Abstract

The connection provisioning problem attempts to achieve its objective of guaranteeing the maximum throughput and minimal blocking probability. In optical networks, this problem is mainly the classical routing and wavelength assignment (RWA) problem, which includes many constraints. In this study, we investigate the RWA problem for connection provisioning under multicast traffic while considering the optical power constraints. The problem is first formulated as a mixed-integer linear program (MILP) with the objective of minimizing the session blocking rate. In order to provide fast and efficient solutions, the paper introduces a novel heuristic solution that divides the problem into subproblems and solves them separately, while still taking the interdependency between them into account. The results obtained from both solutions are found to be closely comparable. The results obtained from the heuristic also provide insight for the network operators about the maximum performance enhancement that can be achieved by upgrading the network capacity.

© 2010 Optical Society of America

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References

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  1. H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, 2000.
  2. A. Hamad, T. Wu, A. Kamal, A. Somani, “Multicasting protocols for wavelength routing networks,” Comput. Netw., vol. 50, no. 16, pp. 3105–3164, 2006.
    [CrossRef]
  3. G. Rouskas, “Optical layer multicast: rationale, building blocks, and challenges,” IEEE Networks, vol. 17, no. 1, pp. 60–65, 2003.
    [CrossRef]
  4. L. Sahasrabuddhe, B. Mukherjee, “Light trees: optical multicasting for improved performance in wavelength routed networks,” IEEE Commun. Mag., vol. 37, no. 2, pp. 67–73, 1999.
    [CrossRef]
  5. D. Yang, W. Liao, “Design of light-tree based logical topologies for multicast streams in wavelength routed optical networks,” in IEEE INFOCOM 03, 2003, vol. 1, pp. 32–41.
  6. M. Ali, B. Ramamurthy, J. Deogun, “Routing and wavelength assignment with power considerations in optical networks,” Comput. Netw. ISDN Syst., vol. 32, no. 5, pp. 539–555, 2000.
    [CrossRef]
  7. A. Hamad, A. Kamal, “Optimal power-aware design of all-optical multicasting in wavelength routed networks,” in Proc. IEEE ICC 04, 2004, vol. 3, pp. 1796–1800.
  8. A. Hamad, A. Kamal, “Optical amplifier placement in WDM mesh networks for optical multicasting service support,” J. Opt. Commun. Netw., vol. 1, pp. 85–102, June 2009.
    [CrossRef]
  9. A. Hamad, A. Kamal, “Efficient power-aware network provisioning for all-optical multicasting in WDM mesh networks,” in IEEE GLOBECOM 08, 2008, pp. 1–5.
  10. B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Trans. Netw., vol. 6, no. 6, pp. 755–767, 1998.
    [CrossRef]
  11. B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol., vol. 16, no. 9, pp. 1560–1569, 1998.
    [CrossRef]
  12. A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.
  13. A. Sripetch, P. Saengudomlert, “Optimization for optical network designs based on existing power grids,” IEICE Trans. Commun., vol. E91-B, no. 3, pp. 689–699, 2008.
    [CrossRef]
  14. J. W. K. Wu, C. Yang, “Multicast routing with power consideration in sparse splitting WDM networks,” in IEEE Int. Conf. on Communication (ICC01), 2001, vol. 2, pp. 513–517.
  15. Y. Xin, G. Rouskas, “Multicast routing under optical layer constraints,” in IEEE INFOCOM 04, 2004, pp. 2731–2742.
  16. G. Markidis, S. Sygletos, A. Tzanakaki, I. Tomkos, “Impairment aware based routing and wavelength assignment in transparent long haul networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 48–57, 2007.
    [CrossRef]
  17. R. Ramaswami, K. N. Sivarajan, Optical Networks: A Practical Perspective. Morgan Kaufmann, 2nd ed., 2002.
  18. X. Zhang, J. Y. Wei, C. Qiao, “Constrained multicast routing in WDM networks with sparse light splitting,” J. Lightwave Technol., vol. 18, no. 12, pp. 1917–1927, 2000.
    [CrossRef]
  19. http://www.ilog.com/products/cplex/.

2009

2008

A. Sripetch, P. Saengudomlert, “Optimization for optical network designs based on existing power grids,” IEICE Trans. Commun., vol. E91-B, no. 3, pp. 689–699, 2008.
[CrossRef]

2007

G. Markidis, S. Sygletos, A. Tzanakaki, I. Tomkos, “Impairment aware based routing and wavelength assignment in transparent long haul networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 48–57, 2007.
[CrossRef]

2006

A. Hamad, T. Wu, A. Kamal, A. Somani, “Multicasting protocols for wavelength routing networks,” Comput. Netw., vol. 50, no. 16, pp. 3105–3164, 2006.
[CrossRef]

2003

G. Rouskas, “Optical layer multicast: rationale, building blocks, and challenges,” IEEE Networks, vol. 17, no. 1, pp. 60–65, 2003.
[CrossRef]

2000

M. Ali, B. Ramamurthy, J. Deogun, “Routing and wavelength assignment with power considerations in optical networks,” Comput. Netw. ISDN Syst., vol. 32, no. 5, pp. 539–555, 2000.
[CrossRef]

X. Zhang, J. Y. Wei, C. Qiao, “Constrained multicast routing in WDM networks with sparse light splitting,” J. Lightwave Technol., vol. 18, no. 12, pp. 1917–1927, 2000.
[CrossRef]

1999

L. Sahasrabuddhe, B. Mukherjee, “Light trees: optical multicasting for improved performance in wavelength routed networks,” IEEE Commun. Mag., vol. 37, no. 2, pp. 67–73, 1999.
[CrossRef]

1998

A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol., vol. 16, no. 9, pp. 1560–1569, 1998.
[CrossRef]

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Trans. Netw., vol. 6, no. 6, pp. 755–767, 1998.
[CrossRef]

Ali, M.

M. Ali, B. Ramamurthy, J. Deogun, “Routing and wavelength assignment with power considerations in optical networks,” Comput. Netw. ISDN Syst., vol. 32, no. 5, pp. 539–555, 2000.
[CrossRef]

Balestra, G.

A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.

Deogun, J.

M. Ali, B. Ramamurthy, J. Deogun, “Routing and wavelength assignment with power considerations in optical networks,” Comput. Netw. ISDN Syst., vol. 32, no. 5, pp. 539–555, 2000.
[CrossRef]

Fumagalli, A.

A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.

Hamad, A.

A. Hamad, A. Kamal, “Optical amplifier placement in WDM mesh networks for optical multicasting service support,” J. Opt. Commun. Netw., vol. 1, pp. 85–102, June 2009.
[CrossRef]

A. Hamad, T. Wu, A. Kamal, A. Somani, “Multicasting protocols for wavelength routing networks,” Comput. Netw., vol. 50, no. 16, pp. 3105–3164, 2006.
[CrossRef]

A. Hamad, A. Kamal, “Efficient power-aware network provisioning for all-optical multicasting in WDM mesh networks,” in IEEE GLOBECOM 08, 2008, pp. 1–5.

A. Hamad, A. Kamal, “Optimal power-aware design of all-optical multicasting in wavelength routed networks,” in Proc. IEEE ICC 04, 2004, vol. 3, pp. 1796–1800.

Iness, J.

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Trans. Netw., vol. 6, no. 6, pp. 755–767, 1998.
[CrossRef]

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol., vol. 16, no. 9, pp. 1560–1569, 1998.
[CrossRef]

John, M.

A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.

Jue, J.

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, 2000.

Kamal, A.

A. Hamad, A. Kamal, “Optical amplifier placement in WDM mesh networks for optical multicasting service support,” J. Opt. Commun. Netw., vol. 1, pp. 85–102, June 2009.
[CrossRef]

A. Hamad, T. Wu, A. Kamal, A. Somani, “Multicasting protocols for wavelength routing networks,” Comput. Netw., vol. 50, no. 16, pp. 3105–3164, 2006.
[CrossRef]

A. Hamad, A. Kamal, “Efficient power-aware network provisioning for all-optical multicasting in WDM mesh networks,” in IEEE GLOBECOM 08, 2008, pp. 1–5.

A. Hamad, A. Kamal, “Optimal power-aware design of all-optical multicasting in wavelength routed networks,” in Proc. IEEE ICC 04, 2004, vol. 3, pp. 1796–1800.

Liao, W.

D. Yang, W. Liao, “Design of light-tree based logical topologies for multicast streams in wavelength routed optical networks,” in IEEE INFOCOM 03, 2003, vol. 1, pp. 32–41.

Markidis, G.

G. Markidis, S. Sygletos, A. Tzanakaki, I. Tomkos, “Impairment aware based routing and wavelength assignment in transparent long haul networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 48–57, 2007.
[CrossRef]

Mukherjee, B.

L. Sahasrabuddhe, B. Mukherjee, “Light trees: optical multicasting for improved performance in wavelength routed networks,” IEEE Commun. Mag., vol. 37, no. 2, pp. 67–73, 1999.
[CrossRef]

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Trans. Netw., vol. 6, no. 6, pp. 755–767, 1998.
[CrossRef]

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol., vol. 16, no. 9, pp. 1560–1569, 1998.
[CrossRef]

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, 2000.

Qiao, C.

X. Zhang, J. Y. Wei, C. Qiao, “Constrained multicast routing in WDM networks with sparse light splitting,” J. Lightwave Technol., vol. 18, no. 12, pp. 1917–1927, 2000.
[CrossRef]

A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.

Ramamurthy, B.

M. Ali, B. Ramamurthy, J. Deogun, “Routing and wavelength assignment with power considerations in optical networks,” Comput. Netw. ISDN Syst., vol. 32, no. 5, pp. 539–555, 2000.
[CrossRef]

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Trans. Netw., vol. 6, no. 6, pp. 755–767, 1998.
[CrossRef]

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol., vol. 16, no. 9, pp. 1560–1569, 1998.
[CrossRef]

Ramaswami, R.

R. Ramaswami, K. N. Sivarajan, Optical Networks: A Practical Perspective. Morgan Kaufmann, 2nd ed., 2002.

Rouskas, G.

G. Rouskas, “Optical layer multicast: rationale, building blocks, and challenges,” IEEE Networks, vol. 17, no. 1, pp. 60–65, 2003.
[CrossRef]

Y. Xin, G. Rouskas, “Multicast routing under optical layer constraints,” in IEEE INFOCOM 04, 2004, pp. 2731–2742.

Saengudomlert, P.

A. Sripetch, P. Saengudomlert, “Optimization for optical network designs based on existing power grids,” IEICE Trans. Commun., vol. E91-B, no. 3, pp. 689–699, 2008.
[CrossRef]

Sahasrabuddhe, L.

L. Sahasrabuddhe, B. Mukherjee, “Light trees: optical multicasting for improved performance in wavelength routed networks,” IEEE Commun. Mag., vol. 37, no. 2, pp. 67–73, 1999.
[CrossRef]

Sivarajan, K. N.

R. Ramaswami, K. N. Sivarajan, Optical Networks: A Practical Perspective. Morgan Kaufmann, 2nd ed., 2002.

Somani, A.

A. Hamad, T. Wu, A. Kamal, A. Somani, “Multicasting protocols for wavelength routing networks,” Comput. Netw., vol. 50, no. 16, pp. 3105–3164, 2006.
[CrossRef]

Sripetch, A.

A. Sripetch, P. Saengudomlert, “Optimization for optical network designs based on existing power grids,” IEICE Trans. Commun., vol. E91-B, no. 3, pp. 689–699, 2008.
[CrossRef]

Sygletos, S.

G. Markidis, S. Sygletos, A. Tzanakaki, I. Tomkos, “Impairment aware based routing and wavelength assignment in transparent long haul networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 48–57, 2007.
[CrossRef]

Tomkos, I.

G. Markidis, S. Sygletos, A. Tzanakaki, I. Tomkos, “Impairment aware based routing and wavelength assignment in transparent long haul networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 48–57, 2007.
[CrossRef]

Tzanakaki, A.

G. Markidis, S. Sygletos, A. Tzanakaki, I. Tomkos, “Impairment aware based routing and wavelength assignment in transparent long haul networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 48–57, 2007.
[CrossRef]

Valcarenghi, L.

A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.

Wei, J. Y.

Wu, J. W. K.

J. W. K. Wu, C. Yang, “Multicast routing with power consideration in sparse splitting WDM networks,” in IEEE Int. Conf. on Communication (ICC01), 2001, vol. 2, pp. 513–517.

Wu, T.

A. Hamad, T. Wu, A. Kamal, A. Somani, “Multicasting protocols for wavelength routing networks,” Comput. Netw., vol. 50, no. 16, pp. 3105–3164, 2006.
[CrossRef]

Xin, Y.

Y. Xin, G. Rouskas, “Multicast routing under optical layer constraints,” in IEEE INFOCOM 04, 2004, pp. 2731–2742.

Yang, C.

J. W. K. Wu, C. Yang, “Multicast routing with power consideration in sparse splitting WDM networks,” in IEEE Int. Conf. on Communication (ICC01), 2001, vol. 2, pp. 513–517.

Yang, D.

D. Yang, W. Liao, “Design of light-tree based logical topologies for multicast streams in wavelength routed optical networks,” in IEEE INFOCOM 03, 2003, vol. 1, pp. 32–41.

Zang, H.

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, 2000.

Zhang, X.

Comput. Netw.

A. Hamad, T. Wu, A. Kamal, A. Somani, “Multicasting protocols for wavelength routing networks,” Comput. Netw., vol. 50, no. 16, pp. 3105–3164, 2006.
[CrossRef]

Comput. Netw. ISDN Syst.

M. Ali, B. Ramamurthy, J. Deogun, “Routing and wavelength assignment with power considerations in optical networks,” Comput. Netw. ISDN Syst., vol. 32, no. 5, pp. 539–555, 2000.
[CrossRef]

IEEE Commun. Mag.

L. Sahasrabuddhe, B. Mukherjee, “Light trees: optical multicasting for improved performance in wavelength routed networks,” IEEE Commun. Mag., vol. 37, no. 2, pp. 67–73, 1999.
[CrossRef]

IEEE Networks

G. Rouskas, “Optical layer multicast: rationale, building blocks, and challenges,” IEEE Networks, vol. 17, no. 1, pp. 60–65, 2003.
[CrossRef]

IEEE/ACM Trans. Netw.

B. Ramamurthy, J. Iness, B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Trans. Netw., vol. 6, no. 6, pp. 755–767, 1998.
[CrossRef]

IEICE Trans. Commun.

A. Sripetch, P. Saengudomlert, “Optimization for optical network designs based on existing power grids,” IEICE Trans. Commun., vol. E91-B, no. 3, pp. 689–699, 2008.
[CrossRef]

J. Lightwave Technol.

J. Opt. Commun. Netw.

Lect. Notes Comput. Sci.

G. Markidis, S. Sygletos, A. Tzanakaki, I. Tomkos, “Impairment aware based routing and wavelength assignment in transparent long haul networks,” Lect. Notes Comput. Sci., vol. 4534, pp. 48–57, 2007.
[CrossRef]

Opt. Engr.

A. Fumagalli, G. Balestra, L. Valcarenghi, M. John, C. Qiao, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Opt. Engr., vol. 3531, pp. 268–279, 1998.

Other

H. Zang, J. Jue, B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,” Opt. Networks Mag., vol. 1, no. 1, 2000.

A. Hamad, A. Kamal, “Optimal power-aware design of all-optical multicasting in wavelength routed networks,” in Proc. IEEE ICC 04, 2004, vol. 3, pp. 1796–1800.

D. Yang, W. Liao, “Design of light-tree based logical topologies for multicast streams in wavelength routed optical networks,” in IEEE INFOCOM 03, 2003, vol. 1, pp. 32–41.

R. Ramaswami, K. N. Sivarajan, Optical Networks: A Practical Perspective. Morgan Kaufmann, 2nd ed., 2002.

A. Hamad, A. Kamal, “Efficient power-aware network provisioning for all-optical multicasting in WDM mesh networks,” in IEEE GLOBECOM 08, 2008, pp. 1–5.

J. W. K. Wu, C. Yang, “Multicast routing with power consideration in sparse splitting WDM networks,” in IEEE Int. Conf. on Communication (ICC01), 2001, vol. 2, pp. 513–517.

Y. Xin, G. Rouskas, “Multicast routing under optical layer constraints,” in IEEE INFOCOM 04, 2004, pp. 2731–2742.

http://www.ilog.com/products/cplex/.

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Figures (10)

Fig. 1
Fig. 1

Illustration of the approximate linear conversion approach between power levels in dBm and mW.

Fig. 2
Fig. 2

Illustration of the approximate linear conversion approach between the total input power of an OA in mW and the OA gain in dB.

Fig. 3
Fig. 3

Flow chart of the PAM algorithm operation.

Fig. 4
Fig. 4

Flow chart of the operation of the PA module. The number associated with each task box is used in the algorithm description in Subsection 5D to refer to the corresponding operation.

Fig. 5
Fig. 5

Six-node network.

Fig. 6
Fig. 6

NSFNET.

Fig. 7
Fig. 7

Greedy heuristic results with respect to the MILP for the six-node mesh network, when Λ = 4 and for different values of sessions, K.

Fig. 8
Fig. 8

Number of accepted sessions when the fixed scheme is used and Λ is 10. Min-P refers to the case of the Min power scheme with one alternate path, while RP-P(i) refers to the case of the Rand power scheme with the ith alternate paths.

Fig. 9
Fig. 9

System behavior with the existence of power constraints in the 6-node network for 30 connections.

Fig. 10
Fig. 10

System behavior with the existence of power constraints in the NSFNET for 20 connections.

Tables (3)

Tables Icon

Table 1 Typical Values for the System Parameters a

Tables Icon

Table 2 Number of Accepted Sessions for the Fixed and Rerouting Schemes When K = 10 , 20, and 30

Tables Icon

Table 3 Consumed Network Resources for Fixed (F) and Rerouting (R) Schemes When K = 10 , 20, and 30, and One Alternate Path

Equations (39)

Equations on this page are rendered with MathJax. Learn more.

G ( P in ) = MIN { G 0 , ( P MAX P in ) } ,
Minimize : W 1 a = 0 K 1 φ a + W 2 R ,
R = e ( i , j ) E o OA i , j a = 0 K 1 λ Λ TP i , j , mW beg , a , λ , o + e ( i , j ) E o OA i , j G i , j o .
φ a i , i D a ϑ i a | D a | , 0 a < K ,
φ a i , i D a ϑ i a ( | D a | 1 ) , 0 a < K .
ϑ j a i , i j , e ( i , j ) E λ Λ T i , j a , λ M , j N ; 0 a < K ,
ϑ j a i , i j , e ( i , j ) E λ Λ T i , j a , λ , j N ; 0 a < K .
I i , j a λ Λ T i , j a , λ M , i , j N ; 0 a < K ,
I i , j a λ Λ T i , j a , λ , i , j N ; 0 a < K .
Υ i , j a = 0 K 1 I i , j a M , Υ i , j a = 0 K 1 I i , j a , e ( i , j ) E .
Γ i a + λ Λ e ( i , k ) E T i , k a , λ M e ( k , i ) E T k , i a , λ + ( 1 φ a ) × M i N { src a } ; 0 a < K .
a = 0 K 1 e ( i , j ) E T i , j a , λ 1 , i , j N ; i j ; λ Λ .
e ( i , j ) E T i , j a , λ 1 , i N { src a } ; i SP ; 0 a < K ; λ Λ .
e ( i , j ) E T i , j a , λ e ( j , k ) E T j , k a , λ M , j N { src a } ; 0 a < K .
P i , j , dBm beg , a , λ , o P Sen dBm × T i , j a , λ + P 1 × ( 1 T i , j a , λ ) , e ( i , j ) E ; 0 a < K ; λ Λ ; o OA i , j ,
P i , j , dBm end , a , λ P Sen dBm × T i , j a , λ + P 1 × ( 1 T i , j a , λ ) , e ( i , j ) E ; 0 a < K ; λ Λ .
P i , j , dBm beg , a , λ P 2 × ( 1 T i , j a , λ ) , e ( i , j ) E ; 0 a < K ; λ Λ .
TP i , j , mW beg TP MAX mW × Υ i , j + TP MIN mW × ( 1 Υ i , j ) , e ( i , j ) E ; 0 a < K ; e ( i , j ) E .
P i , j , mW beg , a , λ , o = 10 P i , j , dBm beg , a , λ , o 10 , e ( i , j ) E ; λ Λ ; 0 a < K ; o OA i , j .
P i , j , mW beg , a , λ , o A y P i , j , dBm beg , a , λ , o + B y ,
e ( i , j ) E ; λ Λ ; 0 a < K ; y Y ; o OA i , j .
TP i , j , mW beg = λ Λ a = 0 K 1 P i , j , mW beg , a , λ , e ( i , j ) E ,
TP i , j , mW beg , o = λ Λ a = 0 K 1 P i , j , mW beg , a , λ , o , e ( i , j ) E ; o OA i , j .
P i , j , dBm beg , a , λ , 1 = P i , j , dBm beg , a , λ β × L i , j 0 , 1 , e ( i , j ) E ; o OA i , j ; 0 a < K ; λ Λ ,
P i , j , dBm end , a , λ = [ ( 1 NOA i , j ) × ( P i , j , dBm beg , a , λ β × L i , j ) ] + [ NOA i , j × ( P i , j , dBm beg , a , λ , | OA i , j | + G i , j o β × L i , j | OA i , j | , | OA i , j | + 1 ) ] , e ( i , j ) E ; o OA i , j ; 0 a < K ; λ Λ .
P i , j , dBm beg , a , λ , o + 1 = P i , j , dBm beg , a , λ , o + G i , j o β × L i , j o , o + 1 , e ( i , j ) E ; o OA i , j ; 0 a < K ; λ Λ .
( 1 T i , j a , λ ) × v + P i , j end , a , λ SL j a , λ γ ( 1 T j , k a , λ ) × w + P j , k beg , a , λ , e ( i , j ) , e ( j , k ) E ; 0 a < K ; λ Λ ,
( 1 T i , j a , λ ) × w + P i , j end , a , λ SL j a , λ γ ( 1 T j , k a , λ ) × v + P j , k beg , a , λ , e ( i , j ) , e ( j , k ) E ; 0 a < K ; λ Λ .
( P Sat TP i , j , mW beg , o ) + δ AP i , j o , e ( i , j ) E ; o OA i , j .
( 1 AP i , j o ) + G i , j o G 0 M 0 , e ( i , j ) E ; o OA i , j ,
AP i , j o + G i , j o ( A y × TP i , j , mW beg , o + B y ) M 0 , e ( i , j ) E ; o OA i , j .
SL i a , λ M SP i , i N ; 0 a < K ; λ Λ .
SL i a , λ = 10 × log 10 f .
j , j s r c a , e ( i , j ) E T i , j a , λ f + δ M A f , i N ; 0 a < K ; λ Λ ; 2 f < Out i ,
A f × { 10 × log 10 f } SL i a , λ , i N ; 0 a < K ; λ Λ ; 2 f < Out i ,
SL i a , λ 0 , i N ; 0 a < K ; λ Λ .
| Λ i , j MAX | = MIN ( | Λ | , TP MAX mW P i , j , mW λ , MIN ) .
MIN ( TP MAX mW λ | Λ i , j Busy | P i , j , mW beg , a , λ P i , j , mW λ , MIN , | Λ i , j Free | ) ,
c e ( i , j ) = | Λ i , j MAX | | Λ i , j Add | .