Propagation Delay and Receiver Collision Analysis in WDMA Protocols I.E. Pountourakis, P.A. Baziana...

Propagation Delay and Receiver Collision Analysis in WDMA Protocols

I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos

School of Electrical and Computer Engineering,

National Technical University of Athens, Greece,

e-mail: [email protected]

5th Int. Con. on Communication Systems, Networks and Digital Signal Processing

CSNDSP 2006 – July 19-21, 2006

We present:

• A network protocol:

• for Wavelength Division Multiple Access (WDMA)

• for synchronous transmission

• in passive star topology

• with multiple control channels: Multi-channel Control Architecture (MCA)

• We achieve performance improvement exploiting:

• MCA: less processing overhead for control information

• propagation delay latency: simple MAC protocol to avoid data channel conflicts

• Analysis:

• discrete time Markovian model

• for finite number of stations and WDM channels

• with receiver collision effect

CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos

WDMA Protocols

• Performance parameters: • control channel collisions• data channel collisions• receiver collisions• propagation delay

• Single common-shared control channel vs MCA:• Single control channel:

stations can not receive and process all control packets maximum processing rate is limited to the speed of electronic interface

• MCA: multiple control channels to exchange control information elimination of electronic processing bottleneck MAC techniques to avoid of data channel collisions

• Normalized propagation delay R:• is the ratio of propagation delay to data packet transmission time L• has large values in WDM networks• is a useful attribute to develop WDMA algorithms

• Receiver collisions:• are usually neglected in analysis• have significant effect on performance


Passive star multi-wavelength architecture

• Network model:• M – number of stations• v - number of control channels (λc1,..,λcv )• N - number of data channels (λd1,..,λdN)

• Each station has: • a tunable transmitter tuned at all channels

λc1,..,λcv,λd1,..,λdN • v fixed tuned receivers one for each control channel • a tunable receiver for data channels λd1 ,..,λdN

• Time reference: • common clock to all stations • cycle: C=1+(R+1)L time units


Packet Transmission – Access Mode (1)

• Packet generation:• independently at each station• following geometric distribution:

free stations: probability p backlogged stations: probability p1

• The station attempting to transmit:• chooses randomly a wavelength for data packet transmission• informs the other stations by sending a control packet:

chooses randomly one of the v control channels transmits the control packet according to Slotted Aloha protocol: control channel collisions

• monitors the MCA with its fixed tuned receivers• (R×L) time units later knows the data channel transmission claims of all stations


Packet Transmission – Access Mode (2)Cases: • if control channel collision: the station becomes backlogged• if no control channel collision:

if the selected data channel is chosen from some other station:data channel collision avoidance algorithm is applied

only one among the competed stations transmits the others stations become backlogged


Packet Transmission – Reception Mode

• The destination station:

• waits R×L time units after data packet transmission

• adjusts its tunable receiver to the data channel for reception

• Receiver collisions:

• if two or more packets are addressed to the same destination

• one of them is correctly received

• the others are aborted

• Free stations become backlogged in case of:

• control channel collision

• data channel collision

• receiver collision at destination


Model analysis

Performance is described by a discrete time Markov chain:

• Markov system state Xt: is the number of busy stations in each cycle computes:

the one step transition probabilities the steady state probabilities

• performance measures in steady state: throughput Src number of backlogged stations B input rate Sin

delay D


One step transition probabilities Pij=(Xt+1=j | Xt=i)

Case A: if j<i-N then: Pij=0

Case B: if j = i-N then: Pij=

Case D: if j=i then: Pij=

Case E: if j>i then: Pij=


Case C: if i-N<j<i then: Pij=

)1v,2nmin(

Nsrc

i

2Nnni

rc

)v,imin(

Nnnii0

)N,N,s,n(q

)N,N,n,n(qQ

Φ

Φ

)N,smin(

jimlrc

)1v,2mnmin(

jims

)jiN,iMmin(

0mmi

i

2jinni

)N,nmmin(

jimlrc

)nv,jiN,iMmin(

0mmi

)v,imin(

jinni

)jim,l,s,mn(

Qq

)jim,l,mn,mn(

Qq

Φ

Φ

)N,smin(

mlrc

)1v,2mnmin(

ms

)N,iMmin(

1mmi

i

2nni

)N,mnmin(

mlrc

)nv,N,iMmin(

1mmi

)1v,imin(

0nni

i

2nrcnii0rci0i0

)m,l,s,mn(

Qq

)m,l,mn,mn(

Qq

)0,0,0,n(qQ)0,0,0,0(Qq

Φ

Φ

ΦΦ

)N,smin(

jimlrc

)1v,2mnmin(

jims

)jiN,iMmin(

1ijmmi

i

0nni

)N,mnmin(

jimlrc

)nv,iMmin(

1ijmmi

)ij1v,imin(

0nni

i

0nrcnii,ij

)jim,l,s,mn(

Qq

)jim,l,mn,mn(

Qq

)0,0,0,ijn(qQ

Φ

Φ

Φ

Performance Measures (1)

• Steady state probabilities by solving the system of the linear equations:• π = π P •

P: transition matrix with elements the probabilities Pij π: row vector with elements the steady state probabilities πi

• Conditional throughput Src(i): the expected value of the output rate, Src(i)=E[At | Xt=i]= :

M

0ii 1

where: )p,i,n(binq 1in )p,i,nM(binQin ji ,)p1(pj

i)p,j,i(bin jij


),min(

),min(

0

),min(

)(),max(

)1,2min( ),min(

0 )(),max(1

),,,(Φ

),,,(Φ

Nmn

klrc

nviM

knmvm

mi

vi

iMiMknni

vmn

ks

Ns

klrc

iM

knmm

mi

i

iMiMknni

N

k

klmnmn

Qq

klsmn

Qqk

Performance Measures (2)

• Steady state average throughput Src:

• Steady state number of backlogged stations B:

• Conditional input rate Sin(i): the expected number of arrivals:

• Steady state average input rate Sin:

• Throughput per data channel Sd:

• Delay D: the average cycles that a packet has to wait until its transmission:


M

iircrcrc )i(S

C

L)]i(S[E

C

LS

0

π

M

iii)i(EB

0

p)iM(]iX|H[E)i(S ttin

M

0iiin )iM(pS

N

SS rc

d

inS

B}L)R({}L)R({D 1111

Throughput per data channel Sd – dependence on N


As N increases for fixed stations:

• probability of data packet successful transmission: increases

• probability of data packet rejection at destination: increases

• Throughput per data channel Sd decreases

Rejection probability – dependence on N


As N increases for fixed stations:

• probability of data packet successful transmission: increases

• probability of data packet rejection at destination: increases

Throughput per data channel Sd – dependence on R


As R increases:

• C increases: increasing function of R

• Sd decreases: inverse proportional function of C

• cycle percentage for successful transmission: decreases

• essential reduction of Sd

Delay D vs Throughput per data channel Sd – dependence on R


As R increases:

• significant increase of D

• performance deterioration

• strong dependence of both Sd and D from R

Results

• System efficiency in WDMA depends on:

• powerful influence of R

• key role of receiver collisions (correlation of v, N, M)

• Both R and receiver collisions:

• sought be taken into consideration

• Our motivation:

• “exploitation” of R

• introduction of access algorithm to avoid data channel collisions

• use of MCA to minimize headers processing requirements

• improvement of system performance


Thank you for your attention

Questions…


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Propagation Delay and Receiver Collision Analysis in WDMA Protocols I.E. Pountourakis, P.A. Baziana...

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