Performance Analysis of Multiclass FIFO: Motivation, Difficulty and a Network Calculus Approach

Transcription

1 Performace Aalysis of Multiclass FIFO: Motivatio, Difficulty ad a Network alculus Approach Yumig Jiag Norwegia Uiversity of Sciece ad Techology (NTNU) 1 19 March 2014, 2d Workshop o Network alculus, Bamberg, Germay

2 Outlie Motivatio Performace Aalysis of Multi-lass FIFO: Difficulty with the lassic Queueig Theory Direct Aalysis usig Network alculus A New Idea for Aalysis usig Network alculus ocludig Remarks 2

3 Motivatig Scearios Iteret packet size distributio 40 (60%) (40%) Flows with differet packet sizes sharig the same output lik 3

4 Motivatig Scearios (cot ) Dowlik sharig i wireless etworks (e.g. DSH dowlik shared chael) 4 Figure from WDMA for UMTS, edited by Harri Holma ad Atti Toskala, 2002

5 Motivatig Scearios (cot ) Iput queueig i switches / routers 5

6 Performace Aalysis of Multi-lass FIFO: System Model A packet-switched etwork ode serve packets i FIFO maer. FIFO There are N traffic classes. The service rate of each class is costat i bps. 6

7 Aalysis usig Queueig Theory: Difficulty How to defie system states? Is (# of each class packet i queue) sufficiet? If ot, what else? FIFO Assume Poisso arrival process ad expoetially distributed packet legths of each class. What is the state trasitio diagram? Or, is it possible to get oe? If iterarrival times are ot expoetially distributed, or packet times are ot expoetially distributied, how to do the aalysis? 7

8 Aalysis usig Network alculus Assumptio: The traffic flow of each class is (σ, ρ)-costraied: FIFO A ( s, t) σ + r ( t s) 8

9 Direct Results from Network alculus A(t) If the service rates to all classes are the same, the system becomes the ormal sigle-class FIFO; The total iput A(t) is costraied by: A*(t) A( s, t) σ + r ( t s) 9

10 Direct Delay Boud from Network alculus (with igorig the last packetizer effect) Amout of Traffic/Service σ 0 Max. Delay h(α,β) β ( t ) = t α (t) = rt + σ t If the total arrival rate is smaller tha, the delay of ay packet is bouded by: D σ 10

11 Aalysis of Multiclass FIFO: Network alculus Approach Easy But, wait: What if the service rate (i bps) for each class is differet? A(t) A*(t) 11

12 Direct Delay Boud from Network alculus Amout of Traffic/Service β ( t) = α (t) = rt + σ mi t For multiclass FIFO, the miimum service rate to ay class is mi. 12 σ 0 Max. Delay h(α,β) t If the total arrival rate is smaller tha mi, the delay is bouded: D mi σ

13 Aalysis of Multi-lass FIFO: A ew idea for the etwork calculus approach Iequality: For ay packet arrivig at t, its delay is bouded by: FIFO D sup s t [ A ( s, t) r ( t s)] 13

14 Improved Delay Boud Suppose the followig coditio holds FIFO r < 1 The delay of ay packet is bouded by: D σ 14 The boud is tight!

15 ompariso of Delay Bouds oditio: oditio: r mi < 1 r < 1 Direct bouded: Improved Boud: 15 D σ mi D σ

16 ompariso of Delay Bouds 16 Two classes 1 = 10 Mbps 2=100 Mbps Each class has oe flow. Each flow is (σ, ρ)- costraied with burstiess parameter 1KB ad rate parameter 100 Kbps. A i ( s, t) 8Kb + 100Kbps ( t s) oditio: Direct bouded: oditio: 100Kbps 100Kbps + < 1 10Mbps 100Mbps Improved Boud: 100Kbps 10 Mbps < 1 8Kb 8Kb D + = 0. 88ms 10Mbps 100Mbps 2 8Kb D = 1. 6ms 10Mbps 2

17 Implicatio of the Delay Boud Differece Suppose the same 2-class FIFO system. Questio: How may lass 1 & lass 2 flows, (M 1, M 2 ), may be admitted if a delay boud of 8ms eeds to be guarateed? Must cosider both the coditio ad the correspodig delay boud i fidig the regio for (M 1, M 2 ). 17

18 ocludig Remarks 18 Surprisigly difficult to aalyze multi-class FIFO usig Queueig Theory. Network calculus approach may be used directly, but with limited applicatio scearios ad/or loose bouds. A ew idea for the etwork calculus approach ca improve the bouds. The aalysis has bee exteded to stochastic ad etwork cases. The aalysis has bee exteded for other performace metrics e.g. backlog ad leftover service, but more diffficult ad has room to improve. Part of the results were preseted at 2d Europea Teletraffic Semiar (ETS), Sept 2013, ad icluded i arxiv (