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Table 5 Collision scenarios for up to eight colliding tags per slot

From: A smart collision recovery receiver for RFIDs

Scenarios

R = 1

R = 2

R = 3

R = 4

R = 5

R = 6

R = 7

R = 8

Unique

Ps 1 = 1

Ps 1 = 0.875

Ps 1 = 0.656

Ps 1 = 0.410

Ps 1 = 0.205

Ps 1 = 0.077

Ps 1 = 0.019

Ps 1 = 0.002

 

1

1 + 1

1 + 1 + 1

1 + 1 + 1 + 1

1 + 1 + 1 + 1

1 + 1 + 1 + 1

1 + 1 + 1 + 1

1 + 1 + 1 + 1

     

1

1 + 1

1 + 1 + 1

1 + 1 + 1 + 1

Mixed scenario

 

Ps 2 = 0.125

Ps 2 = 0.328

Ps 2 = 0.492

Ps 2 = 0.513

Ps 2 = 0.385

Ps 2 = 0.202

Ps 2 = 0.067

  

2

2 + 1

2 + 1 + 1

2 + 1 + 1 + 1

2 + 1 + 1

2 + 1 + 1

2 + 1 + 1

      

1 + 1

1 + 1 + 1

1 + 1 + 1 + 1

   

Ps 3 = 0.016

Ps 3 = 0.041

Ps 3 = 0.154

Ps 3 = 0.288

Ps 3 = 0.337

Ps 3 = 0.252

   

3

2+2

2+2+1

2+2+1

2+2+1

2+2+1

      

1

1 + 1

1 + 1 + 1

    

Ps 4 = 0.055

Ps 4 = 0.103

Ps 4 = 0.019

Ps 4 = 0.084

Ps 4 = 0.168

    

3+1

3+1 + 1

2 + 2 + 2

2 + 2 + 2

2 + 2 + 2

       

1

1 + 1

    

Ps 5 = 0.002

Ps 5 = 0.017

Ps 5 = 0.128

Ps 5 = 0.112

Ps 5 = 0.011

    

4

3 + 2

3 + 1 + 1

3 + 1 + 1

2 + 2 + 2

      

1

1 + 1

2

     

Ps 6 = 0.009

Ps 6 = 0.077

Ps 6 = 0.168

Ps 6 = 0.067

     

4 + 1

3 + 2 + 1

3 + 2 + 1

3 + 1 + 1 + 1

       

1

1 + 1

     

Ps 7 = 2·10-4

Ps 7 = 0.002

Ps 7 = 0.017

Ps 7 = 0.224

     

5

3 + 3

3 + 2 + 2

3 + 2 + 1

        

1 + 1

      

Ps 8 = 0.019

Ps 8 = 0.112

Ps 8 = 0.084

      

4 + 1 + 1

3 + 3 + 1

3 + 2+ 2

        

1

      

Ps 9 = 0.003

Ps 9 = 0.028

Ps 9 = 0.028

      

4 + 2

4 + 1  +  1

3 + 3 + 1

       

1

1

      

Ps 10 = 0.001

Ps 10 = 0.017

Ps 10 = 0.006

      

5 + 1

4 + 2 + 1

3 + 3 + 2

      

Ps 11 = 3·10-5

Ps 11 = 0.001

Ps 11 = 0.028

      

6

4 + 3

4 + 1  +  1

        

1  +  1

       

Ps 12 = 0.003

Ps 12 = 0.042

       

5 + 1  +  1

4 + 2 + 1

        

1

       

Ps 13 = 6·10-4

Ps 13 = 0.004

       

5 + 2

4 + 2 + 2

       

Ps 14 = 2·10-4

Ps 14 = 0.006

       

6 + 1

4 + 3 + 1

       

Ps 15 = 4·10-6

Ps 15 = 1·10-4

       

7

4 + 4

        

Ps 16 = 0.006

        

5 + 1  +  1  +  1

        

Ps 17 = 0.003

        

5 + 2 + 1

        

Ps 18 = 2·10-4

        

5 + 3

        

Ps 19 = 6·10-4

        

6 + 1  +  1

        

Ps 20 = 9·10-5

        

6 + 2

        

Ps 21 = 3·10-5

        

7 + 1

        

Ps 22 = 5·10-7

        

8

  1. Collision scenarios for up to eight tags colliding in the same slot are listed in Table 5. Here, the numbers in italics of the form 2+1+1… represent the number of tags with the same postpreamble. Italic digit ‘ 1’ indicates single occurrences of colours; italic digit ‘ 2’ indicates single pairs occurring.