Presenter: Jonathan Murphy On Adaptive Routing in Wavelength-Routed Networks Authors: Ching-Fang Hsu Te-Lung Liu Nen-Fu Huang

Overview Background Information Adaptive Routing Algorithms Analytical Model Numerical Results Conclusion

Background Information Alternate Routing –Predefined set of paths assigned for each s-d pair –If ever s-d pair has only one path, it’s fixed routing Adaptive Routing –Routing path dynamically determined based on present state of network

Background Information Assumption: All wavelength routers have full wavelength conversion capabilities –Therefore, wavelength assignment is not discussed, only routing Adaptive routing is focus for this paper

Adaptive Routing Algorithms Shortest Path Strategy (SP) –Objective is to minimize Link cost Wavelength conversion cost * Link Cost Wavelength conversion cost

Adaptive Routing Algorithms Shortest Path Strategy (SP) –Advantage Minimizes use of resources –Disadvantage Does not balance link utilization –One link may be overburdened while another is not used at all

Adaptive Routing Algorithms Least-Loaded Path Strategy (LLP) –Objective is to balance link utilization F(e i ) = Number of free wavelengths For each possible path, find the link with the fewest number of free wavelengths Select the Path with the largest value Maximize: *

Adaptive Routing Algorithms Least-Loaded Path Strategy (LLP) –Advantages Balances link utilization across the network –Disadvantages May lengthen connection paths –Wasted bandwidth –Higher blocking rate *

Adaptive Routing Algorithms Weighted-Shortest Path Strategy (WSP) –Focus of this paper –Tries to balance utilization without cost of increased resource usage or blockage –Hybrid method of above to strategies Minimize value of B Psd X C Psd B Psd = Busy Factor C Psd = Cost of links on path from s to d

Adaptive Routing Algorithms –Goal: Minimize value of B Psd X C Psd B Psd = Busy Factor C Psd = Cost of links on path from s to d *

Exploits single-link model –Analysis of blocking probability –Extended to develop blocking performance of Weighted-Shortest Path Model Also uses overflow model –Used to obtain set of non-linear mathematical equations Final stage –Use successive substitution in iterative fashion for final solution Analytical Model

Assumptions –Every node is a full wavelength router –All connection calls request circuit connections –Arrival of connection requests is Poisson process with individual arrival rates. –Assume wavelength conversion cost = zero Analytical Model

Begin with the distribution of the number of free wavelengths on a single link –Can be done because of Poisson process of connection requests –From here can find the blocking probability of a link Now, Find the distribution of the number of free wavelength channels on a single path –Use and create a recursion function based on single link information above

Analytical Model Find the traffic load of a specific route –Use a cost function –Use this to determine probability that cost of current link is less than all other links Find network-wide blocking probability –Calculate blocking probability of specific route –Use this to find network-wide block probability equation, P Finally, use successive substitution of all above formulas to evaluate P

Numerical Results

Compares the three strategies (as well as the analytical model performance for blocking) Compares across the 3 network topologies as well Numerical Results

Blocking probability (W=4) Numerical Results Logarithmic Scale Number of connection requests per unit connection holding time Available # of wavelengths

Blocking probability (W=4) Numerical Results

Blocking probability (W=4) Numerical Results

Blocking probability (W=8) Numerical Results

Blocking probability (W=8) Numerical Results

Blocking probability (W=8) Numerical Results

Blocking probability results –Blocking probability is higher with increasing traffic load for all strategies –Both SP and WSP better than LLP LLP takes more hops thus uses more bandwidth –SP and WSP have similar performance WSP 12% less than SP when W=8 and #connections = 150 in NSFNET WSP 16% less for interconnected rings when W=8 and #connections = 50 Numerical Results

Overall WSP is best at higher loads Also, results of analytical model within an acceptable range –Best with mesh network though Numerical Results

Average Number of Hops (W=4) Numerical Results

Average Number of Hops (W=4) Numerical Results

Average Number of Hops (W=4) Numerical Results

Average Number of Hops (W=8) Numerical Results

Average Number of Hops (W=8) Numerical Results

Average Number of Hops (W=8) Numerical Results

Average # of hops results –LLP taking more hopes very obvious here SP and WSP very close Notice that average # of hops decreases as connection requests –Blocking probability increases here –Therefore, networks ability to grant longer connections (and thus more hops) decreases –Especially true when W=4 Numerical Results

Standard Deviation of Link Utilization (W=4) Numerical Results

Standard Deviation of Link Utilization (W=4) Numerical Results

Standard Deviation of Link Utilization (W=4) Numerical Results

Standard Deviation of Link Utilization (W=8) Numerical Results

Standard Deviation of Link Utilization (W=8) Numerical Results

Standard Deviation of Link Utilization (W=8) Numerical Results

Standard Deviation of Link Utilization results LLP performs best here!!! –But at cost previously mentioned WSP performs significantly better than SP Numerical Results

Conclusion Weighted-Shortest Path (WSP) adaptive routing strategy proposed –Seeks to combine best features of SP and LLP Analytical model proposed as well Results –WSP works well –Analytical model is accurate Best with mesh network