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Recently, Mobile IP has been widely used to support seamless internet user mobility. However, unnecessary registration process of Mobile IP system for tracking mobile users' movement causes large increase of signaling costs, and affects the scalability. Therefore, it is necessary to investigate how to reduce the signaling costs in Mobile IP. This paper proposes a Two Step Paging In External Sub-Paging Area and Adaptive Individual Paging in Internal Sub-Paging Area. For Mobile IP (TSAP-MIP) to reduce signaling costs and the sensitivity of the system with various user parameters. The main concept is to partition Sub-Paging Area and select the optimal paging sequence. The performance of the proposed TSAP-MIP is compared with three conventional schemes, namely, Two-Step Paging for Mobile IP (TSP-MIP) and Adaptive Individual Distributed Local Paging Scheme (ADLP-MIP) via analysis and simulation results. The reported results show that the total signaling costs of TSAP-MIP is the lowest, compared with those three conventional schemes.
Index Terms-Mobile IP , External Sub-Paging, Internal Sub-Paging Area.
As the ascribable need of unlined real-time application, such as All wireless communication networks, the networks must be designed to support the user's mobility to maintain the continuity of ongoing communication services. Mobile IP ,  has been proposed to support a simple mobility mechanism. In Mobile IP , a mobile node's (MN) location is tracking by its registration while moving by using simple mechanism for routing IP packets to MNs. In this mechanism MN is tracking by home agent (HA) by using two IP address. The first IP address is a monumental address, called home address , and else address is called care-of-address (COA) which is a temporary address used by MN in a visited network. However, it still has several aspects that have to be solved but one of the problem is the increases signaling cost overhead and power consumption.
In mobile internet protocol, registration and paging process are used to reduce the signaling overhead. paging is process that the system searches for idle MN by broadcasting or multicasting the paging request message in paging areas (PA). Also the author  Paging mobile IP (P-MIP) introduce the paging to reduce the signaling cost for mobile IP . However, the signaling cost of P-MIP is not always less than that of mobile IP when the PA size is large.
to solve P-MIP problem, various author  proposed an adaptive and individual paging scheme for each MN computes its optimal PA and optimization parameter are time varying. However, the significant problems is difficult to be tracked by MN.
In , the author proposed Distributed Local Paging scheme (DLP-MIP) that can reduce both the total signaling cost and power consumption of an MN by partitioning the paging area into sun-paging area (SPA). However, DLP-MIP cause large paging signaling cost when each (SPA) consists of many cells.
solve DLP-MIP problem In , the author proposed a two-step paging for mobile IP (TSP-MIP) by partitioning the SPA into an inner SPA and an Outer SPA together with selecting the optimal paging sequence, TSP-MIP can reduce the signaling cost but the significant problem is times delay because MN paging 2 times ,when the first paging attempts to page the inner sub-paging area. if mobile user is not found, the paging initiator continues to second paging in outer sub-paging area.
In this paper, we propose a two-step paging in external sub-paging area and adaptive individual paging internal sub-paging area together with optimal PA by selecting the optimal paging sequence. This paper is organized as follow in Section II, we review TSP-MIP,ADLP and propose TSAP-MIP. In Section III, we present the analysis of signaling cost. the performance comparison by mathematical analysis and simulation result is provided in Section IV. Section. Finally, Section V concludes the paper.
II. Overview of ADLP-MIP,TSP-MIP and the Proposed TSAP-MIP
A. Two Step Paging scheme for mobile IP (TSP-MIP)
TSP-MIP  can reduce the total signaling cost by configuring sub paging-area (SPA) within partition each SPA into an inner SPA and an outer SPA , as show in Figure 1. The first paging is skipped. if not, the second paging step is done in the outer SPA.
Figure 1. Partitioning in TSP-MIP
This scheme assumes that all for foreign agents (FA) support paging, that is all FAs can perform as pFA in . The first FA in a PA that an MN visited will be registered by an MN as the pFA of that MN. This scheme allows an MN to operate in to states as in . an active MN , it operates exactly the same as that in Mobile IP . For an idle MN, it has to registration its pFA with HA only when cross PA boundary. if it move within the same SPA, it's not need to perform registration. when it had already moved out from the same SPA but still in the same PA, it performs location update with its pFA to inform a new sub-pFA, Which is the FA that the MN visits first in SPA. A sub -pFA is responsible for tracking movement of MN when an MN still in the same SPA.
Dividing the paging into two-step can reduce signaling cost because skipping the second paging step (when the first paging step succeeds) eliminate flooding in the outer SPA the probability that MN locates in the inner SPA depend on paging area construction .
B. Adaptive Individual Distributed Local Paging Scheme for Reducing Signaling Cost in Mobile IP (ADLP-MIP)
ADLP-MIP  can reduce the total signaling cost by paging area configuration, each MNs user a paging area that size and shape are shape are dynamically adjusted. The "optimal size" of paging area essentially depends on the MN 's communication pattern such as incoming data session rate and its mobility speed. A MN's paging area size can actually be computed by the MN itself or by the network, However it is obviously easier and more scalable for the MN monitor these parameter and compute its optimal size.
The "optimal shape" of paging area depend essentially on the MN mobility pattern. In fact MN is driving along a highway would benefit from, a linear paging area. In contrast, a MN moving an urban area with random pattern would benefit from a symmetrical, i.e. a circular paging area. The mobility of MN depends on the geographic layout of the environment it is roaming in. There are two possible configuration alternative: In MN configuration. each MN derives its paging area shape from its mobility pattern. A MN then need to keep in memory the history of its movements and derives from it the optimal paging area in each network it visit. this solution has two drawback: first the memory requirement might be very large and second the history might not always be available (i.e. when the MN visit a network for the first time) or out-of date. Another possibility is network configuration where the network derive an aggregated paging area shape from the mobility pattern of the hosts in its coverage. this solution might not be optimal as the previous on because it does not capture the particular mobility pattern of each MN. However it reduce the memory requirement of MN. Additionally it does not require that each host builds its own mobility history. As result a host can obtain an optimal paging area even in network it did not visited previously.
Figure 2. Adaptive paging area sizes and shapes
C. Two Step Paging In External Sub-Paging Area and Adaptive Individual Paging in Internal Sub-Paging Area (TSAP-MIP)
This paper propose a Two-Step Paging in External Sub-Paging Area and Adaptive Individual Paging in Internal Sub-paging Area (TSAP-MIP), Which can further reduce signaling cost, compared to TSP-MIP and ADLP-MIP. In doing so ,the operating of TSAP-MIP is similar like TSP-MIP  and ADLP-MIP , we further partition each SPA into External Sub-paging Area (E-SPA) and each SPA into Internal Sub-paging Area (I-SPA). We define each base station nearly area with as show in Figure 3 other base station which refer to the FA and paging agent (PA) is central of paging area.
Figure 3. TSAP-MIP base station (FA) extend area
TSAP-MIP has two type of information for paging operation such as : Internal sub-paging area identification (I-SPAI) and External sub-paging area identification (E-SPAI)
In  the author proposed the status of MN when Active and idle as show in figure 4.
Figure 4. Status of MN
In case 1: the first step paging found MN When user 's MN in status is active and moving cross PA boundary and MN has already moved out from the same SPA. A MN's paging area size can actually be computed by the MN itself or by the network, in doing so HA checks whether the MN is in a sub-pFA's visitor (E-SPAI) and (I-SPAI) list or not. if there not found a record for the MN paging area, that MN will registers to nearly pFA and sent data binding update (I-SPAI) to server HA for update location. if HA founds a record for the MN paging area. A MN will not register to nearly pFA.
In case 2: the first step paging not found MN When user 's MN in status is idle and moving cross PA boundary and MN has already moved out from the same SPA. For the MN paging area so the system TSAP-MIP will paging by second step paging , if found MN, A MN will registers to nearly pFA and sent data binding update (E-SPAI) to server HA for update location.
III. Analysis of Total Signaling cost
The total signaling cost of Mobile IP , P-MIP, DLP-MIP, ADLP-MIP and TSAP are analyze in ,, and are presented here for convenience. We analyzed total signaling cost of TSAP. In addition , the analysis is base on the fluid flow model ,and take into various parameter, i.e., paging area size and mobile's movement speed. The signaling cost is defined as the product of the weighted distance between MN and FA,HA, we consider only the non-overlapping PA approach.
The shape of the PAs, SPSs and wireless cells is assumed to be square as in . The perimeter of cell is. The perimeter of SPA is and the perimeter of PA is .We assume that MNs move at average Velocity of (m/sec) in direction that are uniformly distributed over [0,2] and are uniformly distributed with density . The rate of cell boundary crossing is . the rate of SPA boundary crossing is . the rate of PA boundary crossing rate is .
A. Mobile IP
The total signaling cost of mobile IP  is
is the total signaling cost of mobile IP (weighted hop*packet/s)
is the average distant between FA and HA,
is the ratio of the number of hops in core, network to the total number of hops between HA and FA,
is the ratio of the number of hops in local access network to the total number of hop between HA and FA,
is the weight of each hop in the IP core network,
is the weight of each hop in access network,
is the cell crossing rate (mobile node/s)
is the mobile nod density (mobile node/)
is the number of cell in a consider PA,
is the cell perimeter (m)
is the average MN registration refresh as associated with register for life time.
This formula used for compute the total signaling cost P-MIP is
is the total signaling cost of P-MIP
is the average distance between FAs within a PA,
is the PA crossing rate (mobile nodes/s),
is the ratio of active node to the total number of mobile nodes,
is the incoming data session of MN (1/s),
is the outgoing data session rate of MN (1/s),
is the weight of wireless hop for paging.
This formula used for compute the total signaling cost DLP-MIP is
is the total signaling cost of DLP-MIP,
is the average distance between FAs within a SPA,
is the SPA crossing rate (mobile node/s),
is the number of cells in a sub-paging area,
This formula used for compute the total signaling cost TSP-MIP is
is the total signaling cost of TSP-MIP
is number of cell in an inner SPA,
is the probability of locating an MN in an outer SPA.
E. The Signaling cost in an Internal Sub-paging Area for TSAP-MIP
We follow method , to find The Total Signaling cost Internal Sub-paging Area. We define The perimeter of I-SPA is
is amount of cells in SPA for Tier when pFA Extend area as show in figure 5.
Figure 5. The perimeter of cell
is area of SPA
Where: is area of one cell
The total registration of signaling cost I-SPA depend with MN, average distant MN between pFA and average distant MN between HA
The total signaling cost average distant MN between pFA,
The total signaling cost average distant MN between HA,
The signaling cost per hops for wireless network,
The signaling cost per hops for wire line network,
average distant MN between pFA ,
average distant MN between pFA.
The signaling cost depend on transmutation of the signal to each cell in SPA
According to the fluid flow model we can find the rate of cell boundary crossing in I-SPA
Where: is average of movement speed of MN,
The rate of SPA boundary crossing SPA in I-SPA
The rate registration of MN when crossing SPA in I-SAP
The total signaling cost of MN in the I-SAP to calculate The "optimal size", we can find from the sum of Eq. 8 , Eq 9, Eq. 10 and Eq. 13. All in above are depend on the parameter (data session of MN ), amount of cell tier and (average movement speed of MN) show as in Eq.14
F. The Total Signaling cost for TSAP-MIP
As defined we can find the total signaling cost in a External Sub-paging area from Eq. 4 (E-SPA) and replace the SAP outer by Eq. 14 (I-SPA) is
VI. Analysis and Simulation Results
In this section we present the performance of TSAP-MIP compare to five conventional schemes (Mobile IP, P-MIP ,DLP-MIP, ADLP-MIP) with the MN velocity. consider cellular macro system, which have an average perimeter cell size of 4000 m, maximum MN velocity of 45m/s and MN density of 0.0002 MN/. the parameter used in this analysis are set to typical value as in . (See table 1.)
Table 1. Input Parameters
About the analytical, We proposed scheme via simulation results by varying velocity. the mobility model is assumed to be random walk a connected graph model. We consider only single MN in the simulation period (10,000 timeslots), which result in 92% of confidence interval. For the random walk model, MN will change its FA with assigned probability and stay within the same FA with probability 1-. depend on the given average velocity of MN, but does not depend on number of cell, All parameter we apply same Table 1.
Figure 6. Effect of MN speed on the total signaling cost
Figure 6 shows the signaling cost as a function of MN velocity. We set a PA size to 144 cell and in a SPA, and then the number of cells in an I-SPA is 16 cell. when MNs move faster, TSAP-MIP ,TSP-MIP , DLP-MIP , ADLP-MIP perform better than Mobile IP an P-MIP. However, when MN move slower the total signaling cost of Mobile IP is slightly lower than TSAP-MIP,TSP-MIP and ADLP-MIP . TSAP performs better than Mobile IP up to 81% .
Figure 7. Effect of MN speed on the total signaling cost (TSAP-MIP compared TSP-MIP and ADLP-MIP)
Figure 7 shows the signaling cost as a function of MN velocity. We set a PA size to 144 cell and in a SPA, and then the number of cells in an I-SPA is 16 cell. when MNs move faster, TSAP-MIP ,TSP-MIP perform better than ADLP-MIP. However, when MN move slower the total signaling cost of TSP-MIP is slightly lower than TSAP-MIP. TSAP performs better than TSP-MIP, ADLP-MIP up to 24% and 34% respectively.
This paper , We proposed a two-step paging in External sub-paging area and adaptive in internal sub-paging area to reduce the total signaling cost and the sensitivity of the system with various user parameter by partition a sub-paging area into external sub-paging area and internal sub-paging area by adaptive individual . The first paging attempt to adaptive individual for MN to "optimal size" of paging area essentially. If mobile user is found then the first paging procedure is terminate. if not, the paging imitator continues to send paging message to the external sub-paging area, which mean the rest of sub paging area receive paging messages in the second step. The performance of TSAP-MIP is compare via mathematical analysis and simulation. In addition, investigate the performance of TSAP-MIP when MNs move faster TSAP-MIP performs batter than TSP-MIP, ADLP-MI, DLP-MIP. P-MIP and Mobile IP. so in further we will analysis and simulation for the time average paging delay for TSAP-MIP.