Iran Journal of Computer Science

, Volume 1, Issue 4, pp 227–236

# Artificial immune system (AIS)-based location management scheme in mobile cellular networks

• Sanjay Kumar Biswash
• Mahasweta Sarkar
• Dhirendra Kumar Sharma
Original Article

## Abstract

In this paper, we are proposing a bio-inspired location management (LM) technique for personal communication system (PSC). It is based on artificial immune system (AIS), with self-adaptation and self-update attributes to perform the location management, and helps to achieve better quality of service (QoS) and quality of experience (QoE) for the mobile users. Here, we are suggesting a modified mobile switching center (MSC) architecture, and an adaptive self-modified location management procedure. The proposed mobile switching center architecture has an advantage of rule-based and fact-based system to store the rules and facts related to location management procedure, and it shows the intelligent behavior of system. The mobile switching center calculates the best method for location management and the rule-based system trigged the rules to perform the techniques. The system stores the result (techniques for location management) in fact-based system for future use. The efficiency and effectiveness of the proposed techniques have been analyzed, and it observed that the proposed system has 45–50% improvement in performance over the current location management techniques. Here, we are using performance parameters such as signaling cost, database update cost, overhead measurement, and mobility management cost.

## Keywords

Artificial immune system Cellular networks Personal communication system Location management Mobility management

## 1 Introduction

The anytime–anywhere communication with mobility is a basic requirement for cellular networks, and it a challenging task for service providers. The researchers are working on pervasive network interface to provide better service to the mobile subscriber. It is a mandatory condition for better QoS/QoE, and a highly sophisticated challenge for the next generation networks. The mobile networking is one of possible solutions to archive the QoE/QoS in dynamic scenario, but it has several challenges related to performance [1, 2, 3, 4, 5].

The effective network management is one of major issues in personal communication system, and it is very technical with high mobility [1, 2]. The cellular network performance depends on networks’ availability and mobility management [3, 6]. The user’s mobility is dealt with using mobility management (MM), and it has two parts: handoff management (HM) and location management (LM). These techniques are used to track mobile users (MU)/user equipment (UE) within the service area (SA). The service is divided into several location areas (LA) and cells [1, 2]. The mobility management is essential for all cellular technologies like 3G, 4G, long-term evolution (LTE), etc. In LTE, the mobility management entity (MME) is responsible for the network management (mobility management) function [4, 7, 8, 9], which connects a group of mobile users with the base station (BS), and it is also managed by mobile switching center (MSC), where each cell has a unique cell identity. The MSC is responsible for location information, routing information, billing issue, and services to UE [1]. The complete PCS architecture and its working can be found in [1, 2, 10], and this is the traditional system that is usually used for location management in cellular networks. At present, mobility management is not limited to access points (AP) and BS, it is also about exploring end-to-end mobility support and energy management [4].

Modern science uses animals’ behavior as a base for their research, and it introduces a new field, i.e., nature-inspired computing. It also used to solve complex problems of information and communication technology (ICT) [11, 12]. Several type of networks such as, wireless sensor networks (WSN), cognitive radio (CR), mobile ad hoc networks (MANET), and personal communication system (PCS) are using the nature-inspired computing to solve complex issues such as, routing, resource allocation, optimization, reliability, and network-related operations [11].

The rest of the paper is organized as follows. The artificial immune system for the location management is discussing in Sect. 2. The proposed model formulation and constraints analysis are available in Sect. 3. The performance analysis and results are given in Sect. 4. Section 5 presents the conclusions of the work and this is followed by references.

## 2 Related works

With the development of wireless networks and associated devices, researchers are motivated to enhance communication technologies, and looking forward to pervasive communication system. The user devices must have unique network management, so that UE can avail better QoS and QoE [2, 11, 13, 14, 15, 16, 17, 18]. The existing mobility management schemes are classified into two categories: tunnel-based schemes and routing-based schemes [9]. Most of the mobility management techniques are proposed for individual users, and they are widely investigated by the researcher and it reached a new hype, but actually network mobility (NEMO) performance is still very poor. To enhance the performance of the network mobility, researchers are working on device mobility interface techniques. In [2, 4], the authors proposed a traditional technique for location management, and it is globally used by 3G networks.

In the PCS, all areas under coverage are divided into cells. The mobile base station serves each cell and a group of cells is called as location area (LA). All base stations (BS) of location areas are directly connected to the mobile stitching center (MSC) through physical links [1, 2, 3, 4]. The connectivity between user equipment (UE) and BS is wireless. Cellular networks have two databases that can be used to store the user information: home location register (HLR) and visitor location register (VLR).The HLR maintains the records for its own users, and VLR keeps the information about visitors [1, 2, 9]. With every movement, the mobile user may change the serving base stations. Then, the mobile users need a new registration with the new base station. The completed procedure of this technique can be found in [1, 2, 4, 10], and we compared our proposed scheme with the location management procedure of [1, 2].

The authors of [19] proposed a new mobility management scheme which provides seamless connectivity and reliable execution of context-aware transactions during mobility of users, and it is a combination of different queuing models. They conducted various experiments to prove the effectiveness of the proposed scheme. In [7], the authors proposed a concept of group-based network roaming in proxy mobile IPv6 (PMIPv6) domain, and they are considering it for 6LoWPAN-based wireless body area networks. The PMIPv6 is a standard used to manage the network-based mobility in all IP networks [20]. Then, several mathematical formulations have been proposed for the location management, and most of them are related to cost analysis of mobility management [2]. The authors of [8] developed an approach of embedded Markov chain model to analyze the signaling cost for movement-based location management (MBLM) scheme in cellular network, and it is applicable for 4G and LTE network. Now, researchers have found that a nature-inspired system is also applicable in communication networks [11, 21]. The working of nature-based networking is not limited to ant system, bee system, swarm intelligence, etc. In this paper, we are focusing on the artificial immune system for location management. Very limited work is available in the area of nature-based networks. In [12], the author proposed a new mobility aware bio-inspired routing protocol for MANETs, and they also introduced a mobility aware-termite (MA-Termite) system using pheromone smoothing.

### 2.1 The artificial immune system

The Chordata phylum of animals has notochord; it is an important structure in the vertebrate, and leads to having a strong immune system. The immune system has fundamental attributes of adaptability, distribution, robustness, and self-regulation (self-updated) according to the situations. These properties are managed by cells (smallest unit of living animal called). These cells make tissues, and organs. The immune system protects the body from known and unknown diseases such as virus and bacteria attacks. The natural immune systems works as a defense system for body against pathogens, and this field of the study is called as artificial immune systems (AIS). Surviving from the massive attack of different viruses/bacteria is a complex procedure, thus the body needs a unique flexible immune system. It should efficiently be strong enough to neutralize the specific antigens. To enhance the performance of the body’s immune system, a multilevel defense system is required, and it should have self-adaptive, upgradeable and generic behavior. Nowadays, several researchers have been motivated by the immune system’s behavior and have been applying its behavior to many complex issues such as fault detection and pattern recognition. In [22], the author proposed constrains for immune system-based paradigm, and it is based on the response principle of system. A new cell signal transfer prospective, cell interaction techniques, and optimizations conditions are discussed in [23]. The authors of [24] proposed a new multiclass classifier based on immune system principles. The proposed work has a unique feature of classifier for embedded property with local feature selection. In [25], the authors proposed an optimization technique for the RIFD-based position system and they produced several results for the three-benchmark functions. In [24], they are indicating that the proposed system performs better than other algorithms. In addition, the evaluation results produced in [25] shows that it can predict the picking cart’s position more accurately. The authors of [26] introduced a new sub-pixel mapping strategy based on the immune system, and is used for the sub-pixel mapping in remote sensing imagery system. The AIS, inspired by the immune system, has powerful information processing capabilities such as clustering/classification, anomaly detection, optimization, and data mining.

### 2.2 Motivation and contributions

There are several location management techniques that are available in literature. Each has its own advantages and disadvantages. Now, we are looking for a robust, scalable, and pervasive location management scheme. The immune system is helpful in achieving this objective. The artificial immune system is a growing paradigm in computational intelligence (CI) and it has several application domains, such as recognition, detection, elimination of foreign threats and non-self-entities. It has the ability to learn, update, upgrade, and adapt. The artificial immune system has a unique feature of “ability to learn” and “self-adaptability”. In this work, we are using these components for our research purpose. There are several location management techniques available with many pit falls, but none of them follows the natural phenomena. The mobile users are seeking robust, intelligent, adaptive and self-configurable mechanisms for location management. This has motivated us to apply the mechanism of immune system for location management in mobile cellular networks. Here we are introducing immune system-based location management scheme for cellular networks and it has made the following contributions.
1. (A)

We are introducing modified mobile switching center architecture for location management. It contains rule-based techniques, fact-based system, and an inferring machine. This proposed architecture achieves better QoS and QoE for the mobile users.

2. (B)

A new nature-inspired location management technique which follows the fundamental principal of artificial immune system. This technique has the properties of self-configurability and adaptation and shows intelligent behavior for a system.

3. (C)

A mathematical analysis and software-based implementation for performances analysis.

4. (D)

The system adaptability and update mechanism (within FBS and RBS) used to update the domain knowledge.

## 3 Artificial immune system for location management

The proposed work has two parts: the modified mobile switching architecture and the location management procedure.

### 3.1 The mobile switching center architecture

The self-healing and robust system mechanism is a fundamental part of the immune system. Here, we are mapping these attributes with proposed MSC architecture. In consequence, we are introducing the rule-based system (RBS), fact-based system (FBS) and inferring machine (IM) system for mobile switching center(as shown in Fig. 1).

The RBS that is used to store all kinds of rules is associated with location management. If the mobile user is not residing in native LA, then it needs a location update. It computes optimized least metrics-based method for location management. The fact-based system is responsible for all kinds of fact, such as appropriate location management scheme for a particular location. The inferring machine mapped the information between RBS and FBS. As per the availability of the new information in the system, the FBS and RBS are ready for self-update. For example, if there exist any best method for location management. Then, the FBS will overwrite this information and this mechanism will lead to self-adaptability in AIS. The update mechanism is completely an adaptive base and it is a scalable system.

### 3.2 The LM technique

The natural systems are very simple and effective, and its behavior will be used for research. It helps people to solve several complex challenges. In this decade, natural behaviors are widely used and applied to solve several issues of networking. In this work, we are using artificial intelligent system’s behaviors. The artificial immune system automatically increases body resistance power, after the infections of virus or bacteria, and here we are using this strategy for location management procedure.

The following steps are used in the proposed location management scheme, and they are shown in Fig. 2.
1. 1.

The UE is moving from one LA to another LA. So, mobile user will go through the location update procedure.

2. 2.

The mobile user sends the location update message to the serving BS, and BS forwards it to the associated mobile switching center.

3. 3.

The mobile switching center checks the RBS for the particular movement of the user.

4. 4.

If there is a new movement, and there is no related information in RBS, then the mobile switching center will compute the best possible procedure to perform the location update.

5. 5.

If location update information is available in FBS (by old location updates), the, mobile switching center fetches the corresponding rules from the RBS, and the FBS performs the location update procedure. After a successful location update, the procedure will be stored in the fact-based system for future use.

6. 6.

The current mobile switching center sends the de-registration message to the old mobile switching center and the mobile user receives the acknowledgement message.

7. 7.

A successful registration message is sent to the mobile user.

### 3.3 RBS and FBS update procedure

The RBS and FBS update procedure is very important and it has the following methodology. A new mobile user performs a registration procedure with the above described method (as mention in Sect. 3.2), and then the system will store the method for the other UE. If a new mobile user sends the location update request with the same circumstances (with reference to first mobile user), then the system will fetch the associated method from rule-based system and perform the location update procedure.

Note If a new unique and least cost-/effort-/metrics-based procedure is available between source to destination, then system will go through a self-update mechanism in FBS. It will be helpful for the new user, and it shows an adaptive behavior of system. For example, if a mobile user’s request for location update is from the location area#1(LA1), and the best method M1 is available in face-based system, then the system will perform the location update with M1. After some time, the system observed that there is another most favorable method M2 available for LA#1. Then, the fact-based system will overwrite the M1 by M2 for better QoS/QoE.

### 3.4 Illustration of procedure

In this section, we are elaborating our work with an example. We are assuming, there are four facts and their associated rules are available in fact-based and rule-based systems, respectively (as shown in Fig. 3). The facts and rules are: F1–F4 and R1–R4, respectively.

The UE moves out from the native location area and needs a location update. This procedure will be initiated by network (self-initiate). The request is received by BS and forwarded to mobile switching center. In the fact-based system, F1 will be active. Then, rule R1 will trig to perform the location management. The rule-based system will find the last updated information, and according to the appropriate rules corresponding action is taken by RBS (as mention in R1, R2 and R3). It will inform to fact-based system, the facts will be stored for future reference, and it will used for other mobile users. This procedure will reduce the overheads for location update.

## 4 Model formulation

In this section, we are formulating a proposed location management scheme and using some mathematical notions (as describe in Table 1).
Table 1

Notation and descriptions

Notation

Description

$$\upsilon$$

The average speed of the UE

$$\rho$$

The population density within a LA

$$L$$

The perimeter of the region L

$$R_{\text{handoff}}$$

Rate of handoff

N

Number of LAs in the service area

$$\pi$$

Steady-state probability of the user in a LA

$$\pi_{o}^{o} /\pi_{o}^{V} /\pi_{V}^{V} /\pi_{V}^{o}$$

Steady-state probability from own LA to own LA/visitor LA to own LA/visitor LA to visitor LA/own to visitor LA

$$R_{o}^{o} /R_{o}^{V} /R_{V}^{V} /R_{V}^{o}$$

Handoff rate from own LA to own LA/visitor LA to own LA/visitor LA to visitor LA/own to visitor LA

$$C_{\text{MAT}}$$

Cost of matching

$$C_{\text{FAT}}$$

Cost of fetching

$$C_{\text{UP}}$$

Cost of update

cL

cU

Expected cost per byte of update

Avg(D)

Average number of data to be updated

C SIGNAL

Signaling cost

h

Number of hop between shortest paths

N MT /N CN

Number of UEs/Corresponding node

$$\chi$$

Linear coefficient of LM

v

Per unit per association lookup cost

$$\eta$$

Proportionality constant

TP/S

Processing cost/Delay

$$\phi$$

Binding transmission cost

The mobility model has an important role in formulating the wireless networks, and most of the researchers are using random waypoint mobility model for this purpose. In the cellular networks, user movement is a stochastic process, and it follows the random walk mobility [1, 2]. To correlate the proposed work with random walk model, we are calculating all possible user movements. In the PCS network, the movement can be differentiating in three levels, as follows.
1. Case 1.

Moves within the own LA.

2. Case 2.

Moves from own LA to adjacent LA.

3. Case 3.

Moves from the adjacent LA to own LA.

4. Case 4.

5. Case 5.

Moves from new adjacent LA to own LA.

6. Case 6.

Now, we are formulating the Markov model with the associated movement probability (as discussed above “p”), which is shown in Fig. 4. Here, we are calculating the mobility pattern between three location areas, and it will be repeated for all movements’ pattern. For example, if we consider a seven-cell structure and applying mobility pattern, then it will be the same as the three LA movement, because the movement of user will always repeat the three LA systems.
The average speed of mobile user (υ), and its direction are measured with a straight line, leading to center of the cell from the initial location of UE. The amount of traffic passing through this region is proportional to the population density (ρ) with the region and perimeter L, and “p” is the user movement probability. The approximate number of boundary crossing: $$\varOmega = \frac{\upsilon \rho L}{\pi }$$ [2]. The possible handoff rate is $$R_{\text{handoff}} = \frac{\upsilon \rho L}{\pi }N$$, where $$N$$ is the number of location areas within the service area. The $$\pi$$ is steady-state probability for UE, within a location area (own LA/adjacent LA). The user movement pattern has four steady states, as shown in Fig. 5.
1. 1.

User is staying in a location area and make a movement within the own area.

2. 2.

User moves away from native location area to adjacent LA.

3. 3.

User is moving within the adjacent location area.

4. 4.

User is moving from adjacent location area to own native area.

The steady-state-associated probabilities have been calculated, and it is the same as the user’s mobility, as shown in Eq. 14..
$${\text{Case}}\,\,1\, = \,\,\pi_{O}^{O} \, = \,\frac{{R_{O}^{O} }}{{R_{O}^{O} \, + \,R_{V}^{O} }}$$
(1)
$${\text{Case}}\,\,2\, = \,\pi_{V}^{O} \, = \,\frac{{R_{V}^{O} }}{{R_{O}^{O} \, + \,R_{V}^{O} }}$$
(2)
$${\text{Case}}\,4\, = \,{\text{CASE}}\,6\, = \,\,\,\pi_{V}^{V} \, = \,\frac{{R_{V}^{V} }}{{R_{V}^{V} \, + \,R_{O}^{V} }}$$
(3)
$${\text{Case}}\,\,3\, = \,\,{\text{Case}}\,\,5\, = \,\pi_{O}^{V} \, = \,\frac{{R_{O}^{V} }}{{R_{V}^{V} \, + \,R_{O}^{V} }}.$$
(4)
The localization probability ($$p$$) is the probability of mobile users who move within the own location area, and the handoff rates will be as follows (from Eq. 5 to 10):
$${\text{Case1}}:\frac{{\upsilon \rho L \times \left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times p}}{{R_{O}^{O} }}$$
(5)
$${\text{Case}}\;2:\frac{{\upsilon \rho L\left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times (1 - p)}}{{R_{V}^{O} }}$$
(6)
$${\text{Case}}\;3:\frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{3}}} \right]}}{{R_{O}^{V} }}$$
(7)
$${\text{Case}}\;4:\frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }}$$
(8)
$${\text{Case}}\;5:\frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{O}^{V} }}$$
(9)
$${\text{Case}}\;6:\frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }}.$$
(10)

The artificial immune system-based technique is responsible for search, retrieving and matching the information to perform the LM procedure.

In the matching process [27], the user is residing in a particular location area, and UE is trying for location registration with the current base station. This update request information message will be forwarded to mobile switching center via associated BS. The mobile switching center performs a matching procedure for the mobile user (within the RBS/FBS).

For each given query, matching procedure is average of self-information set of t tuple $${\text{Sat}}(t)$$ with respect to tuples to the query. That is, matching information can be written as follows.

Let $$(t,\mu_{\text{r}} (t))$$ be a tuple in the extended fuzzy relation $$\left| t \right| = \,k$$ and $$\left| {{\text{Sat}}(t)} \right|\, = \,n\,$$, where $$n\,\, \le \,\,k$$. Then, matching information of $$t,\,I_{\text{mat}} (t),\,$$ is $$I_{\text{mat}} \,(t)\, = \,\frac{n}{k}\left( {{{\sum\limits_{i = 1}^{n} {\mu_{\text{r}} (t_{i} )} } \mathord{\left/ {\vphantom {{\sum\limits_{i = 1}^{n} {\mu_{\text{r}} (t_{i} )} } n}} \right. \kern-0pt} n}} \right)\, = {{\left( {\sum\limits_{i = 1}^{n} {\mu_{\text{r}} (t_{i} )} } \right)} \mathord{\left/ {\vphantom {{\left( {\sum\limits_{i = 1}^{n} {\mu_{\text{r}} (t_{i} )} } \right)} k}} \right. \kern-0pt} k}$$
$$\mu_{\text{r}} (t)\, = \,\,{\text{MIN}}\,\left( {\mu \left( {t\left[ {A_{1} } \right]} \right), \ldots \mu \left( {t\left[ {A_{n} } \right]} \right)} \right)\;{\text{and}}\;\mu \left( {t\left[ {A_{i} } \right]} \right)\, = \,\,{\text{MAX}}\,\left( {\mu \left( {a_{i\,1\,} } \right), \ldots ,\mu \left( {a_{im\,} } \right)} \right).$$
The expected value of cost of matching is shown in Eq. 11.
\begin{aligned} & C_{\text{MAT}} \, =\, \int\limits_{0}^{\infty } {Cr\left\{ {{\text{MIN}}\,\left( \begin{aligned} {\text{MAX}}\,\left( {\mu \left( {a_{i\,1\,} } \right),\, \ldots ,\mu \left( {a_{i\,n\,} } \right)} \right) \hfill \\ , \ldots {\text{MAX}}\,\left( {\mu \left( {a_{i\,1\,} } \right),\, \ldots ,\mu \left( {a_{i\,m\,} } \right)} \right) \hfill \\ \end{aligned} \right) \ge t} \right\}{\text{d}}t} \, \\ & \quad \,\, - \,\,\,\int\limits_{\infty }^{0} {{\text{Cr}}\left\{ {\left( {{\text{MIN}}\,\left( \begin{aligned} {\text{MAX}}\,\left( {\mu \left( {a_{i\,1\,} } \right), \ldots ,\mu \left( {a_{i\,n\,} } \right)} \right), \ldots {\text{MAX}}\, \hfill \\ \left( {\mu \left( {a_{i\,1\,} } \right), \ldots ,\mu \left( {a_{i\,m\,} } \right)} \right) \hfill \\ \end{aligned} \right)} \right) \le t} \right\}{\text{d}}t} . \\ \end{aligned}
(11)
where, $$\forall \,a_{i\,j\,} \in \,t\left( {A\left[ i \right]} \right)\,{\text{and}}\,i\, = \,1,\, \ldots n$$.

In the fetching process [28], the system will fetch the information from the RBS and FBS, and we can set the range of the information from {0,1}. To fetch the information from database, we are considering a unit scale with datasets (A), the A of zero representing the average position of relevant documents being available inside the database at the beginning of the search process, and an A of one being at the end of the search process. The parameter A is then the expected proportion of documents examined in an optimal ranking if one examines all the documents up to the document in the average position of a relevant document. It is the expected available position of the relevant information, and it is scaled from zero to one. The variable A is computed by noting, that documents with feature frequency d are at the low end of the A spectrum (good performance), and those with feature frequency $$\overline{d}$$ at the high end of the spectrum (poor performance).

The middle (average) position for each of the profiles, when they had been arranged in order, in such cases $$Pr(d)/2$$, is the average position for availability of documents with feature frequency d. The mean position of available information is $$1 - Pr(d)/2$$ for the documents with feature frequency d; that is, when the feature frequency is zero. Thus, the estimated value of A is written as in Eq. 12.
$$A\, = \,{{Pr(d|{\text{rel}}\,)\,\,Pr(d)} \mathord{\left/ {\vphantom {{Pr(d|{\text{rel}}\,)\,\,Pr(d)} 2}} \right. \kern-0pt} 2}\, + \,Pr(\overline{d} |{\text{rel}}\,)\,(1 - \,Pr(\overline{d} )$$
(12)

Using a similar technique, we find that $$\overline{A}$$, the A value for the worst case ranking, is 1A. It is simplified algebraically to $$A\, = \,\frac{1\, + \,Pr(d)\, - \,Pr(d|rel)}{2}$$. $$C_{\text{FAT}} \, = \,\,nA\,\, = \,n \times \left( {\frac{{1\, + \,Pr(d)\, - \,Pr(d|{\text{rel}})}}{2}} \right)\,$$, where n represents the number of fetched information.

The update process [29] is responsible for the update of the information in rule-/fact-based system. The associated cost is based on cost of reading an average-sized sub-tuple multiplied by the probability of a read versus the cost of writing an average-sized sub-tuple multiplied by the probability of a write-up in the database.

Based on the above discussion, we are remarking that, when the system observes, there are more frequent availabilities of large clean sub-tuples, and this will make the clean sub-tuples buffer expand. The following equation formally defines this
\begin{aligned} C_{UP} & = \text{e} {\text{xpected cost per byte of loading}}\\ & \quad \times {\text{expected cost per byte of update}} \\ &\quad \times {\text{ Avarage number of data to be updated}} \\ & = cL \times \,cU \times \,Avg(D). \\ \end{aligned}
(13)
The LM procedure cost is the combination of location management’s operational cost, database manipulation and signaling cost. The signaling cost has a major role in the user mobility. The movement of the users can be classified as: Inter LA, Inter MSC, Inter VLR, Inter HLR, and its signaling cost can be computed as, 4, 4, 8 and 10 units, respectively [4]. The per unit signaling cost for the location management is shown in Eq. 14 and [1].
C_{\text{SIGNAL}} \, = \,\left( \begin{aligned} \,N_{\text{MT}} \, \times \,\,\frac{{2\,(\,h - 1\, + \,\eta )\,v\, + \,T_{P} }}{d}\, + \,\,N_{\text{MT}} \, \times \,\,N_{\text{CN}} \times \, \,\,\frac{2\,(\,h - 1\, + \,\eta )\,\varphi }{d}\,\, + \, \hfill \\ \,N_{\text{MT}}^{2} \times \,N_{\text{CN}} \times \,\frac{{\chi \,\,\,\lambda_{\text{CALL}} }}{S} \hfill \\ \end{aligned} \right) \times {\text{SIZE}}_{\text{DATA - PACKET}} .
(14)
The location management cost in existing techniques is, as shown in Eq. 15.
\begin{aligned} & C_{\text{LU}}^{\text{Existimg}} \, = \,\pi_{O}^{O} \, \times \frac{{\upsilon \rho L \times \left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times p}}{{R_{O}^{O} }} \times 4\\ & \quad \times C_{\text{SIGNAL}} + \,\,\,\pi_{V}^{O} \times \frac{{\upsilon \rho L\left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times (1 - p)}}{{R_{V}^{O} }}\\ & \quad \times 4 \times C_{\text{SIGNAL}} + \,\,\, \\ & \quad \pi_{O}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{3}}} \right]}}{{R_{O}^{V} }} \times 8 \\ & \quad \times C_{\text{SIGNAL}} + \,\pi_{V}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }}\,\,\, \times \\ & \quad 8 \times C_{\text{SIGNAL}} + \,\pi_{O}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{O}^{V} }}\, \times 10 \\ & \,\quad \, \times C_{\text{SIGNAL}} + \pi_{V}^{V} \, \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }} \\ & \,\,\, \times 10 \times C_{\text{SIGNAL}} + 2C_{\text{MAT}} + 2C_{\text{FAT}} + 2C_{\text{UP}} . \\ \end{aligned}
(15)

It is the cost of location management through the traditional system; in our proposed system, there will be two cases: best case and worst case.

Best case The mobile user does not make a full registration, and the required information can be fetched from RBS and FBS (information’s are already available). All the information required for the location update is available in the system, and it leads to less communication cost, because there are only two pairs of information exchange (we are taking on a pair of signal exchange for the same cost as that of one unit signaling [1, 2, 3, 4], as shown in Eq. 16).
\begin{aligned} & C_{\text{LU}}^{\text{Proposed}} ({\text{Best}}) \, = \, \pi_{O}^{O} \, \times \frac{{\upsilon \rho L \times \left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times p}}{{R_{O}^{O} }} \times 2 \times C_{\text{SIGNAL}}\\ & \quad + \,\,\,\pi_{V}^{O} \times \frac{{\upsilon \rho L\left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times (1 - p)}}{{R_{V}^{O} }} \\ &\quad \times 2 \times C_{\text{SIGNAL}} + \,\,\,\pi_{O}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{3}}} \right]}}{{R_{O}^{V} }} \times 2 \\ &\quad \times C_{\text{SIGNAL}} + \,\pi_{V}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }}\,\, \\ &\quad \times 2 \times C_{\text{SIGNAL}} + \,\pi_{O}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{O}^{V} }}\, \times 2 \\ & \quad \times C_{\text{SIGNAL}} + \pi_{V}^{V} \, \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }}\,\, \\ & \quad \times 2 \times C_{\text{SIGNAL}} + 2C_{\text{MAT}} + C_{\text{FAT}} + 2C_{\text{UP}} \\ \end{aligned}
(16)
Worst case The system needs to collect all the required information and it leads to high update, fetching and matching cost. The singling cost (cost associated with signal exchange) of the system will be also high, because it needs to find more information for better LM technique, and its associated cost is shown in the following equation.
\begin{aligned} & C_{\text{LU}}^{\text{Proposed}} ( {\text{Worst}}) \, = \, \pi_{O}^{O} \, \times \frac{{\upsilon \rho L \times \left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times p}}{{R_{O}^{O} }} \times 4 \\ &\quad \times C_{\text{SIGNAL}} + \,\,\,\pi_{V}^{O} \times \frac{{\upsilon \rho L\left[ {R_{O}^{O} \, + \,R_{V}^{O} } \right] \times N \times (1 - p)}}{{R_{V}^{O} }} \\ &\quad \times 4 \times C_{\text{SIGNAL}} + \,\,\,\pi_{O}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{3}}} \right]}}{{R_{O}^{V} }} \times 4 \\ &\quad \times C_{\text{SIGNAL}} + \,\pi_{V}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }}\,\, \\ &\quad \times 4 \times C_{\text{SIGNAL}} + \,\pi_{O}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{O}^{V} }}\, \times 4 \\ & \quad \times C_{\text{SIGNAL}} + \,\pi_{V}^{V} \times \frac{{\upsilon \rho L\left[ {R_{V}^{V} \, + \,R_{O}^{V} } \right] \times N \times \left[ {{\raise0.7ex\hbox{{(1 - p)}} \!\mathord{\left/ {\vphantom {{(1 - p)} {12}}}\right.\kern-0pt} \!\lower0.7ex\hbox{{12}}}} \right]}}{{R_{V}^{V} }}\,\, \\ & \quad \times 4 \times C_{\text{SIGNAL}} + 2C_{\text{MAT}} + C_{\text{FAT}} + 2C_{\text{UP}} \,\,\,\,\,\,\,\,\,\,\,\,\,(17) \\ \end{aligned}
(17)

## 5 Result and discussions

To evaluate the efficiency and effectiveness of the proposed work, we are taking some initial values from [1, 2, 3, 4]. We are assuming the movement probability of the user $$p\, = \,0.05$$, number of tuples in the RBS and FBS = 1000, the number of cells in a LA is 50, and the number of LAs inside the SA is 1000. The communication media is uniform and we are considering the number of users per LA to be 1000. The average speed of the mobile user is 50 m/h. The value of L is 1000 m2.

Figure 6 shows the effect of the number of mobile users in a LA over the associated cost. Figures 6 and 7 represent the overall cost and signaling cost vs. user’s density in a LA, respectively. The user’s density varies from 10–90/LA, and the mobility probability is fixed at 0.05. The graphical observation indicates that, the traditional procedure has higher cost with respect to artificial immune-based system, because of the greedy technique.
Figure 8 shows the overall LM cost vs. user movement probability(Fig. 8) and average call arrival rate (Fig. 9). The value of movement probability will vary from 0.05 to 0.4 and the average call rate varies from 10 to 90 within a LA. It has been observed that the traditional and AIS scheme (worst case) have almost the same level of growth for overall cost, but the AIS scheme with best case has a remarkable reduction of the cost, because the related information for the LM does not need to be calculated by the system (it is available in FBS and RBS).
Figure 10 represents the overall cost vs. service to user’s probability inside a LA (Fig. 10) and overall cost vs. call-to-mobility (CMR) in Fig. 11. Here, the AIS-based scheme has a better result because it calculates the related information through RBS
With the help of Fig. 12, we can check the effectiveness of proposed scheme over the traditional scheme in the terms of hop counts to the destination users. Figure 12 shows the hop count for the LM, and Fig. 13 is used to measure hop count between caller and target mobile node.

## 6 Conclusions and future works

In this paper, we proposed an artificial immune system-based location management technique. We have introduced modified mobile switching center architecture, and it contains rule-based, fact-based systems and an inferring machine. The mobile switching center performs the location management based on the available and associated rules/facts. After a successful location update, the system will store the fact-based system for future use. If a new registration request arrives with the same circumstance, the system will select the pre-applied method for registration and it has less communication overheads and associated cost. If other appropriated methods are available, then the system updates itself (self-updating) and shows the adaptive and robust behavior. This proposed technique is applicable for inter and intra domain (MSC/HLR/VLR) movement of UE. Finally, the effectiveness of proposed system has been checked by comparing with the traditional 3G LM scheme and has shown sufficient improvement. In our next work, we would like to implement this work for 5G networks with respect to several other nature-based algorithms.

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© Springer Nature Switzerland AG 2018

## Authors and Affiliations

• Sanjay Kumar Biswash
• 1
• Mahasweta Sarkar
• 2
• Dhirendra Kumar Sharma
• 3
1. 1.Department of Computer Science and EngineeringNIIT UniversityNeemranaIndia
2. 2.Department of Electrical and Computer EngineeringSan Diego State UniversitySan DiegoUSA
3. 3.Department of Computer Science and EngineeringAvantika UniversityUjjainIndia