Markov model for analysis and modeling of Distributed Coordination Function of Multirate IEEE Mateusz Wielgosz
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1 Marov odel for analyss and odelng of Dstruted Coordnaton Functon of Multrate IEEE Mateusz elgosz 1
2 Introducton Dstruted Coordnaton Functon Creatng a Marov odel Solvng the chan Collson roalty and Throughut Valdaton Proer odel Alcatons Concluson References 2
3 Dstruted Coordnaton Functon (DCF Dstruted Coordnaton Functon s access ethod of MAC layer for It deals wth transort of asynchronous est-effort traffc. It s CSMA/CA technque. Man attrutes: - Sensng the edu - Usng nterfrae saces (IFS ters - Usng ostve acnowledgeents and collson avodance aroach - Executng exonental acoff algorth - Four-way handshae 3
4 Dstruted Coordnaton Functon (DCF - at for channel to e dle for Dstruted InterFrae Sace (DIFS - Generate a rando acoff nterval (Collson Avodance - Bacoff te counter s decreented when cannel s dle and frozen when transsson s detected on the channel and reactvated after edu s dle for DIFS te. Transsson egns once t reaches 0. - Transsson starts wth Request To Send (RTS frae then wats for Clear To Send (CTS frae. After that ayload s transtted. - Lstenng statons udate Networ Allocaton Vector (NAV wth nforaton fro RTS or CTS frae (erod of te n whch the channel wll rean usy 4
5 Dstruted Coordnaton Functon (DCF SIFS s shorter than DIFS hence other statons wll not regard channel dle durng that te. If oth statons eloy RTS/CTS echans collson occurs only on RTS frae and s detected y lac of CTS. Very effectve n ters of syste erforance (esecally for large acets 5
6 Exonental acoff schee Bacoff te or atng Rando Duraton (RD s calculated as follows: RD = C * rando( * SlotTe C or s called Contenton ndow t s rangng fro C n to C ax after each falure C s douled untl reachng axu value. C ax =2 C n. rando( s rando value rangng fro 0 to 1. SlotTe = nal delay to deterne the state of the channel + + Rx-Tx turnaround te + roagaton te. For convenence: = C n axu acoff stage so that =2 and =2 where (0 s called acoff stage 6
7 Bdensonal rocess Let s(t e stochastc rocess reresentng the acoff stage of gven staton. Let (t e stochastc rocess reresentng acoff te counter for gven staton. condtonal collson roalty. Constant and ndeendent. τ statonary roalty that the staton transts a acet n gven slot te. {s(t(t} densonal rocess 7
8 Marov Chan for the acoff wndow sze 8
9 9 Marov Chan for the acoff wndow sze 1 (0 / (1 1 (0 / 1 (0 1 (0 / (1 0 (0 2 ( P P P P t s t s t s t s P P
10 10 Otanng closed-for soluton for the chan Statonary dstruton of the chan: (1 1 (0 (0 ( ( l t t s P t for (1-1: j j ( 0 0 (
11 Otanng closed-for soluton for the chan th revous equatons and 0 0 /(1 we get: (0 (0 1 Now we can exress all as functon of 0 value and condtonal collson roalty. Now ose noralzaton condton: (2 ( Fro that: 2(1 2(1 (1 2( 1 (1 (2 0 11
12 Transsson roalty Proalty τ that a staton transts n randoly chosen slot te: 0 1 (1 2 ( 2(1 2 1 (1 (2 0 0 condtonal collson roalty (at least one of n-1 reanng statons transts: 1 (1 n1 Usng nuercal ethods: 2 ( (2 τ ( - contnuous and onotone functon. 12
13 Throughut P tr there s at least one transsson P 1 (1 tr n P s transsson occurrng on the channel s successful P s n (1 P tr n1 n (1 1 (1 n1 n S noralzed syste throughut fracton of te the channel s used to successfully transt ayload ts: S = E[ayload nforaton transtted n a slot te] E[lengt of a slot te] 13
14 Valdaton 14
15 Proer odel Suortng non-saturated condtons Addtonal acoff stages Unloaded stage Pacet drong 15
16 Alcatons Marov odel rovdes very accurate analytcal fraewor for coutng networ throughut n It can e extended to evaluate erforance of varous asects: - Multrate algorths - Frae loss due to SNR (n addton to collson nduced frae loss - Networ Codng - Rate anoaly - Farness crtera 16
17 Concluson Marov odel for analyss of CDF erforance: Sle Accurate Allows detaled analyss of varous asects Can e extended to suort varous needs 17
18 References 1. Gusee Banch IEEE Saturaton Throughut Analyss 2. Gusee Banch Perforance Analyss of the IEEE Dstruted Coordnaton Functon 3. K. Duffy D. Malone D. Leth Modelng the Dstruted Coordnaton Functon n Non- Saturated Condtons 4. M. Laddoada F. Mest M. Mondn and F. Daneshgaran On the Throughut Perforance of Multrate IEEE Networs wth Varale-Loaded Statons: Analyss Modelng and a Novel Proortonal Farness Crteron 5. N. Dao R. Malaney A New Marov Model for Non-Saturated Networs 6. F. Daneshgaran M. Laddoada F. Mest M. Mondn - Modellng and Analyss of the Dstruted Coordnaton Functon of IEEE wth Multrate Caalty 7. D. ong S. Zheng C. Tha Perforance Analyss of a Mult-Rate IEEE MAC wth Networ Codng 8. H. Laod H. Aff C. De Sants -F Bluetooth ZgBee and Max 9. L. Kannan N. Agarwal M. Tacca A Marov Chan Model to Account for Mult-Rate Transsson and Node Cooeratve Behavor n IEEE Data Ln Protocol 10. G. Bolch S. Grener H. de Meer K. Trved Queueng Networs and Marov Chans 18
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