Chapter 6 Conclusions and Future Works
A.2 Notation for Chapter 3
z Lj=(xj,yj): the coordinate of the SGSN where the MS resides after j movements
z K: the number of AVs obtained from the HSS/AuC in an ADR
z T: the reservation timeout period
z ti: the SGSN residence time of the i-th visit to L0
z Ni: the number of ADRs performed at the i-th visit to L0
z Ri: the number of unused AVs left when the MS leaves L0 at the i-th visit
z λ: the arrival rate of UAR
z 1/µ: the expected SGSN residence time
z Pj: the probability that the MS returns to L0 at the j-th movement (i.e., Pj = Pr[Lj =L0])
z Q2n: the probability that the MS first returns to L0 at the 2n-th movement (i.e., Q2n = Pr[L2n =L0, L2l ≠ L0 for 0<l<n])
z t*j: the residence time at SGSN Lj
z t r: the period between when the MS leaves L0 and when it returns.
That is, t r = t*1 + t*2+…+ t*(2n-1), where L2n = L0, and L2l ≠ L0 for 0<l<n
z F(2n, tr): the cumulative distribution function that the MS returns to L0 at 2n-th movement at time t r
z Sk: a state indicating that there are k AVs stored in SGSN L0
z πk: the probability that k AVs are stored in SGSN L0 while the system is at the steady state. That is, πk = Pr[the process is at state Sk]
z H(∆s)= (pi,j): transition probability matrix, where pi,j presents the transition probability from Si to Sj
z H: transition rate matrix
z
ψ
T: the expected AV storage consumed when T>0z Θ(Ni, Ri-1, Ri, ti): the probability that at the i-th visit to L0, Ri-1 unused AVs are stored in SGSN L0, where R0=0. The residence time of the i-th visit to L0 is ti. During ti, Ni ADRs occur, and Ri unused AVs are left when the MS leaves L0
z φ(Ni, Ri-1): the probability that when the MS enters L0 at the i-th visit, Ri-1 unused AVs is stored in SGSN L0, and Ni ADRs are performed during the residence time of i-th visit
z Γ(Ni, T): the probability that Ni ADRs occur at the i-th visit to L0, where i ≥ 1, Ni,>0, and the length of the RT period is T
z E[N|K]: the expected number of ADRs performed during one visit to SGSN L0, were K AVs are obtained in one ADR
z Vs: the variance of Gamma distributed SGSN residence times
z α: the probability that the MS re-enters L0 within timeout period T
z β: the expected AV storage consumed when T>0, which is normalized by the expected AV storage consumed when T=0
z δ: the number of ADRs performed in one visit to SGSN L0 as comparing with that when K=1. That is
] 1
| [
]
| [
= =
K N E
K N
δ
EReference
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Curriculum Vita
Lin-Yi Wu was born in Taipei, Taiwan, R.O.C., in 1976. She received the B.S. and M.S.
degrees from National Chiao Tung University, Hsinchu, Taiwan, in 1999 and 2001, respectively. Her current research interests include heterogeneous networks integration, personal communications services, and mobile computing.
Publication Lists
Journal Papers
1. Wu, L.-Y., and Lin, Y.-B. Authentication Vector Management for UMTS. submitted to IEEE Transactions on Wireless Communications.
2. Wu, L.-Y., Tsai, M.-H., Lin, Y.-B., and Yang, J.-S. A Client-Side Design and Implementation for Push to Talk over Cellular Service. Accepted and to appear in Wireless Communications & Mobile Computing Journal.
3. Chang, M.-F., Wu, L.-Y., and Lin, Y.-B. Performance Evaluation of a Push Mechanism for WLAN and Mobile Network Integration. IEEE Transactions on Vehicular Technology, 55(1): 380-383, 2006.
4. Lin, Y.-B., Chang, M.-F., Hsu M.-T., and Wu, L.-Y. One-Pass GPRS and IMS Authentication Procedure for UMTS. IEEE Journal on Selected Areas in Communications, 23(6): 1233-1239, 2005.
5. Wu, L.-Y., Chang, M.-F., and Lin, Y.-B. Corrigendum: WGSN: WLAN-based GPRS Support Node with Push Mechanism. The Computer Journal, 47(5): 624, 2004.
6. Feng, W.-S., Wu, L.-Y., Lin, Y.-B., and Chen, W.-E. WGSN: WLAN-based GPRS Support Node with Push Mechanism. The Computer Journal, 47(4): 405-417, 2004.
Conference Papers
1. Wu, L.-Y., Chang, M.-F., and Lin, Y.-B. Modeling the Push Mechanism for WGSN.
Internal Workshop on Broadband Wireless Services and Applications 2004 (BroadWISE 2004), San Jose, U.S., Oct. 2004.
2. Feng, W.-S., Wu, L.-Y., Lin, Y.-B., and Chen, W.-E. WGSN: Wireless LAN based GPRS Support Node. National Computer Symposium 2003, TaiChung, Taiwan, Dec.
2003.
Awards
1. Best Paper Award, Computer Society of the Republic of China, 2003.
2. Best Paper Award, National Computer Symposium 2003 (NCS2003).