Exercise N.1                                

 

  1. Create the GSPN model of the Knockout ATM switch architecture using the following parameters:

 

·        Number of input ports = 4

·        Speed up (SU) = 2

·        Internal buffer size (IB) = 1

·        Output buffer size (M) = 50

 

The priorities that must be assigned to immediate transitions are:

 

TRANSITION NAME

PRIORITY VALUE

cell, no_cell

1

internal_loss

2

next, flush

3

switch, all_empty

4

output_loss, accept

5

transmit

6

 

The rate of the timed transition clock is equal to 1.0 with 1-server semantic.

 

  1. Solve the model in steady-state for the following scenarios:

 

a1=a2=a3=a4=0.125 such that the total load offered to the output buffer is r = 0.5

a1=a2=a3=a4=0.15 such that the total load offered to the output buffer is r = 0.6

a1=a2=a3=a4=0.2 such that the total load offered to the output buffer is r = 0.8

a1=a2=a3=a4=0.24 such that the total load offered to the output buffer is r = 0.96

 

For each of the previous scenarios compute the following performance indexes:

                    

Output Cell Loss Ratio (OCLR) = SU * X(output_loss) / r

Internal Cell Loss Ratio (ICLR) = SU * ∑ X(internal_loss) / r

Average Buffer Availability (ABA) = TOK(OUTPUT_BUFFER_SPACE)

 

Where TOK(OUTPUT_BUFFER_SPACE) denotes the mean number of tokens in place OUTPUT_BUFFER_SPACE.

 

  1. Repeat all the previous analysis with output buffer size equal to 30 cells

 

                                           Exercise N.2                                

 

  1. Repeat Exercise N.1 for the Gauss ATM switch architecture provided that:

 

The priorities that must be assigned to immediate transitions are:

 

TRANSITION NAME

PRIORITY VALUE

cell, no_cell

1

internal_loss

2

next, flush

3

load

4

shift_full, shift_empty

5

output_loss, accept

6

transmit

7

 

The rate of the timed transition clock is equal to 1.0 with 1-server semantic.

 

                                           Exercise N.3                                

 

Analyse the possible unfairness of the Gauss ATM switch architecture (that is, compute the ICLR values) by considering several load scenarios where the probabilities of incoming cells at each input line are not equal (as in Exercise N.1 and Exercise N.2). In particular, consider the following scenarios:

 

For this type of analysis, the output buffer size can be set equal to 0.

 

                                           Exercise N.4                                

 

Analyse and compare the performance of the Knockout and Gauss ATM switch architectures when the internal speed up (SU) is set equal to 3 (instead of 2 as in the previous exercises). Consider the load scenarios of Exercises N.1 and N.2 and one among those in Exercise N.3; consider increasing values of the output buffer size (M). In particular, plot a graph for each scenario where the x-axis represents the output buffer size values and the y-axis represent the OCLR. Consider M ranging from 10 to 100 step 10.