This section studies the effects of MS mobility behaviors on the r(td) and ρ(td) performances.
From (3) and (34), it is clear that r(td) and ρ(td) are independent from the distribution for tm, indicating that the MS mobility behavior in non-overlapped areas of the macrocell does not affect the r(td) and ρ(td) performances. Therefore, in the following, we only study the effects of MS mobility behavior in the overlapped femtocell.
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
r(td) (%)
10−5 10−4 10−3 10−2
E[td] (unit: 1/λ)
. .
..............................................................................................................................................................................................................................................................................................................................................................................................................................................................
⊲
⊲
⊲
⊲
.
..................................................................................................................................................................................................................................................................................................................................................................................................................................................................
⋆
⋆
⋆
⋆
. .
...................................................................................................................................................................................................................................................................................................................................................................................................................................................................
◦
◦
◦
◦
.
.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................
⋄
⋄
⋄
⋄
⊲ηf = λ
⋆ηf = 10λ
◦ηf= 102λ
⋄ηf= 103λ
(a) Performance of Signaling Overhead Ratio
75 80 85 90 95 100
ρ(td) (%)
10−5 10−4 10−3 10−2
E[td] (unit: 1/λ)
.
..............................................................................................................................................................................................................................................................................................................................................................................................................
⊲................................................................................................................................⊲....................................................................................................................................⊲......................................................................................................................................⊲.....
⋆................................................................................................................................⋆....................................................................................................................................⋆..............................................................................................................................................................⋆.........
◦ ◦ ◦
◦
.
.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
⋄ ⋄
⋄
⋄
⊲ηf = λ
⋆ηf = 10λ
◦ηf= 102λ
⋄ηf= 103λ
(b) Performance of Potential Offload Traffic Ratio
Fig. 3. The effects ofηf onr(td)andρ(td)(ηm = 25λ,vm = 1/ηm2,vf = 100/ηf2)
Effects of Mean of Femtocell Residence Time 1/ηf: In Figure 3, we study the effects of the femtocell residence time, where E[td] is set from 10−5/λ (i.e., 0.03 seconds) to 10−2/λ (i.e., 30 seconds), ηm = 25λ (i.e., E[tm] = 2 minutes), and vm = 1/ηm2. We set vf = 100/ηf2 to simulate the real MS mobility behavior that the MS either stays in the femtocell for a long period or just passes by the femtocell.
As shown in Figure 3 (a), r(td) decreases as ηf increases. A larger ηf implies that the MS stays in the overlapped femtocell for a shorter period. This is when a transient phenomenon might likely occur, during which more registration traffic can be avoided in the DR algorithm. Figure 3 (a) also indicates that the longer we set the delay timer, the more registration avoided, i.e., r(td) decreases as E[td] increases. In Figure 3 (a), we observe that the DR algorithm reduces at least 85% of registration signaling overhead.
On the other hand, in Figure 3 (b), ρ(td) decreases as ηf increases, i.e., with the delay timer, the transient phenomenon reduces traffic offloading capability of the femtocell.
We observe that the DR algorithm causes at most 24% of the degradation of the traffic of-floading capability (i.e., ρ(td) ≈ 76% when ηf = 103λ and E[td] = 10−2/λ). To summarize,
the DR algorithm significantly reduces the registration signaling overhead. Meanwhile, the DR algorithm sustains good performance for the traffic offloading capability of the femtocell.
In the following, we discuss how to set up the delay timer adapting to different MS mobility behaviors to achieve better r(td) performance while minimizing the loss in traffic offload capability. Observe the “⋄” curves in Figure 3 (a) and (b), where ηf = 103λ (i.e., E[tf] = 3 seconds). In this mobility scenario, the MS stays in the overlapped femtocell for transient periods. Figure 3 (a) indicates how the r(td) values drop linearly (i.e., better r(td) performance is obtained; from 9% to 2.3%) as E[td] increases from 10−5/λ to 10−2/λ. However, Figure 3 (b) indicates that when E[td] ≤ 10−3/λ, the ρ(td) performance decreases slightly (from 100% to 95%) as E[td] increases, but when E[td] >
10−3/λ, the ρ(td) performance drops very quickly (from 95% to 76%). To summarize, we prefer to set E[td] ≤ 10−3/λ (i.e., 3 seconds).
For other mobility scenarios, ηf = λ, ηf = 10λ, and ηf = 100λ (see “⊲”, “⋆”, and “◦”
curves), we prefer to set E[td] = 10−2/λ (i.e., 30 seconds) because when E[td] = 10−2/λ, we achieve the best r(td) performance with loss of traffic offloading capability no larger than 5% (i.e., ρ(td) = 95%).
Effects of Variance of Femtocell Residence Time vf: In Figure 4, we study the effects of the variance vf of the femtocell residence time, where E[td] is set from 10−5/λ (i.e., 0.03 seconds) to 10−2/λ (i.e., 30 seconds), ηm = 25λ, ηf = 100λ, and vm = 1/η2m. As vf
increases, it is more likely to observe an MS with short and long residence time in an overlapped femtocell, so the MS mobility behavior in the femtocell is more “dynamic”.
For short tf periods, it is more likely that an MS moves out of an overlapped femtocell before the delay timer td expires. The MS has less chance to execute the registration in the overlapped femtocell, reducing more signaling overhead caused by registration.
Therefore, we observe r(td) decreases as vf increases in Figure 4 (a).
On the other hand, for longer tf periods, the MS is more likely to have call requests
0 10 20 30 40 50 60 70 80 90 100
r(td) (%)
10−1 1 10 102 103 104
vf (unit: 1/η2f)
..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
⊲
⊲
⊲
⊲ ⊲ ⊲
...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
⋆
⋆
⋆
⋆
⋆ ⋆
.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
◦ ◦
◦
◦
◦ ◦
.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
⋄ ⋄
⋄
⋄
⋄ ⋄
⊲E[td] = 10−2/λ
⋆E[td] = 10−3/λ
◦E[td] = 10−4/λ
⋄E[td] = 10−5/λ
(a) Performance of Signaling Overhead Ratio
30 40 50 60 70 80 90 100
ρ(td) (%)
10−1 1 10 102 103 104
vf(unit: 1/ηf2)
.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
⊲
⊲
⊲
⊲ ⊲ ⊲
.
..................................................................................................................................................................................................................................................................................................................................................................................................................................................
⋆ ⋆
⋆ ⋆ ⋆ ⋆
.
...................................................................................................................................................................................................................................................................................................................................................................................................................................
◦..............................................................................◦....................................................................................◦....................................................................................◦....................................................................................◦....................................................................................◦......
⋄ ⋄ ⋄ ⋄ ⋄ ⋄
⊲E[td] = 10−2/λ
⋆E[td] = 10−3/λ
◦E[td] = 10−4/λ
⋄E[td] = 10−5/λ
(b) Performance of Potential Offload Traffic Ra-tio
Fig. 4. The effects ofvf onr(td)andρ(td)(ηm = 25λ,ηf = 100λ,vm = 1/η2m)
through the long-residence femtocell. More requests are potentially processed by the femtocell. Therefore, larger ρ(td) is observed as vf increases in Figure 4 (b).
To summarize, when the MS mobility is more dynamic, the DR algorithm can work more effectively (i.e., both r(td) and ρ(td) have better performance when vf is larger).
In addition to the Gamma distribution, in this study, we also considered the Weibull distribution for MS mobility behaviors, which has also been widely used to approximate real MS mobility patterns in many MCN studies (e.g., [22], [23]). Note that the Weibull distribution does not have a closed-form expression for its Laplace transform [24]. Therefore, the closed-form expressions of r(td) and ρ(td) for the Weibull distribution do not exist in our analytical models. Instead, we run simulation experiments to study effects of MS mobility on r(td) and ρ(td) for the Weibull distributed residence times. We observe similar performance trends for both the Weibull and Gamma distributions, and thus we do not include the performance evaluation for the Weibull distributed residence times.
0
Solid lines: Exponential td
Dashed lines: Fixed td
⊲E[td] = 10−1/λ
⋆E[td] = 10−2/λ
(a) Performance of Signaling Overhead Ratio
0
Solid lines: Exponential td
Dashed lines: Fixed td
⊲E[td] = 10−1/λ
⋆E[td] = 10−2/λ
(b) Performance of Potential Offload Traffic Ra-tio
Fig. 5. The effects of fixed and exponential td on r(td) and ρ(td) (ηm = 25λ, vm = 1/ηm2, vf = 100/ηf2).
4.2 Effects of Fixed and Exponential td
In Figure 5, based on the simulation experiments, we study r(td) and ρ(td) against E[tf] for fixed and exponential td, where ηm = 25λ, vm = 1/ηm2, vf = 100/ηf2, and tf is Gamma distributed. We observe that the performance trends of r(td) and ρ(td) for fixed td are similar to those for exponential td.
In Figure 5 (a), when E[td] = 10−1/λ and E[td] = 10−2/λ, r(td) for fixed td is about 0.5%
lower than that for exponential td. As E[tf] increases from 10−3/λ to 1/λ, this difference remains the same.
On the other hand, in Figure 5 (b), as E[tf] increases from 10−3/λ to 1/λ, the difference between ρ(td) of fixed td and that of exponential td diminishes from 2.5% to 0% for E[td] = 10−2/λ, and from 15% to 0% for E[td] = 10−1/λ. This difference is larger when E[td] is longer.
To summarize, the performance trends for E[td] = 10−1/λ and E[td] = 10−2/λ are very similar. To achieve better r(td) and ρ(td), we suggest to use exponential td setup when E[tf] < 10−1/λ and use fixed td setup when E[tf] ≥ 10−1/λ.
5 C
ONCLUSIONSIn this paper, we proposed a Delay Registration (DR) algorithm to reduce signaling overhead caused by frequent registrations, while noticing the slight decrease in traffic offloading capa-bility of femtocells. To avoid registrations during the transient period, in the DR algorithm, we introduce a delay timer to postpone the registration until the timer expires. We conducted analytical models and simulation experiments to study the performance of the DR algorithm in terms of the signaling overhead ratio r(td) and potential offload traffic ratio ρ(td). The analytical model is general enough to accommodate various MS mobility behaviors. Our performance study can provide network operators with guidelines to configure the delay timer. Our study indicates that the DR algorithm can significantly reduce the signaling overhead with slight loss of traffic offloading capability of the femtocells. Moreover when the MS mobility is more dynamic, the DR algorithm can work more effectively, i.e., lower signaling overhead ratio and higher potential offload traffic ratio.
A
CKNOWLEDGEMENTThe authors would like to express thanks to the four anonymous reviewers for their valuable comments. Their comments have significantly improved the quality of this paper.
R
EFERENCES[1] 3GPP, “3rd Generation Partnership Project; Technical Specification Group Radio Access Network; UTRAN Architec-ture for 3G Home Node B (HNB); Stage 2 (Release 9),” Tech. Rep. 3G TS 25.467, 3GPP, September 2009.
[2] Femto Forum. Femtocells, http://www.femtoforum.org.
[3] Chandrasekhar, V., Andrews, J. G., and Gatherer, A., “Femtocell Networks: A Survey,” IEEE Communications Magazine, vol. 46, pp. 59–67, September 2008.
[4] 3GPP, “3rd Generation Partnership Project; Technical Specification Group Services and Systems Aspects; Network architecture (Release 9),” Tech. Rep. 3G TS 23.002, 3GPP, November 2009.
[5] Broad Forum. Broadband, http://www.broadband-forum.org.
[6] 3GPP, “3rd Generation Partnership Project; Technical Specification Group Core Network and Terminals; Location Management Procedures (Release 8),” Tech. Rep. 3G TS 23.012, 3GPP, September 2009.
[7] Claussen, H., Ashraf, I., and Ho, L.T.W., “Dynamic Idle Mode Procedures for Femtocells,” Bell Labs Technical Journal, vol. 15, pp. 95–116, September 2010.
[8] Lei, Y. and Zhang, Y., “Efficient Location Management Mechanism for Overlay LTE Macro and Femto Cells,”
Proceedings of IEEE ICCTA’09 Conference, pp. 420–424, December 2009.
[9] Akyildiz, I. F., Ho, J. S. M., and Lin, Y.-B., “Movement-based Location Update and Selective Paging for PCS Networks,”
IEEE/ACM Transactions on Networking, vol. 4, pp. 629–638, Augest 1996.
[10] Lin, Y.-B., “Reducing Location Update Cost in a PCS Network,” IEEE/ACM Transations on Networking, vol. 5, pp. 25–33, February 1997.
[11] Lin, P. and Lin, Y.-B., “Implementation and Performance Evaluation for Mobility Management of a Wireless PBX Network,” IEEE Journal on Selected Areas in Communications, vol. 19, pp. 1138–1146, June 2001.
[12] Xiao, Y. and Guizani, M., “Optimal Paging Load Balance with Total Delay Constraint in Macrocell-Microcell Hierarchical Cellular Networks,” IEEE Transactions on Wireless Communications, vol. 5, pp. 2202–2209, August 2006.
[13] Wu, X., Mukherjee, B., and Bhargava, B., “A Crossing-Tier Location Update/Paging Scheme in Hierarchical Cellular Networks,” IEEE Transactions on Wireless Communications, vol. 5, pp. 839–848, April 2006.
[14] Park, K. I. and Lin, Y.-B., “Reducing Registration Traffic for Multi-tier Personal Communications Services,” IEEE Transactions on Vehicular Technology, vol. 46, pp. 597–602, August 1997.
[15] Lin, Y.-B. and Chlamtac, I., Wireless and Mobile Network Architectures. John Wiley and Sons, 2001.
[16] Fang, Y., “Movement-based Mobility Management and Trade Off Analysis for Wireless Mobile Networks,” IEEE Transactions on Computers, vol. 52, pp. 791–803, June 2003.
[17] Lin, P., Lin, Y.-B., and Jeng, J.-Y., “Improving GSM Call Completion by Call Re-Establishment,” IEEE Journal on Selected Areas in Communications, vol. 17, pp. 1305–1317, July 1999.
[18] Lin, Y.-B. and Lin, P., “Performance Modeling of Location Tracking Systems,” ACM Mobile Computing and Communi-cations Review, vol. 2, pp. 24–27, July-August 1998.
[19] Baccelli, F., Machiraju, S., Veitch, D., and Bolot, J. C., “The Role of PASTA in Network Management,” Proceedings of ACM SIGCOMM’06, pp. 231–242, September 2006.
[20] Nelson, R., Probability, Stochastic Processes, and Queueing Theory. Springer-Verlag, 1995.
[21] Lin, Y.-B. and Yang, S.-R., “A Mobility Management Strategy for GPRS,” IEEE Transactions on Wireless Communications, vol. 2, pp. 1178–1188, November 2003.
[22] Hung, H.-N., Lee, P.-C., and Lin, Y.-B., “Random Number Generation for Excess Life of Mobile User Residence Time,”
IEEE Transactions on Vehicular Technology, vol. 55, pp. 1045–1050, May 2006.
[23] Khan, F. and Zeghlache, D., “Effect of Cell Residence Time Distribution on The Performance of Cellular Mobile Networks,” Proceedings of IEEE Vehicular Technology Conference, pp. 949–953, May 1997.
[24] Fischer, M., Gross, D., Masi, D., and Shortle, J., “Analyzing The Waiting Time Process in Internet Queueing Systems with The Transform Approximation Method,” The Telecommunications Review, vol. 12, pp. 21–32, 2001.
B
IOGRAPHYHuai-Lei Fu received his bachelor and master degrees in Computer Science and Information Engineer-ing from Tatung University and Yuan Ze University in 2005 and 2007, respectively. Since September 2007, he enrolled his Ph.D. program in the Department of Computer Science and Information Engineer-ing (CSIE), National Taiwan University. Now, he is a Ph.D. candidate. His research interests include machine-to-machine communications network, multicast and broadcast service, mobility management, performance modeling, and wireless sensor network. He has received the YZU Academic Silver Medal Award in 2006, the YZU School Work Silver Medal Award in 2006, the Y. Z. Hsu Scholarship Award in 2006 and 2007, and the NTU Outstanding Student Award (Academic Category) in 2009. He is an IEEE student member.
Phone Lin is Professor in National Taiwan University (NTU), holding professorship in the Department of CSIE, Graduate Institute of Networking and Multimedia, Telecommunications Research Center, and Optoelectronic Biomedicine Center. Lin serves on the editorial boards of IEEE Trans. on Vehicular Technology, IEEE Wireless Communications Magazine, ACM/Springer Wireless Networks, Computer Networks, Wireless Communications and Mobile Computing, Security and Communication Networks, IEEE/KICS Journal of Communications and Networks, and Journal of Wireless Mobile Network, Ubiq-uitous Computing and Applications. He is Guest Editor of IEEE Wireless Communications Magazine and ACM/Springer Mobile Networks and Applications. He has also been involved in several prestigious conferences, such as holding the Technical Program Chair of WPMC 2012. Lin has received numerous research awards, including Junior Researcher Award of Academia Sinica in 2010, Ten Outstanding Young Persons Award of Taiwan in 2009, Best Young Researcher of IEEE ComSoc Asia-Pacific Young Researcher Award in 2007, Youth Engineer Award of the Chinese Institute of Electrical Engineering in 2006, Wu Ta You Memorial Award of NSC in 2005, Fu Suu-Nien Award of NTU in 2005, Research Award for Young Researchers of Pan Wen-Yuan Foundation in 2004, and K. T. Li Young Researcher Award honored by ACM Taipei Chapter in 2004. Lin is IEEE Senior Member and ACM Member. He received his BSCSIE and Ph.D. degrees from National Chiao Tung University (NCTU) in 1996 and 2001, respectively. Lin’s email and website address are [email protected] and http://www.csie.ntu.edu.tw/∼plin/, respectively.
Yi-Bing Lin is Vice President and Lifetime Chair professor of National Chiao Tung University (NCTU).
He serves on the editorial board of IEEE Trans. on Vehicular Technology. He is General or Program Chair for prestigious conferences including ACM MobiCom 2002. He is Guest Editor for several journals including IEEE Transactions on Computers. Lin is the author of the booksWireless and Mobile Network Architecture (Wiley, 2001), Wireless and Mobile All-IP Networks(John Wiley, 2005), and Charging for Mobile All-IP Telecommunications(Wiley, 2008). Lin received numerous research awards including 2005 NSC Distinguished Researcher, 2006 Academic Award of Ministry of Education and 2008 Award for Outstanding contributions in Science and Technology, Executive Yuen, 2011 National Chair Award, and TWAS Prize in Engineering Sciences, 2011 (The Academy of Sciences for the Developing World). He is in the advisory boards or the review boards of various government organizations including Ministry of Economic Affairs, Ministry of Education, Ministry of Transportation and Communications, and National Science Council. He is a member of board of directors, Chunghwa Telecom. Lin is AAAS Fellow, ACM Fellow, IEEE Fellow, and IET Fellow.