Email Delay (msec) WFQ Bandwidth as a function of Email Delay

0 20 40 60 80 100 120 140 160 180 200

0 500 1000 1500 2000 2500 3000 3500

Link Capacity (Mbps)

WWW Delay (msec) WFQ Bandwidth as a function of WWW Delay

Figure10.4: WFQCapacityvsEmailandWWWDelayforCase4: increased

Emailand WWW variance

analysis is not able to capture the eects of this nonlinearity hence the

pre-dicted sensitivity coeÆcients for Email and WWW are not accurate. This

inaccuracy inturnaectsthe varianceresults. However wecanobservefrom

the simulationthat Emailis nowthe most signicantfactor, contributingto

about50%ofthevariance,followedbyWWWtraÆc. ForCBQ,Table 10.14

shows thatemail andWWW are themost signicantfactors contributingto

the varianceincapacity, togetheraccounting foralmostallof thevariancein

capacity.

In terms of the sensitivity however, voice is still the highest followed by

emailthen videoandWWW. ThePQresultsare shown inTable 10.15. We

observethesametrendsasforCBQinthevariancecontributionofeachtraÆc

Sensitivity(Mbps/msec) 79.3 5.13 12 3.75

p

Variance(Mbps) 23.2 9.47 497.94 392.25

% Variance 0.13 0.02 61.5 38.35

Table10.14: CBQSimulationResultsforCase4: increasedEmailandWWW

variance

Parameter Voice Video Email WWW

Sensitivity(Mbps/msec) 32.7 3.04 12 3.85

p

Variance(Mbps) 11.6 6.32 506.85 402.74

% Variance 0.03 | 61 38.97

Table 10.15: PQSimulationResultsforCase 4: increased Emailand WWW

variance

type although the sensitivity indices are dierent. Voice has the highest

sensitivityindex followed by email,thenWWW andVideo. ForFIFO,voice

and video are the most signicant factors both in terms of sensitivity and

variance in capacity as shown in Table 10.16. This is because only a small

Parameter Voice Video Email WWW

Sensitivity(Mbps/msec) 2820 182 0.679 0.184

p

Variance(Mbps) 825.8 336.98 64.17 68.65

% Variance 84.8 14.1 0.5 0.6

Table 10.16: FIFO Simulation Results for Case 4: increased Email and

WWW variance

proportion of samples from the email and WWW distributions (0.5% and

0.25%respectively)aresmallenoughtobetheminimumvaluethatdetermine

the capacity.

The four cases in this section have validatedthe methodology and

analy-sis that can be used to perform uncertainty and sensitivity analysis for the

four traÆc handling schemes. Numerical simulations can be used to

per-formthe sensitivity analysiswhilethe theoreticalanalysis isvalidonlywhen

the capacity-delay function is linear. More work is needed to extend and

generalize the theoretical formulation tocoverall cases.

In this chapterwe have shown how astochastic formulationof the delay

re-quirements can be used to provide some understanding of how the capacity

requiredbydierenttraÆchandlingschemesisaectedbyuncertaintyinthe

values ofthe maximumdelaybounds. Wehavedeveloped anddemonstrated

amethodology forperforminguncertaintyand sensitivity analysiswhich can

be used to capture how uncertainty in delay bounds translates into

uncer-tainty inthenetworkcapacity. Apurely analyticsolutionhas beenobtained

with the accuracy being largely dependent on the linearity of the

capacity-delayfunction. Forcaseswherethefunctionsarenotlinear,numericalMonte

Carlo simulations were used to provide accurate results. In the next

chap-ter we conclude by discussing the relevancy of our results in the context of

network planningand design.

Conclusion

11.1 Implications of Results on Network

Ar-chitectures

Weconcludebydiscussing theresults obtainedinthe contextofcurrent and

proposedapproachestothe useoftraÆchandlingformulti-servicenetworks.

 Best-Eort Network

Thebest-eortnetworkusesFIFOinboththeedgeandcoresothatthe

delay guarantees are uniform across all traÆc types. From our results

wend that tosupport theQoS of delay-sensitive applicationssuchas

voicerequires abundantnetwork capacitywhen the voicetraÆc shares

aqueuewithburstytraÆcsuchasemailandWWW.Whenthereisno

bursty traÆcthen anall-FIFOnetworkperformsjustaswell asa

non-FIFO network. This may seem to suggest the use of separate queues

and links (in essence a separate network) for delay sensitive traÆc to

isolateitfromthe burstynon-delay sensitivetraÆc. The appealofthe

best-eort network lies in its simplicity and if network capacity is not

a constraint, then itmay stillbe the network of choice for some.

 Class-BasedNetwork

In a class-based network, ows are grouped into distinct classes and

resources suchas queues and linkbandwidth are allocatedto the class

as whole. TraÆc handlingapproaches for this type of network include

Class-Based Queueing, Priority Queueing and Class-Based Weighted

Fair Queueing among others. Our results show that using class-based

can meet the delay guarantees of all traÆc types with minimal

band-width. Class-based handling in the edge with best-eort handling in

the core requires moderatecapacity while using best-eortin the edge

increases the bandwidth signicantly. The complexity of class-based

handling may range from fair to extreme depending on the exact

im-plementation.

 Flow-Based Network

In a ow-based network, each ow is allocated its own dedicated

re-sources and as such managing the network may prove to be complex

when there are numerous ows. Using ow based handling such as

WFQ requires minimal capacity and any combination of ow-based

handling and class-based handling does not increase the bandwidth

signicantly. Using ow-based handlingwithbest-eorthandlingin

ei-ther the edge or core of the network requires more abundant capacity.

Figure 11.1summarizesthecapacityrequirementsofcombinationsofedge

and core traÆc handlingmechanisms.

Edge