10.62 Chitizadeh and Varghani (IEE Proceedings Communications, 2003) proposed a new crossbar switch with input queue. Crossbar switches are used for connecting multiple inputs to multiple outputs in a matrix manner. They are used in information processing applications such as packet switching as well as in sorting machines.

Chitizadeh and Varghani studied variation in throughput with respect to switch size. The results from a simulation study for a full load and the theoretical throughput (in % of total input)

are listed in listed in the table below for switch sizes 2 to 16.

a Is there a significant difference between the simulated and theoretical mean throughput?
Justify using a 5% level of significance.
b Plot the theoretical throughput against the simulated throughout. Are there any systematic differences? What would you call these? Make suggestions for adjusting the theoretical throughput using this information.

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Switch Switch Size Theory Simulation Size Theory Theory Simulation 23456789 100 98 10 60 51 100 96 11 57 47 100 93 12 53 42 93 84 13 50 41 82 75 14 48 40 76 70 15 42 38 73 60 16 41 35 63 55