Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Performance evaluation for an optical hybrid switch with circuit queued reservations

Eric W. M. Wong and Moshe Zukerman

Open Access Open Access

Abstract

We provide here a new loss model for an optical hybrid switch that can function as an optical burst switch or optical circuit switch or both simultaneously. We introduce the feature of circuit queued reservation. That is, if a circuit request arrives and cannot find a free wavelength, and if there are not too many requests queued for reservations, it may join a queue and wait until such wavelength becomes available. We first present an analysis based on a 3-dimension state-space Markov chain that provides exact results for the blocking probabilities of bursts and circuits. We also provide results for the proportion of circuits that are delayed and the mean delay of the circuits that are delay. Because it is difficult to exactly compute the blocking probability in realistic scenarios with a large number of wavelengths, we derive computationally scalable and accurate approximations which are based on reducing the 3-dimension state space into a single dimension. These scalable approximations that can produce performance results in a fraction of a second can readily enable switch dimensioning.

©2005 Optical Society of America

Full Article  |  PDF Article
More Like This
Performance evaluation of an optical hybrid switch with circuit queued reservations and circuit priority preemption

Eric W. M. Wong and Moshe Zukerman
Opt. Express 14(23) 11043-11070 (2006)

Performance Evaluation of an Optical Burst Switched Core Node With Generalized Arrivals and Partial Wavelength Conversion Capability

Mohamed H. Morsy-Osman, Mohammed Y. S. Sowailem, Ahmed I. Abd El-Rahman, and Hossam M. H. Shalaby
J. Opt. Commun. Netw. 4(12) 997-1007 (2012)

Reservation information sharing enhancement for deflection routing in OBS network

onghui Gao, Hanyi Zhang, and Zhiyu Zhou
Opt. Express 13(5) 1702-1709 (2005)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)
Fig. 1.
Fig. 1. Blocking probability versus normalized combined traffic intensity.

Download Full Size | PDF

Fig. 2.
Fig. 2. Mean queueing delay for a delayed circuit [sec.] (left) and probability of a circuit being delayed (right) versus normalized combined traffic intensity.

Download Full Size | PDF

Fig. 3.
Fig. 3. Blocking probability versus normalized combined traffic intensity.

Download Full Size | PDF

Fig. 4.
Fig. 4. Mean queueing delay for a delayed circuit [sec.] (left) and probability of a circuit being delayed (right) versus normalized combined traffic intensity.

Download Full Size | PDF

Fig. 5.
Fig. 5. Blocking probability versus normalized combined traffic intensity.

Download Full Size | PDF

Fig. 6.
Fig. 6. Mean queueing delay for a delayed circuit [sec.] (left) and probability of a circuit being delayed (right) versus normalized combined traffic intensity.

Download Full Size | PDF

Fig. 7.
Fig. 7. Blocking probability versus normalized traffic intensity for burst traffic only.

Download Full Size | PDF

Fig. 8.
Fig. 8. Blocking probability versus normalized combined traffic intensity.

Download Full Size | PDF

Fig. 9.
Fig. 9. Mean queueing delay for a delayed circuit [sec.] (left) and probability of a circuit being delayed (right) versus normalized combined traffic intensity.

Download Full Size | PDF

Equations (67)

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

π i , j , k ( ( i + k ) μ b + j μ c + ( M − i − j − k ) λ )
= π i , j , k + 1 ( k + 1 ) μ b + π i , j + 1 , k ( j + 1 ) μ c
+ π i , j , − 1 , k ( M − ( i + j − 1 + k ) ) λ c
+ π i − 1 , j , k ( M − ( i − 1 + j + k ) ) λ b
+ π i + 1 , j , k ( i + 1 ) μ b ,
π i , j , k ( ( M − K − k ) λ + ( k + i ) μ b + j μ c )
= π i , j − 1 , k ( M − K + 1 − k ) λ c
+ π i − 1 , j , k ( M − K + 1 − k ) λ b
+ π i , j , k − 1 ( M − K − k + 1 ) λ b
+ π i , j + 1 , k ( j μ c )
= π i , j , k + 1 ( k + 1 ) μ b + π i + 1 , j , k ( i + 1 ) μ b .
π i , j , k ( ( M − K − k ) ( λ b + a j λ c ) + ( k + i ) μ b + j μ c )
= π i , j − 1 , k b j ( M − K + 1 − k ) λ c
+ π i , j , k − 1 ( M − K − k + 1 ) λ b + π i , j + 1 , k ( K − i ) μ c
+ π i , j , k + 1 ( k + 1 ) μ b + π i + 1 , j , k ( i + 1 ) μ b
a j = ∑ n = i + j − K + 1 N c ( n )
b j = ∑ n = i + j − K N c ( n ) .
∑ i , j , k π i , j , k = 1
O c = ∑ i , j , k ( M − i − j − k ) ( λ c μ c ) π i , j , k .
C c = ∑ i , j , k min ( j , K ) π i , j , k .
B c = 1 − C c O c .
O b = ∑ i , j , k ( M − i − j − k ) ( λ b μ b ) π i , j , k ,
C b = ∑ i , j , k iπ i , j , k .
B b = 1 − C b O b .
C q = ∑ ∀ k , i + j ≥ K a j ( M − i − j − k ) ( λ c μ c ) π i , j , k
a j = ∑ n = i + j − K + 1 N c ( n ) .
D p = C q C c .
Q c ¯ = ∑ ∀ k , i + j ≥ K ( i + j − K + 1 ) a j ( M − i − j − k ) ( λ c μ c ) π i , j , k C q
a j = ∑ n = i + j − K + 1 N c ( n ) .
R c = ∑ i + j = K , k ( i μ b + j μ c ) π i , j , k ∑ i + j = K , k π i , j , k .
D ¯ c = Q c ¯ R c .
1 λ * = 1 λ + p b B b μ b .
1 μ * = C c μ c C b μ b + C c μ c 1 μ c + C b μ b C b μ b + C c μ c 1 μ b
C b = ∑ i = 0 K − 1 ( M − i ) p b λ * μ b p i
C c = ∑ i = 0 K − 1 ( M − i ) p c λ * μ c p i + ∑ i = K K + N − 1 ( M − i ) a i p c λ * μ c p i
a i = ∑ n = i − K + 1 N c ( n ) .
B c = 1 − C c O c
O c = ∑ i = 0 K + N ( M − i ) p c λ * μ c p i ,
p i = ( M − i + 1 ) λ * i μ * p i − 1
p i = ( M − i + 1 ) b i p c λ * K μ * p i − 1
b i = ∑ n = i − K N c ( n )
∑ i = 0 K + N p i = 1
B c = 1 − C c O c .
O b = ∑ i = 0 K + N ( M − i ) p b λ * μ c p i .
B b = 1 − C b O b .
C q = ∑ i = K K + N − 1 ( M − i ) a i p c λ * μ c p i
a i = ∑ n = i − K + 1 N c ( n ) .
D p = C q C c
Q c ¯ = ∑ i = K K + N − 1 ( i + 1 ) ( M − i ) a i p c λ * μ c p i C q
a i = ∑ n = i − K + 1 N c ( n ) .
D ¯ c = Q c ¯ R c .
1 λ * = 1 λ b + B b μ b .
p i = ( M − i + 1 ) λ * i μ b p i − 1
∑ i = 0 K p i = 1
B b = 1 − C b O b
O b = ∑ i = 0 K ( M − i ) λ * μ b p i
C b = ∑ i = 0 K − 1 ( M − i ) λ * μ b p i .
M K ( λ b μ b + λ c μ c ) .
BP = λ b μ b λ b μ b + λ c μ c .
1 λ ′ = λ c λ ( 1 λ ) + λ b λ ( 1 λ + 1 μ b + 1 λ ′ ) ,
1 λ ′ = 1 λ + λ b λ c ( 1 λ + 1 μ b ) .
p j ′ = ( M − j + 1 ) λ ′ j μ c p j − 1 ′
p j ′ = ( M − j + 1 ) ( ∑ n = j − k N c ( n ) ) λ ′ K μ c p j − 1 ′ .
∑ j = 0 K + N p j ′ = 1 ,
O pc = ∑ j = 0 K + N ( M − j ) λ ′ μ c p j ′
C pc = ∑ j j = 0 K + N p j .
B pc = 1 − C pc O pc .
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use