IP Paging Schemes Adaptive to Mobile Host Parameters

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1 948 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.4 APRIL 25 PAPER Special Section on Selected Papers from the 17th Workshop on Circuits and Systems in Karuizawa IP Paging Schemes Adaptive to Mobile Host Parameters Hung Tuan DO a), Student Member and Yoshikuni ONOZATO, Member SUMMARY One of the remaining issues of Mobile IP is a mobile host (MH) needs to update its location each time it moves from one subnet to another, even when it is in dormant mode while roaming. This practice is apparently not efficient in terms of location update cost and power consumption. Recent research works have attempted to address that problem by extending Mobile IP with a layer 3 paging mechanism so-called IP paging. Particularly, IP Individual Paging schemes, which are customized to each MH, have attracted considerable interest of researchers. The employment of adaptability in some manner to MH parameters in order to enhance the efficiency of IP paging schemes is probably a promising approach. In this paper, we present an analysis on the effects of both host-adaptability and time-adaptability to MH parameters in Individual Paging schemes by comparing the signaling cost of an adaptive Individual Paging scheme to that of a non-adaptive counterpart. From our analysis, specifying the optimal paging area (PA) is critical in saving signaling cost of IP paging. Thus, our investigation is focused on the adaptability of PA to maintain its optimality. key words: mobile IP, IP paging, individual paging 1. Introduction In the next generation of wireless networks as all IP-based networks, mobility management should be most appropriately performed at IP layer. The current standard protocol of IP layer mobility management is Mobile IP. Unfortunately, the mobility management performance of Mobile IP is still ineffective, and thus, it calls for further extension and enhancement. Similar to PCSs, the demand of reduced signaling cost and power saving is greatly desirable for inactive but moving MHs in this setting. This demand has led to the current efforts of research on a new protocol to support paging at IP layer, which is referred to as IP Paging. In IP paging, a dormant MH while moving from one subnet to another within the PA does not need to update its location as it does in the standard MIP. When the MH moves out of its current PA to another PA, it performs a location update. Also, when there is an incoming IP session destined to the MH in standby mode, the network will page the MH within the current PA to locate it, and then IP packet delivery can be followed. Although there are no official definitions, the terms of paging protocol and paging scheme are sometimes dif- Manuscript received June 29, 24. Manuscript revised October 7, 24. Final manuscript received December 6, 24. The authors are with the Department of Computer Science, Graduate School of Engineering, Gunma University, Kiryu-shi, Japan. a) hung@nztl.cs.gunma-u.ac.jp DOI: 1.193/ietfec/e88 a ferentiated in IP paging. Paging protocols [1] determine which node initiates paging process and defines the messages exchanged among nodes and are responsible for updating and maintaining paging state. Three paging protocols proposed in [1] are Home Agent (HA) paging, Foreign Agent (FA) paging and Domain paging where the paging initiators are HA, FA and domain root router, respectively. Paging schemes, on the other hand, determine the mechanism to construct PAs and update them. IP paging schemes proposed so far can be broadly categorized into two groups: Static Aggregate Paging (SAP) [6] schemes and Individual or Personal Paging schemes. SAP is the traditional approach employed in PCSs and current IP paging proposals of the IETF, in which PAs are static and common to all MHs. Individual paging schemes are motivated by the observation that mobility and communication patterns of MHs vary, and thus, a paging scheme adaptive to each MH would perform more efficiently. Individual Paging schemes may differ from one to another on how adaptive they are as presented in [2], [5] and [6]. We differentiate further two sub-groups of Individual Paging schemes: Static Individual Paging (SIP): The optimal PA size k opt in terms of the number of subnets covered is pre-computed before the time of investigation and will not be changed during that time; Dynamic Individual Paging (DIP): the optimal PA size k opt is adaptive to the MH s current mobility and call parameters such as dwell time and incoming IP session rate. The obvious advantages of SAP are the ease of its implementation and low complexity of computation. At the same time, since MH mobility and communication parameters vary from one to another, and from time to time, SAP may not work effectively for individual MH. In contrast, Individual Paging schemes are customized accordingly to each MH, depending on its parameters. While they enjoy distinct advantages over SAP, the implementation of Individual schemes is usually much more difficult and requires the participation of MHs in terms of computation and communication. Several initial research works have been done on IP paging. An exhaustive description of the research works in literature can be found in [6]. In [5], the authors proposed a practical solution for adaptive Individual IP Paging by sharing load of configuration and calculation between the network and MHs. More precisely, the optimal PA size is computed per-host while the PA shape is constructed based on the aggregate mobility patterns of all MHs. In essence, Copyright c 25 The Institute of Electronics, Information and Communication Engineers

2 DO and ONOZATO: IP PAGING SCHEMES ADAPTIVE TO MOBILE HOST PARAMETERS 949 this solution may construct quasi-optimal PAs, but how far they are from the optimal was not evaluated in the paper. Reference [4] presents a methodology to numerically evaluate the performance of dynamic schemes of location area (LA) management in the context of cellular networks in comparison with the static counterpart. Reference [3] follows this approach in contrasting the performance of dynamic LA management schemes and that of static schemes in the setting of MIP and the wireless Internet. This methodology is employed in our paper to investigate the adaptability in IP paging schemes. While the merits of Individual Paging schemes, compared with SAP schemes, are investigated in the literature [2], [6], the effect of the adaptability of individual paging schemes is still an open problem and that is the focus of our work. Due to the fact that MH parameters can be variable, the optimal PA in terms of its shape and size might be highly changing. Therefore, it is desirable not only to configure the PA individually adaptive to each MH, according to its parameters, but also to specify time-adaptive PA that minimizes the total signaling cost of the MH, depending on its current parameters. In this paper, we concentrate on evaluating both time adaptability and host adaptability to mobility and communication parameters in Individual Paging schemes. The findings would help to evaluate the efficiency of adaptive schemes with respect to different variant parameters since the adaptability certainly incurs more computation complexity. For this purpose, we compare analytically the signaling cost of DIP an adaptive Individual Paging scheme, to that of SIP a non-adaptive counterpart under the impact of host-variant and time-variant mobility and communication parameters, namely dwell time and incoming IP session rate. The rest of the paper is organized as follows. Section 2 describes our mobility model and total signaling cost function for the Individual Paging scheme at hand. Section 3 discusses the host adaptability and time adaptability in IP paging. Our numerical analysis and results are presented in Sect. 4. Finally, Sect. 5 concludes the paper and mentions some directions of our future works. 2. Signaling Cost Function 2.1 Mobility Model In this paper, we assume that MH mobility follows the discrete system model [3], in which each MH can move randomly among N subnets and the probability of its movement from one subnet to any of the others is 1/(N 1). Let M be a random variable so that the MH moves out of the PA at the Mth movement [3]. This model well captures the spatial nature of the wireless Internet: a subnet can take an arbitrary shape and the distance between two points of attachment should be considered in terms of the number of hops. In our Individual Paging schemes, a PA is customized to each MH, and more precisely, the PA consists of the first Fig. 1 Adaptive PA in Individual Paging schemes. k non-repeated subnets visited by the MH, supposed that the PA size is k as illustrated in Fig. 1 where k = 5andM = 6. The idle MH moving among the subnets within the PA is not required to update its location. When the MH moves out of the PA with the rate denoted as U k, it is then required to make a location update to the HA. Subsequently, a new PA will be constructed adaptively to the MH s movement in the same way. The expectation of M in these schemes is the summation of the expectation of the number of movements with which an MH has visited different k subnets and the expectation of the number of movements that an MH moves within specific k subnets. Similar to [3] and [4], the expectation of M in SIP and DIP can be derived: E[M SIP ] = E[M DIP ] = 1 + (N 1) k i=1 The rate U k in these schemes can be obtained: U k = 1 E[M SIP ]T d = 1 N i (1) 1 E[M DIP ]T d (2) where T d denotes the dwell time of an MH in a subnet. 2.2 Assumptions and Parameters All parameters and their notations used in our analysis are shown in Table 1. In this paper, we make the following assumptions: The MH-HA distance d mh is assumed as fixed during the time of investigation. Successive calls are not overlapped, i.e., the MH always accomplishes a call then turns into standby mode before the next call arrives. With this assumption, the MH is paged at each incoming IP session. 2.3 Total Signaling Cost Functions As we have shown in [6], the total signaling cost function of MIP with the FA paging protocol and Individual paging schemes comprises of three cost elements: paging cost P,

3 95 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.4 APRIL 25 Table 1 List of parameters. the cost of location update following each paging U 1 and the cost of location update due to the movement of the MHU 2. P consists of the cost of paging via air interfaces of all k subnets in the PA and the cost of wired communication when the last-registered FA contacts other FAs in the PA via wired links and routers. Under the assumption of one level of hierarchy of FAs, P is derived as shown in [6]: P = kλ(c p + αc u ) (3) U 1 is equal to the cost of the registration of the MH s new FA to the HA with acknowledgment plus the communication cost when the new FA contacts the last-registered FA and the last-registered FA forwards the buffered packet to the new FA as demonstrated in [6]: U 1 = 2λαC u (d mh + d fp + β) (4) U 2 is the product of the registration cost and the location update rate U k as obtained in [6]: U 2 = 2αC u (d mh + β)u k (5) The total signaling cost functions of SIP and DIP denoted as S SIP and S DIP, respectively, are given as follows: S SIP (k,λ,t d ) = S DIP (k,λ,t d ) = P + U 1 + U 2 (6) 3. Host Adaptability and Time Adaptability In general analysis, it is desirable for a paging scheme to be both host and time adaptive so that the PAs constructed are optimal for each MH at any time. However, the effects on the total signaling cost of adaptability to various parameters may not be the same as shown in our numerical results. Thus, to be efficient, considering the extra computing load incurred by the adaptability and the benefit in terms of signaling cost obtained by employing the adaptability, a paging scheme may not need to be adaptive to all varying parameters at the same time. In this paper, our analysis is focused on the effects of both host adaptability and time adaptability to varying host parameters. More precisely, different aspects of the adaptability of PA in IP paging schemes are evaluated by comparing the total signaling costs of SIP and DIP. Host-adaptive PA is customized to each MH while time-adaptive PA is changed adaptively to varying host parameters such as dwell time T d and incoming IP session rate λ. Aswehaveshown in [6], PA size and shape are critical in saving the signaling costs of MHs. The bigger the PA is, the less frequently the MH updates its location due to its moving out of the PA. At the same time, with the blanket polling, the paging cost is proportional to the PA size. This is the tradeoff between paging cost and location update cost. Regarding the shape of PAs, a PA customized to the MH s mobility pattern may cover the MH longer, and hence, results in lower location update cost. The shape of PAs in our IP Paging schemes SIP and DIP is specified in the same way as described in Sect. 2. Thus, what we need to consider is the adaptability of the optimal PA size k opt to varying parameters when comparing these two schemes. Asshownin[6],k opt can be considered as a function of T d and λ. The total signaling cost functions of SIP and DIP with the optimal PA sizes can be denoted as S SIP (k opt SIP (λ, T d ),λ,t d )ands DIP (k opt DIP (λ, T d ),λ,t d ), respectively, where k opt SIP (λ, T d ) is the optimal PA size of SIP that is pre-computed before the time of investigation, based on the average IP session arrival rate λ and the average dwell time T d ; k opt DIP (λ, T d ) represents the optimal PA size of DIP that is adaptively changed according to the current host parameters during the time of investigation. We evaluate the merit of the adaptability of the optimal PA size by comparing SIP and DIP under the impacts of hostvariant and time-variant parameters, similar to the method presented in Sect. 5 of [3]. 4. Numerical Results In this section, we present the computational models that represent four cases of consideration: host-variant T d, timevariant T d, host-variant λ and time-variant λ, and then, the numerical results are demonstrated accordingly. Based on the numerical results with various ranges of parameters, we investigate the impacts of host and time adaptability to T d and λ. The assumed numerical values of the parameters used in our computation are as follows: N = 3, d mh = 3, d fp = 2, C p = 3, C u = 1, α = 1, and β = Impact of Adaptability to Dwell Time T d First, we evaluate the host adaptability to dwell time T d by investigating SIP and DIP under the impact of host-variant T d. Similar to [3], [4], we assume there are two groups of MHs: the high mobility MHs of Group 1 with T d of the exponential distribution f 1 (T d ) with the mean T d1 =.1; and

4 DO and ONOZATO: IP PAGING SCHEMES ADAPTIVE TO MOBILE HOST PARAMETERS 951 Fig. 2 DIP vs. SIP under the impact of host-variant dwell time T d. (T d1 =.1, T d2 = 1., σ = 1.) Fig. 3 DIP vs. SIP under the impact of host-variant T d. (T d1 = 5., T d2 = 6., σ = 1.) the low mobility MHs of Group 2 with T d of the Normal distribution f 2 (T d ) with the mean T d2 = 1. and the variance σ 2 = 1. Each group accounts for 5% of the total number of MHs. This model typically represents the scenario in which T d varies from host to host. The pdf f (T d )ofthet d of a randomly selected host is given by: f (T d ) =.5 f 1 (T d ) +.5 f 2 (T d ) The total signaling costs of SIP and DIP denoted as C SIP and C DIP, respectively, can be computed for host-variant T d as: C SIP = C DIP = f 1 (T d )S SIP [k opt SIP (λ, T d1 ),λ,t d ]dt d (7) f 2 (T d )S SIP [k opt SIP (λ, T d2 ),λ,t d ]dt d (8) f (T d )S DIP [k opt DIP (λ, T d ),λ,t d ]dt d (9) Figure 2 shows the total signaling costs of SIP and DIP with respect to λ under the impact of host-variant T d.itis obvious from the figure that, the total signaling cost of DIP is lower than that of SIP at any value of λ. This result is due to the host adaptability of DIP to changing T d of the host concerned. The optimal PA size is pre-computed then fixed in SIP, but it is computed adaptively to the changing T d of the MH in DIP. When the values of T d1 and T d2 are close, however, the cost gap between the two schemes becomes narrower. This tendency is illustrated in Fig. 3 with T d1 = 5. andt d2 = 6.. This shows that the benefit of DIP over SIP owing to the host adaptability to T d mainly depends on the diversity of MH population in terms of T d. In the scenario that mobility of the MH population becomes roughly uniform, the benefit offered by the host adaptability to T d is insignificant. Secondly, we consider the time adaptability to T d by comparing SIP and DIP under the impact of time-variant T d. In this investigation, λ is fixed while T d has the exponential distribution f 3 (T d ) with the mean T d,wheret d is varying with the time. Fig. 4 DIP vs. SIP under the impact of time-variant T d.(λ = 3.) The total signaling costs of SIP and DIP for timevariant dwell time T d are given by: C SIP = C DIP = f 3 (T d )S SIP (k opt SIP,λ,T d )dt d (1) f 3 (T d )S DIP [k opt DIP (λ, T d ),λ,t d ]dt d (11) Figure 4 shows the total signaling costs of these schemes against T d when λ = 3., given the optimal PA size k opt SIP was pre-computed with T d =.1andT d = 1., respectively. It is observed from our investigation with various values of λ from 1 to 1, that when T d is large, i.e. low mobility, the advantage of DIP over SIP is not very much, but when T d is low, i.e. high mobility, the advantage is considerable. DIP is better than SIP for any value from.1to1. of T d that is used to pre-compute k opt SIP in SIP. While T d is changing, the total signaling cost calculated with the precomputed optimal PA size k opt SIP is usually far from the optimal because k opt SIP itself is far from the optimal during the time of investigation. Based on our numerical results, the optimal PA size is very sensitive to T d. The time adaptability to T d is shown to be substantially rewarding when MH mobility varies greatly with the time.

5 952 IEICE TRANS. FUNDAMENTALS, VOL.E88 A, NO.4 APRIL 25 Fig. 5 DIP vs. SIP under the impact of host-variant λ. (λ 1 =.1, λ 2 = 1., σ 2 = 1.) Fig. 6 DIP vs. SIP under the impact of host-variant λ. (T d = 1.) Our results also underline the importance of estimating the T d value used to pre-compute k opt SIP in SIP. When this estimated value is far from its real time value, the total signaling cost of SIP may be much higher than that of DIP. 4.2 Impact of Adaptability to λ Similarly, first, we evaluate the host adaptability to λ by assessing SIP and DIP under the impact of host-variant λ. The value of T d is fixed in this assessment. We assume there are two independent groups of MHs: Group 1 consists of the MHs with the incoming IP session rate λ of the exponential distribution with the mean λ 1 =.1; Group 2 comprises of the MHs with λ of the Normal distribution with the mean λ 2 = 1. and the variance σ 2 = 1. This assumption reflects the diversity of MH population regarding λ. The detailed equations of calculation are similar to those presented in Sect. 4.1, and thus, not shown in this subsection. Figure 5 shows the total signaling costs of SIP and DIP with respect to T d. It is observed that the total signaling costs of SIP and DIP are not much different under the impact of host-variant λ. This is due to the fact that the optimal PA size is less sensitive to the host-variant λ than to T d.more generally, the host adaptability to λ is not beneficial even when the MH population is highly diversified in terms of λ. Next, we investigate the time adaptability to λ by comparing the total signaling costs of DIP and SIP under the impact of time-variant λ. ForallMHs,T d is fixed while λ has the exponential distribution with the average incoming IP session rate λ. Figure 6 plots the total signaling costs as functions of λ when T d = 1., indicating low mobility. The optimal PA size k opt SIP was pre-computed with λ =.1 andλ = 1., respectively. When k opt SIP is pre-computed with the values of λ in the range from.1to 1., our results with various values of T d 4 indicate that the difference between the total signaling cost of SIP and that of DIP is negligibly small. This fact once again confirms that the optimal PA size is not sensitive Fig. 7 DIP vs. SIP under the impact of host-variant λ. (T d =.2) to the time-variant λ for the MHs with low mobility, and hence, the time adaptability to λ does not result in critically lower total signaling cost. Nonetheless, for the MHs with high mobility, e.g. T d =.2, the time adaptability to λ is quite effective as shown in Fig. 7, especially when the value of λ for pre-computing k opt SIP is far from its real value. In summary, time adaptability to λ would be beneficial for the MHs of large mobility and highly time-variant λ,but might offer trivial benefit for the MHs of low mobility. 5. Conclusion We have investigated the impact of both host adaptability and time adaptability to dwell time and incoming IP session rate in individual IP paging schemes. Our results demonstrate that while adaptive paging schemes posses certain advantages in terms of signaling cost, the impacts of the user and time adaptabilities to different parameters may vary considerably. Specifically, the adaptability to MH mobility is highly rewarding, while the adaptability to incoming session rate is recommendable only for MHs of high mobility. As the adaptability always incurs more computing load on MHs, the efficiency of the employment of adaptability in

6 DO and ONOZATO: IP PAGING SCHEMES ADAPTIVE TO MOBILE HOST PARAMETERS 953 Individual Paging schemes should be carefully considered based on these impacts. Our data show that predicting the values of MH parameters, particularly dwell time, for precomputing the optimal PA size is very important to the total signaling cost of SIP. In our future works, we will consider constructing the optimal PAs time-adaptive to each MH from implementation viewpoints, taking into account the tradeoff between computation complexity and signaling cost saving. References [1] R. Ramjee, L. Li, T.L. Porta, and S. Kasera, IP paging services for mobile hosts, Wirel. Netw., vol.8, pp , 22. [2] C. Castellucia, Extending mobile IP with adaptive individual paging: A performance analysis, ACM Mobile Computing and Communication Review (MC2R), vol.5, no.2, pp.14 26, April 21. [3] J. Xie and I.F. Akyildiz, A novel distributed dynamic location management scheme for minimizing signaling costs in Mobile IP, IEEE Trans. MobilCom, vol.1, no.3, pp , July Sept. 22. [4] H. Xie, S. Tabbane, and D.J. Goodman, Dynamic location area management and performance analysis, Proc. 43rd IEEE VTC, pp , [5] C. Castellucia and P. Mutaf, An adaptive per-host IP paging architecture, ACM SIGCOMM Computer Communication Review (CCR), vol.31, no.5, pp.48 56, Oct. 21. [6] H.T. Do and Y. Onozato, A comparative analysis on the performance of Mobile IP with paging support, First IFIP TC6 Working Conference, WONS 24, Madonna di Campiglio, Italy, Jan. 24, R. Battiti, M. Conti, and R.L. Cigno, eds., Lecture Notes in Computer Science 2928, pp , Springer. Hung Tuan Do received the B.E. degree in Electrical Engineering and Computer Science from Hanoi University of Technology, Vietnam, and the M.S. degree in Computer Science from Gunma University, Japan. Currently, he is a Ph.D. candidate at Gunma University. His research interests include Mobility Management, Wireless Internet and Mobile Ad hoc Networks. Yoshikuni Onozato is a Professor with Gunma University. His research interests are in satellite systems, computer communication networks and distributed computing systems and span the entire spectrum from the design and performance evaluation of these systems to their implementation. He is a member of IEEE, ACM, IPSJ, and ORSJ.