1. Effects of TSI/TSA (or Wavelength Conversion) on Ring Loading E E 681 - Module 8 W. D. Grover TRLabs & University of Alberta © Wayne D. Grover 2002, 2003

2. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 2 With Time Slot Interchange (TSI) ADM nodes can shift demands around as needed to which ever might be free in the next span. Functionally, TSI in SONET ADMs is the same as Wavelength Conversion in an Optical wavelength ADM (“OADM”). Assuming this capability, all the “loading” formulation needs to consider is the line capacity constraint on each span. Therefore, TSI is an implicit technology assumption in the prior formulations. When TSI is not a capability of the ADMs, the ring is said to be operating in Time Slot Assignment (TSA) mode (or that it is optically “transparent”). The TSA mode ring -loading problem is more computationally complex because each channel (or wavelength) must be associated with a specific demand for its entire path through the ring. Representing Time-slot assignment in the formulations

3. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 3 with TSI (or wavelength conversion) : d1d1 dkdk “colour clash” resolved by TSI (or wavelength conversion) (add / drop) without TSI / wavelength cconversion (i.e., TSA mode): initial assignments must avoid “colour clash” only add / drop allows re-use Representing Time-slot assignment in the formulations

4. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 4 Inputs (“parameters”) Outputs (“variables”) BLSR Ring “Loading” in TSA mode

5. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 5 maximize the number of unit demands served, over all timeslots in both directions. A timeslot t cannot be used more than once in either direction on each span. you can refuse any demand, or serve it entirely. Note: this formulation permits “demand (bundle) splitting” within the ring: - Why is this the case? BLSR Ring “Loading” in TSA mode decisions are binary

6. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 6 Consider what has happened to the complexity: |R| * Cinequality constraints |D|equality constraints 3 |D| * C{0/1} variables |R| inequality constraints |D| equality constraints 2 |D|{0/1} variables BLSR Ring “Loading” in TSA mode Previously (TSI case) had:Now (TSA case) have:

7. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 7 Research questions posed: 1. How important is TSA (or wavelength conversion) to maximizing the loading efficiency of BLSR or OPSR type rings? 2. What is the potential benefit of permitting demand bundle splitting in ring loading? Motivation: Wavelength conversion may be quite costly in optical ADMs.  What is the penalty for optical ring networking without interchange abilities?  RingBuilder development context…. Do we need to solve TSA sub-problems or will TSI be adequate ? Overview of a recent study G. D. Morley, W.D. Grover, "Effects of Channel Interchange and Directional Demand Splitting on the Loading Efficiency of SONET or DWDM Line-switched rings," Journal of Network and Systems Management (Plenum Press), Vol. 10, No. 4, 2002, pp. 457-482.

8. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 8 Study Methodology: - Define 4 mathematical models for loading process: with / without TSI with / without permitting demand splitting - Model random instances of mesh-like, single-hub, dual-hub demand patterns - Treat size of demand pool for each trial case, relative to total ring bw-hops, as a parameter. - consider: - 12- and 48- channel rings of 5 spans, - 12- and 48- channel rings of 10 spans, - somewhat over 12,000 randomized trials (~ 3,000 each ring scenario) - solve each loading formulation for each ring x demand pattern trial case Overview of a recent study

9. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 9 Quantitative Measures defined to characterize the issues of the study: - Loading efficiency: for the TSA case for the TSI case - Relative size of the available demand pool: “circumferential capacity of the ring” Q. What upper limit does |R|C represent? Overview of a recent study

10. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 10 5 node, 48 channel ring, mesh demand, TSI 10 node, 48 channel ring, mesh demand, TSI same ring can vary in efficiency by factor of two even under optimal loading...efficiency is highly dependent on exact demand patterns splitting demand bundles into cw / ccw mixed flows can improve efficiency 10-12 % on average, up to 33% in the 90th percentile cases ring with more spans are harder to load as efficiently or, conversely, require a larger demand pool to achieve high loadings. Selected Results

11. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 11 A more surprising finding: Frequency of cases (merged split / non split data for random mesh, 10 node ring) In only 15 trials (out of 3372) did TSI increase achievable loading efficiency ! Overview of a recent study: Selected Results

12. E E 681 - Module 9 © Wayne D. Grover 2002, 2003 12 This seems counter-intuitive. What is the interpretation ? The optimal solver for the non TSI case is almost always able to find a set of loading choices and fixed timeslot assignments that serves as much demand as the TSI solutions. However both problems (TSI / TSA loading) are being solved “from the ground up”. That is, all postulated demands are assumed known and available at the single ring loading design time. Above may be accurate for entire network design / redesign contexts but an alternate situation is provisioning new demands that arise one-by-one, incrementally. TSI may be much more important in the latter context (we don’t know yet.) Related ongoing research problems: - optimal formulation or algorithm for continuous incremental loading ? - treatment of uncertainty in loading policy ? - how much would limited TSI improve incremental loading efficiency? Overview of recent “loading study”: