Abstract

A wireless–optical broadband access network (WOBAN) is a combination of wireless and optical network segments to optimize the cost and performance of an access network. A WOBAN’s optical backhaul enables it to support high capacity, while its wireless front end [also called a wireless mesh network (WMN)] enables its users to have untethered access. Wireless nodes collect traffic from end users and carry them to the optical part of a WOBAN, possibly using multiple hops, but the traffic also experiences delay at each wireless node. The finite radio capacity at each wireless node limits the capacity on each outgoing link from a wireless node of a WOBAN. Thus, delay and capacity limitation in the WMN of a WOBAN are major constraints. We design a capacity- and delay-aware routing scheme, called CaDAR, to minimize the delay and increase the throughput in the WMN of a WOBAN. Our analysis shows that CaDAR is an efficient routing scheme for WOBAN that can support much higher load and has lower system delay than other approaches (IEEE Network, vol. 22, no. 3, p. 20, 2008) because of better load-balanced routing.

© 2009 Optical Society of America

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References

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  1. S. Sarkar, S. Dixit, B. Mukherjee, “Hybrid wireless-optical broadband access network (WOBAN): a review of relevant challenges,” J. Lightwave Technol., vol. 25, no. 11, pp. 3329–3340, Nov. 2007.
    [CrossRef]
  2. F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
    [CrossRef]
  3. G. Narlikar, G. Wilfong, L. Zhang, “Designing multihop wireless backhaul networks with delay guarantees,” in IEEE INFOCOM, Barcelona, Spain, April 2006, pp. 1–12.
  4. S. Lee, G. Narlikar, M. Pal, G. Wilfong, L. Zhang, “Admission control for multihop wireless backhaul networks with QoS support,” in IEEE Wireless Communications and Networking Conf. (WCNC), Las Vegas, NV, April 2006, pp. 92–97.
  5. T. Liu, W. Liao, “Capacity-aware routing with multi-channel multi-rate wireless mesh networks,” in IEEE ICC, Istanbul, Turkey, June 2006, pp. 1971–1976.
  6. http://standards.ieee.org/getieee802/802.11.html.
  7. R. Draves, J. Padhye, B. Zill, “Routing in multi-radio, multi-hop wireless mesh networks,” in ACM MobiCom, Philadelphia, PA, Sept. 2004, pp. 114–128.
  8. A. Subramanian, M. Buddhikot, S. Miller, “Interference aware routing in multi-radio wireless mesh networks,” in IEEE Int. Workshop on Wireless Mesh Networks (WiMesh), Reston, VA, Sept. 2006, pp. 55–63.
  9. S. Sarkar, H. Yen, S. Dixit, B. Mukherjee, “A novel delay-aware routing algorithm (DARA) for a hybrid wireless-optical broadband access network (WOBAN),” IEEE Network, vol. 22, no. 3, pp. 20–28, May–June 2008.
    [CrossRef]
  10. Tropos Networks, http://www.tropos.com/.
  11. L. Fratta, M. Gerla, L. Kleinrock, “The flow deviation method: an approach to store-and-forward communication network design,” Networks, vol. 3, no. 2, pp. 97–133, March 2007.
    [CrossRef]
  12. L. Kleinrock, Queueing Systems, Volume II: Computer Applications. Wiley-Interscience, 1976.
  13. T. Rappaport, Wireless Communications: Principles and Practice, 2nd ed.Prentice Hall, 2001.
  14. J. Hammond, P. O’Reilly, Performance Analysis of Local Computer Networks. Addison-Wesley Longman Publishing Co., Inc., 1986.
  15. G. Kramer, B. Mukherjee, G. Pesavento, “IPACT: a dynamic protocol for an Ethernet PON (EPON),” IEEE Commun. Mag., vol. 40, no. 2, pp. 74–80, Feb. 2002.
    [CrossRef]
  16. G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
    [CrossRef]
  17. A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

2008 (1)

S. Sarkar, H. Yen, S. Dixit, B. Mukherjee, “A novel delay-aware routing algorithm (DARA) for a hybrid wireless-optical broadband access network (WOBAN),” IEEE Network, vol. 22, no. 3, pp. 20–28, May–June 2008.
[CrossRef]

2007 (3)

L. Fratta, M. Gerla, L. Kleinrock, “The flow deviation method: an approach to store-and-forward communication network design,” Networks, vol. 3, no. 2, pp. 97–133, March 2007.
[CrossRef]

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

S. Sarkar, S. Dixit, B. Mukherjee, “Hybrid wireless-optical broadband access network (WOBAN): a review of relevant challenges,” J. Lightwave Technol., vol. 25, no. 11, pp. 3329–3340, Nov. 2007.
[CrossRef]

2004 (1)

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

2002 (1)

G. Kramer, B. Mukherjee, G. Pesavento, “IPACT: a dynamic protocol for an Ethernet PON (EPON),” IEEE Commun. Mag., vol. 40, no. 2, pp. 74–80, Feb. 2002.
[CrossRef]

Banerjee, A.

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

Buddhikot, M.

A. Subramanian, M. Buddhikot, S. Miller, “Interference aware routing in multi-radio wireless mesh networks,” in IEEE Int. Workshop on Wireless Mesh Networks (WiMesh), Reston, VA, Sept. 2006, pp. 55–63.

Clearly, D.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Dixit, S.

S. Sarkar, H. Yen, S. Dixit, B. Mukherjee, “A novel delay-aware routing algorithm (DARA) for a hybrid wireless-optical broadband access network (WOBAN),” IEEE Network, vol. 22, no. 3, pp. 20–28, May–June 2008.
[CrossRef]

S. Sarkar, S. Dixit, B. Mukherjee, “Hybrid wireless-optical broadband access network (WOBAN): a review of relevant challenges,” J. Lightwave Technol., vol. 25, no. 11, pp. 3329–3340, Nov. 2007.
[CrossRef]

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

Draves, R.

R. Draves, J. Padhye, B. Zill, “Routing in multi-radio, multi-hop wireless mesh networks,” in ACM MobiCom, Philadelphia, PA, Sept. 2004, pp. 114–128.

Effenberger, F.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Fratta, L.

L. Fratta, M. Gerla, L. Kleinrock, “The flow deviation method: an approach to store-and-forward communication network design,” Networks, vol. 3, no. 2, pp. 97–133, March 2007.
[CrossRef]

Gerla, M.

L. Fratta, M. Gerla, L. Kleinrock, “The flow deviation method: an approach to store-and-forward communication network design,” Networks, vol. 3, no. 2, pp. 97–133, March 2007.
[CrossRef]

Ghosal, D.

A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

Hammond, J.

J. Hammond, P. O’Reilly, Performance Analysis of Local Computer Networks. Addison-Wesley Longman Publishing Co., Inc., 1986.

Haran, O.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Kleinrock, L.

L. Fratta, M. Gerla, L. Kleinrock, “The flow deviation method: an approach to store-and-forward communication network design,” Networks, vol. 3, no. 2, pp. 97–133, March 2007.
[CrossRef]

L. Kleinrock, Queueing Systems, Volume II: Computer Applications. Wiley-Interscience, 1976.

Kramer, G.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

G. Kramer, B. Mukherjee, G. Pesavento, “IPACT: a dynamic protocol for an Ethernet PON (EPON),” IEEE Commun. Mag., vol. 40, no. 2, pp. 74–80, Feb. 2002.
[CrossRef]

Lee, S.

S. Lee, G. Narlikar, M. Pal, G. Wilfong, L. Zhang, “Admission control for multihop wireless backhaul networks with QoS support,” in IEEE Wireless Communications and Networking Conf. (WCNC), Las Vegas, NV, April 2006, pp. 92–97.

Li, R.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Liao, W.

T. Liu, W. Liao, “Capacity-aware routing with multi-channel multi-rate wireless mesh networks,” in IEEE ICC, Istanbul, Turkey, June 2006, pp. 1971–1976.

Liu, T.

T. Liu, W. Liao, “Capacity-aware routing with multi-channel multi-rate wireless mesh networks,” in IEEE ICC, Istanbul, Turkey, June 2006, pp. 1971–1976.

Miller, S.

A. Subramanian, M. Buddhikot, S. Miller, “Interference aware routing in multi-radio wireless mesh networks,” in IEEE Int. Workshop on Wireless Mesh Networks (WiMesh), Reston, VA, Sept. 2006, pp. 55–63.

Mukherjee, B.

S. Sarkar, H. Yen, S. Dixit, B. Mukherjee, “A novel delay-aware routing algorithm (DARA) for a hybrid wireless-optical broadband access network (WOBAN),” IEEE Network, vol. 22, no. 3, pp. 20–28, May–June 2008.
[CrossRef]

S. Sarkar, S. Dixit, B. Mukherjee, “Hybrid wireless-optical broadband access network (WOBAN): a review of relevant challenges,” J. Lightwave Technol., vol. 25, no. 11, pp. 3329–3340, Nov. 2007.
[CrossRef]

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

G. Kramer, B. Mukherjee, G. Pesavento, “IPACT: a dynamic protocol for an Ethernet PON (EPON),” IEEE Commun. Mag., vol. 40, no. 2, pp. 74–80, Feb. 2002.
[CrossRef]

A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

Narlikar, G.

G. Narlikar, G. Wilfong, L. Zhang, “Designing multihop wireless backhaul networks with delay guarantees,” in IEEE INFOCOM, Barcelona, Spain, April 2006, pp. 1–12.

S. Lee, G. Narlikar, M. Pal, G. Wilfong, L. Zhang, “Admission control for multihop wireless backhaul networks with QoS support,” in IEEE Wireless Communications and Networking Conf. (WCNC), Las Vegas, NV, April 2006, pp. 92–97.

O’Reilly, P.

J. Hammond, P. O’Reilly, Performance Analysis of Local Computer Networks. Addison-Wesley Longman Publishing Co., Inc., 1986.

Oron, M.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Padhye, J.

R. Draves, J. Padhye, B. Zill, “Routing in multi-radio, multi-hop wireless mesh networks,” in ACM MobiCom, Philadelphia, PA, Sept. 2004, pp. 114–128.

Pal, M.

S. Lee, G. Narlikar, M. Pal, G. Wilfong, L. Zhang, “Admission control for multihop wireless backhaul networks with QoS support,” in IEEE Wireless Communications and Networking Conf. (WCNC), Las Vegas, NV, April 2006, pp. 92–97.

Pesavento, G.

G. Kramer, B. Mukherjee, G. Pesavento, “IPACT: a dynamic protocol for an Ethernet PON (EPON),” IEEE Commun. Mag., vol. 40, no. 2, pp. 74–80, Feb. 2002.
[CrossRef]

Pfeiffer, T.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Ramamurthi, V.

A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

Rappaport, T.

T. Rappaport, Wireless Communications: Principles and Practice, 2nd ed.Prentice Hall, 2001.

Reaz, A.

A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

Sarkar, S.

S. Sarkar, H. Yen, S. Dixit, B. Mukherjee, “A novel delay-aware routing algorithm (DARA) for a hybrid wireless-optical broadband access network (WOBAN),” IEEE Network, vol. 22, no. 3, pp. 20–28, May–June 2008.
[CrossRef]

S. Sarkar, S. Dixit, B. Mukherjee, “Hybrid wireless-optical broadband access network (WOBAN): a review of relevant challenges,” J. Lightwave Technol., vol. 25, no. 11, pp. 3329–3340, Nov. 2007.
[CrossRef]

A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

Singhal, N.

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

Subramanian, A.

A. Subramanian, M. Buddhikot, S. Miller, “Interference aware routing in multi-radio wireless mesh networks,” in IEEE Int. Workshop on Wireless Mesh Networks (WiMesh), Reston, VA, Sept. 2006, pp. 55–63.

Wilfong, G.

S. Lee, G. Narlikar, M. Pal, G. Wilfong, L. Zhang, “Admission control for multihop wireless backhaul networks with QoS support,” in IEEE Wireless Communications and Networking Conf. (WCNC), Las Vegas, NV, April 2006, pp. 92–97.

G. Narlikar, G. Wilfong, L. Zhang, “Designing multihop wireless backhaul networks with delay guarantees,” in IEEE INFOCOM, Barcelona, Spain, April 2006, pp. 1–12.

Ye, Y.

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

Yen, H.

S. Sarkar, H. Yen, S. Dixit, B. Mukherjee, “A novel delay-aware routing algorithm (DARA) for a hybrid wireless-optical broadband access network (WOBAN),” IEEE Network, vol. 22, no. 3, pp. 20–28, May–June 2008.
[CrossRef]

Zhang, L.

G. Narlikar, G. Wilfong, L. Zhang, “Designing multihop wireless backhaul networks with delay guarantees,” in IEEE INFOCOM, Barcelona, Spain, April 2006, pp. 1–12.

S. Lee, G. Narlikar, M. Pal, G. Wilfong, L. Zhang, “Admission control for multihop wireless backhaul networks with QoS support,” in IEEE Wireless Communications and Networking Conf. (WCNC), Las Vegas, NV, April 2006, pp. 92–97.

Zill, B.

R. Draves, J. Padhye, B. Zill, “Routing in multi-radio, multi-hop wireless mesh networks,” in ACM MobiCom, Philadelphia, PA, Sept. 2004, pp. 114–128.

IEEE Commun. Mag. (2)

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

G. Kramer, B. Mukherjee, G. Pesavento, “IPACT: a dynamic protocol for an Ethernet PON (EPON),” IEEE Commun. Mag., vol. 40, no. 2, pp. 74–80, Feb. 2002.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, Y. Ye, “Fair queueing with service envelopes (FQSE): a cousin-fair hierarchical scheduler for subscriber access networks,” IEEE J. Sel. Areas Commun., vol. 22, no. 8, pp. 1497–1513, Oct. 2004.
[CrossRef]

IEEE Network (1)

S. Sarkar, H. Yen, S. Dixit, B. Mukherjee, “A novel delay-aware routing algorithm (DARA) for a hybrid wireless-optical broadband access network (WOBAN),” IEEE Network, vol. 22, no. 3, pp. 20–28, May–June 2008.
[CrossRef]

J. Lightwave Technol. (1)

Networks (1)

L. Fratta, M. Gerla, L. Kleinrock, “The flow deviation method: an approach to store-and-forward communication network design,” Networks, vol. 3, no. 2, pp. 97–133, March 2007.
[CrossRef]

Other (11)

L. Kleinrock, Queueing Systems, Volume II: Computer Applications. Wiley-Interscience, 1976.

T. Rappaport, Wireless Communications: Principles and Practice, 2nd ed.Prentice Hall, 2001.

J. Hammond, P. O’Reilly, Performance Analysis of Local Computer Networks. Addison-Wesley Longman Publishing Co., Inc., 1986.

G. Narlikar, G. Wilfong, L. Zhang, “Designing multihop wireless backhaul networks with delay guarantees,” in IEEE INFOCOM, Barcelona, Spain, April 2006, pp. 1–12.

S. Lee, G. Narlikar, M. Pal, G. Wilfong, L. Zhang, “Admission control for multihop wireless backhaul networks with QoS support,” in IEEE Wireless Communications and Networking Conf. (WCNC), Las Vegas, NV, April 2006, pp. 92–97.

T. Liu, W. Liao, “Capacity-aware routing with multi-channel multi-rate wireless mesh networks,” in IEEE ICC, Istanbul, Turkey, June 2006, pp. 1971–1976.

http://standards.ieee.org/getieee802/802.11.html.

R. Draves, J. Padhye, B. Zill, “Routing in multi-radio, multi-hop wireless mesh networks,” in ACM MobiCom, Philadelphia, PA, Sept. 2004, pp. 114–128.

A. Subramanian, M. Buddhikot, S. Miller, “Interference aware routing in multi-radio wireless mesh networks,” in IEEE Int. Workshop on Wireless Mesh Networks (WiMesh), Reston, VA, Sept. 2006, pp. 55–63.

Tropos Networks, http://www.tropos.com/.

A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. Dixit, B. Mukherjee, “CaDAR: an efficient routing algorithm for wireless-optical broadband access network,” in IEEE ICC, Beijing, China, May 2008, pp. 5191–5195.

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Figures (13)

Fig. 1
Fig. 1

Architecture of a WOBAN.

Fig. 2
Fig. 2

Wireless links and their flows.

Fig. 3
Fig. 3

Anycast in a WOBAN.

Fig. 4
Fig. 4

PON with a WOBAN and other networks.

Fig. 5
Fig. 5

Broadcast and unicast nature of downstream traffic in a WOBAN.

Fig. 6
Fig. 6

Network topology used in this study.

Fig. 7
Fig. 7

System delay for different loads at the wireless nodes.

Fig. 8
Fig. 8

Delay on maximum-delay path for different loads at the wireless nodes.

Fig. 9
Fig. 9

Average number of hops for different loads at the wireless nodes.

Fig. 10
Fig. 10

Load balancing (link congestion) for different loads at the wireless nodes.

Fig. 11
Fig. 11

System delay for CaDAR with equal and unequal ONU loads.

Fig. 12
Fig. 12

Impact of optical load on average number of hops for CaDAR.

Fig. 13
Fig. 13

Delay incurred by LSA for CaDAR.

Tables (3)

Tables Icon

Table 1 Algorithm 1 CaDAR Algorithm

Tables Icon

Table 1 Fraction of Paths Through a Gateway for Different ONU Loads

Tables Icon

Table 2 Distribution (%) of Flow on Wireless Links for CaDAR a

Equations (14)

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

γ = s = 1 N g = 1 | G | ( γ s g + γ g s ) ; s g .
T = 1 γ u = 1 N v = 1 N λ u v μ C u v λ u v ; u , v ω ( N ) ; u v ,
ζ u = v C u v ; u ω ( N ) .
J = T + u l u [ ζ u v C u v ] ; u ω ( N ) ; v η ( u ) ,
J C u v = 0 ; v η ( u ) .
C u v = λ u v μ + ( ζ u v λ u v μ ) λ u v v λ u v ; u ω ( N ) ; v η ( u ) .
τ u v = Υ u C u v ζ u ; u ω ( N ) ; v η ( u ) .
d u v = 1 μ C u v + 1 2 μ C u v + λ u v μ C u v ( μ C u v λ u v ) = 1 2 μ C u v + 1 μ C u v λ u v .
d v w = d v u + d u x + d x w .
d g D N = L g d p + ( u , v ) P g u d u v ; g G ,
d min o = q O ( L q d p + γ q R ) ; o O ; o q .
d WT o = k d min o k 1 ; o O .
d g UP = L g d p + d WT g + ( u , v ) P u g d u v ; g G ,
e λ u v k = ( 3 α 3 α + 1 ) ( λ u v k + e λ u v k 1 ) S 1 α 1 + α ,