. 3: 1252.
https://doi.org/10.3390/app12031252