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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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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=
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
Case C: if i-N<j<i then: Pij=
)1v,2nmin(
Nsrc
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rc
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)0,0,0,ijn(qQ
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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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
),min(
),min(
0
),min(
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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:
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
M
iircrcrc )i(S
C
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C
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Throughput per data channel Sd – dependence on N
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
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
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos
Thank you for your attention
Questions…
CSNDSP 2006 I.E. Pountourakis, P.A. Baziana and G. Panagiotopoulos