Abstract

Service differentiation is a crucial issue in the next -generation Optical Packet Switched networks. In this paper we examine how bursty traffic influences the performance of a service differentiated Optical Packet Switched network. By using time -continuous Markov chains, we derive explicit results for the packet loss rates in the case of a bursty hyper-exponential arrival process. Results indicate that the performance is degraded as the burstiness of the arrival process increases.

©2004 Optical Society of America

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References

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  1. M. O’Mahony, D. Simeonidou, D. Hunter, and A. Tzanakaki, “The Application of Optical Packet Switching in Future Communication Networks,” IEEE Communications Magazine 39, 128–135 (2001).
    [Crossref]
  2. X. Xiao and L. M. Ni, “Internet QoS: A Big Picture,” IEEE Network 13, 8–18 (1999).
    [Crossref]
  3. B. Wydrowski and M. Zukerman, “QoS in Best -Effort Networks,” IEEE Communications Magazine 40, 44–49 (2002).
    [Crossref]
  4. M. Yoo, C. Qiao, and S. Dixit, “QoS Performance of Optical Burst Switching in IP -Over-WDM Networks,” IEEE Journal on Selected Areas in Communications 18, 2062–2071 (2000).
    [Crossref]
  5. H. Øverby and N. Stol, “A Teletraffic Model for Service Differentiation in OPS networks,” in Proceedings of IEEE 8th Optoelectronics and Communications Conference (Institute of Electrical and Electronic Engineers, 2003), pp. 677–678.
  6. Ayman Kaheel, Tamer Khattab, Amr Mohamed, and Hussein Alnuweiri, “Quality-of-Service Mechanisms in IP-over WDM Networks,” IEEE Communications Magazine 40, 38–43 (2002).
    [Crossref]
  7. W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the Self Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking 2, 1–15 (1994).
    [Crossref]
  8. A.L. Schmid et al., “Impact of VC merging on buffer requirements in ATM networks,” Proceedings of Eighth International Conference on High Performance Networking, 203–217 (1998).
  9. Deepankar Medhi, “Some Results for Renewal Arrival to a Communication Link,” Probability Models and Statistics: A J. Medhi Festschrift, 85–107 (1996).
  10. S. Bjørnstad, N. Stol, and D. R. Hjelme, “Quality of service in optical packet switched DWDM transport networks,” in Asia -Pacific Optical and Wireless Communications Conference, Proc. SPIE 4910, 63–74 (2002).
  11. E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).
  12. Leonard Kleinrock, Queueing Systems Volume I: Theory (John Wiley & Sons, 1975).

2002 (3)

B. Wydrowski and M. Zukerman, “QoS in Best -Effort Networks,” IEEE Communications Magazine 40, 44–49 (2002).
[Crossref]

Ayman Kaheel, Tamer Khattab, Amr Mohamed, and Hussein Alnuweiri, “Quality-of-Service Mechanisms in IP-over WDM Networks,” IEEE Communications Magazine 40, 38–43 (2002).
[Crossref]

S. Bjørnstad, N. Stol, and D. R. Hjelme, “Quality of service in optical packet switched DWDM transport networks,” in Asia -Pacific Optical and Wireless Communications Conference, Proc. SPIE 4910, 63–74 (2002).

2001 (1)

M. O’Mahony, D. Simeonidou, D. Hunter, and A. Tzanakaki, “The Application of Optical Packet Switching in Future Communication Networks,” IEEE Communications Magazine 39, 128–135 (2001).
[Crossref]

2000 (1)

M. Yoo, C. Qiao, and S. Dixit, “QoS Performance of Optical Burst Switching in IP -Over-WDM Networks,” IEEE Journal on Selected Areas in Communications 18, 2062–2071 (2000).
[Crossref]

1999 (1)

X. Xiao and L. M. Ni, “Internet QoS: A Big Picture,” IEEE Network 13, 8–18 (1999).
[Crossref]

1994 (1)

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the Self Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking 2, 1–15 (1994).
[Crossref]

Ackaert, A.

E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).

Alnuweiri, Hussein

Ayman Kaheel, Tamer Khattab, Amr Mohamed, and Hussein Alnuweiri, “Quality-of-Service Mechanisms in IP-over WDM Networks,” IEEE Communications Magazine 40, 38–43 (2002).
[Crossref]

Bjørnstad, S.

S. Bjørnstad, N. Stol, and D. R. Hjelme, “Quality of service in optical packet switched DWDM transport networks,” in Asia -Pacific Optical and Wireless Communications Conference, Proc. SPIE 4910, 63–74 (2002).

Breusegem, E. V.

E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).

Cheyns, J.

E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).

Demeester, P.

E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).

Dixit, S.

M. Yoo, C. Qiao, and S. Dixit, “QoS Performance of Optical Burst Switching in IP -Over-WDM Networks,” IEEE Journal on Selected Areas in Communications 18, 2062–2071 (2000).
[Crossref]

Hjelme, D. R.

S. Bjørnstad, N. Stol, and D. R. Hjelme, “Quality of service in optical packet switched DWDM transport networks,” in Asia -Pacific Optical and Wireless Communications Conference, Proc. SPIE 4910, 63–74 (2002).

Hunter, D.

M. O’Mahony, D. Simeonidou, D. Hunter, and A. Tzanakaki, “The Application of Optical Packet Switching in Future Communication Networks,” IEEE Communications Magazine 39, 128–135 (2001).
[Crossref]

Kaheel, Ayman

Ayman Kaheel, Tamer Khattab, Amr Mohamed, and Hussein Alnuweiri, “Quality-of-Service Mechanisms in IP-over WDM Networks,” IEEE Communications Magazine 40, 38–43 (2002).
[Crossref]

Khattab, Tamer

Ayman Kaheel, Tamer Khattab, Amr Mohamed, and Hussein Alnuweiri, “Quality-of-Service Mechanisms in IP-over WDM Networks,” IEEE Communications Magazine 40, 38–43 (2002).
[Crossref]

Kleinrock, Leonard

Leonard Kleinrock, Queueing Systems Volume I: Theory (John Wiley & Sons, 1975).

Lannoo, B.

E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).

Leland, W.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the Self Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking 2, 1–15 (1994).
[Crossref]

Medhi, Deepankar

Deepankar Medhi, “Some Results for Renewal Arrival to a Communication Link,” Probability Models and Statistics: A J. Medhi Festschrift, 85–107 (1996).

Mohamed, Amr

Ayman Kaheel, Tamer Khattab, Amr Mohamed, and Hussein Alnuweiri, “Quality-of-Service Mechanisms in IP-over WDM Networks,” IEEE Communications Magazine 40, 38–43 (2002).
[Crossref]

Ni, L. M.

X. Xiao and L. M. Ni, “Internet QoS: A Big Picture,” IEEE Network 13, 8–18 (1999).
[Crossref]

O’Mahony, M.

M. O’Mahony, D. Simeonidou, D. Hunter, and A. Tzanakaki, “The Application of Optical Packet Switching in Future Communication Networks,” IEEE Communications Magazine 39, 128–135 (2001).
[Crossref]

Øverby, H.

H. Øverby and N. Stol, “A Teletraffic Model for Service Differentiation in OPS networks,” in Proceedings of IEEE 8th Optoelectronics and Communications Conference (Institute of Electrical and Electronic Engineers, 2003), pp. 677–678.

Pickavet, M.

E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).

Qiao, C.

M. Yoo, C. Qiao, and S. Dixit, “QoS Performance of Optical Burst Switching in IP -Over-WDM Networks,” IEEE Journal on Selected Areas in Communications 18, 2062–2071 (2000).
[Crossref]

Schmid, A.L.

A.L. Schmid et al., “Impact of VC merging on buffer requirements in ATM networks,” Proceedings of Eighth International Conference on High Performance Networking, 203–217 (1998).

Simeonidou, D.

M. O’Mahony, D. Simeonidou, D. Hunter, and A. Tzanakaki, “The Application of Optical Packet Switching in Future Communication Networks,” IEEE Communications Magazine 39, 128–135 (2001).
[Crossref]

Stol, N.

S. Bjørnstad, N. Stol, and D. R. Hjelme, “Quality of service in optical packet switched DWDM transport networks,” in Asia -Pacific Optical and Wireless Communications Conference, Proc. SPIE 4910, 63–74 (2002).

H. Øverby and N. Stol, “A Teletraffic Model for Service Differentiation in OPS networks,” in Proceedings of IEEE 8th Optoelectronics and Communications Conference (Institute of Electrical and Electronic Engineers, 2003), pp. 677–678.

Taqqu, M.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the Self Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking 2, 1–15 (1994).
[Crossref]

Tzanakaki, A.

M. O’Mahony, D. Simeonidou, D. Hunter, and A. Tzanakaki, “The Application of Optical Packet Switching in Future Communication Networks,” IEEE Communications Magazine 39, 128–135 (2001).
[Crossref]

Willinger, W.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the Self Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking 2, 1–15 (1994).
[Crossref]

Wilson, D.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the Self Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking 2, 1–15 (1994).
[Crossref]

Wydrowski, B.

B. Wydrowski and M. Zukerman, “QoS in Best -Effort Networks,” IEEE Communications Magazine 40, 44–49 (2002).
[Crossref]

Xiao, X.

X. Xiao and L. M. Ni, “Internet QoS: A Big Picture,” IEEE Network 13, 8–18 (1999).
[Crossref]

Yoo, M.

M. Yoo, C. Qiao, and S. Dixit, “QoS Performance of Optical Burst Switching in IP -Over-WDM Networks,” IEEE Journal on Selected Areas in Communications 18, 2062–2071 (2000).
[Crossref]

Zukerman, M.

B. Wydrowski and M. Zukerman, “QoS in Best -Effort Networks,” IEEE Communications Magazine 40, 44–49 (2002).
[Crossref]

IEEE Communications Magazine (3)

M. O’Mahony, D. Simeonidou, D. Hunter, and A. Tzanakaki, “The Application of Optical Packet Switching in Future Communication Networks,” IEEE Communications Magazine 39, 128–135 (2001).
[Crossref]

B. Wydrowski and M. Zukerman, “QoS in Best -Effort Networks,” IEEE Communications Magazine 40, 44–49 (2002).
[Crossref]

Ayman Kaheel, Tamer Khattab, Amr Mohamed, and Hussein Alnuweiri, “Quality-of-Service Mechanisms in IP-over WDM Networks,” IEEE Communications Magazine 40, 38–43 (2002).
[Crossref]

IEEE Journal on Selected Areas in Communications (1)

M. Yoo, C. Qiao, and S. Dixit, “QoS Performance of Optical Burst Switching in IP -Over-WDM Networks,” IEEE Journal on Selected Areas in Communications 18, 2062–2071 (2000).
[Crossref]

IEEE Network (1)

X. Xiao and L. M. Ni, “Internet QoS: A Big Picture,” IEEE Network 13, 8–18 (1999).
[Crossref]

IEEE/ACM Transactions on Networking (1)

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the Self Similar Nature of Ethernet Traffic (Extended Version),” IEEE/ACM Transactions on Networking 2, 1–15 (1994).
[Crossref]

in Asia -Pacific Optical and Wireless Communications Conference, Proc. SPIE (1)

S. Bjørnstad, N. Stol, and D. R. Hjelme, “Quality of service in optical packet switched DWDM transport networks,” in Asia -Pacific Optical and Wireless Communications Conference, Proc. SPIE 4910, 63–74 (2002).

Other (5)

E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pickavet, and P. Demeester, “Implications of using offsets in all-optical packet switched networks,” in Proceedings of IEEE Optical Network Design and Modelling (Institute of Electrical and Electronic Engineers, 2002).

Leonard Kleinrock, Queueing Systems Volume I: Theory (John Wiley & Sons, 1975).

A.L. Schmid et al., “Impact of VC merging on buffer requirements in ATM networks,” Proceedings of Eighth International Conference on High Performance Networking, 203–217 (1998).

Deepankar Medhi, “Some Results for Renewal Arrival to a Communication Link,” Probability Models and Statistics: A J. Medhi Festschrift, 85–107 (1996).

H. Øverby and N. Stol, “A Teletraffic Model for Service Differentiation in OPS networks,” in Proceedings of IEEE 8th Optoelectronics and Communications Conference (Institute of Electrical and Electronic Engineers, 2003), pp. 677–678.

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Figures (3)

Fig. 1.
Fig. 1. An optical packet switch (a) and the 2-stage hyper-exponential arrival process with priorities (b).
Fig. 2.
Fig. 2. Time continuous Markov chain of the WA with H2-arrival process.
Fig. 3.
Fig. 3. The PLR as a function of the system load (a) and the average PLR as a function of the coefficient of variation (b).

Tables (1)

Tables Icon

Table 1. Simulation and analytical results.

Equations (17)

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

c 2 = ( σ m 1 ) 2 = m 2 m 1 2 1 = ε 1 = 2 a + k 2 a k 2 ( a + k a k ) 2 1
p 0 θ 0 = p 1 μ , r 0 θ 1 = r 1 μ
p i ( i μ + θ 0 ) = a ( p i 1 θ 0 + r i 1 θ i ) + p i + 1 ( i + 1 ) μ 1 i n 1
p n ( n μ + θ 0 ) = a ( p n 1 θ 0 + p n φ 1 , 0 + r n 1 θ 1 + r n φ 1 , 1 ) + p n + 1 ( n + 1 ) μ
p i ( i μ + θ 0 ) = a ( p i 1 φ 0 , 0 + p i φ 1 , 0 + r i 1 φ 0 , 1 + r i φ 1 , 1 )
+ p i + 1 ( i + 1 ) μ n + 1 i N 1
P N θ 0 = a ( p N 1 φ 0 , 0 + p N θ 0 + r N 1 φ 0 , 1 + r N θ 1 )
r i ( i μ + θ 1 ) = ( 1 a ) ( r i 1 θ 1 + p i 1 θ 0 ) + r i + 1 ( i + 1 ) μ 1 i n 1
r n ( n μ + θ 1 ) = ( 1 a ) ( r n 1 θ 1 + r n φ 1 , 1 + p n 1 θ 0 + r n φ 1 , 0 ) + r n + 1 ( n + 1 ) μ
r i ( i μ + θ 1 ) = ( 1 a ) ( r i 1 φ 0 , 1 + r i φ 1 , 1 + p i 1 φ 0 , 0 + p i φ 1 , 0 )
+ r i + 1 ( i + 1 ) μ n + 1 i N 1
r N θ 1 = ( 1 a ) ( r N 1 φ 0 , 1 + r N θ 1 + P N 1 φ 0 , 0 + p N θ 0 )
i = 0 N p i + i = 0 N r i = 1
P H 2 0 = p N φ 0 , 0 + r N φ 0 , 1 φ 0 , 0 i = 0 N p i + φ 0 , 1 i = 0 N r i , P H 2 1 = φ 1 , 0 i = n N p i + φ 1 , 1 i = n N r i φ 1 , 0 i = 0 N p i + φ 1 , 1 i = 0 N r i
P H 2 a v = p N θ 0 + r N θ 1 + φ 1 , 0 i = n N 1 p i + φ 1 , 1 i = n N 1 r i θ 0 i = 0 N p i + θ 1 i = 0 N r i
a = ( 1 + ( c 2 1 ) ( c 2 + 1 ) ) 2 , θ 0 = 2 a λ , θ 1 = 2 λ ( 1 a )
θ 0 = 2 λ ( 1 + ( c 2 1 2 ) ( c 2 + 1 ) ) , θ 1 = 4 λ θ 0 , a = ( θ 0 ( θ 1 1 1 ) ) ( θ 1 θ 0 )

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