Performance of a (σ, ρ) regulator. Consider the on-off MMP in Figure 24.3 as the unregulated source to a (σ, ρ) regulator (Section XXXXXXXXXXLet σ = 1 and ρ = 1/2, with one token created every other...

Performance of a (σ, ρ) regulator. Consider the on-off MMP in Figure 24.3 as the unregulated source to a (σ, ρ) regulator (Section 15.2.1). Let σ = 1 and ρ = 1/2, with one token created every other time slot. What conditions on the “on” injection rate r₁
of the injection process are necessary so that this system is stable (that is, the packet queue in the regulator has a finite expected size)? Create a Markov chain model of this system to determine the average size of the regulators packet queue for
Simulate this model for different values of r₁, record the average queue size and use Little’s law, Equation 23.6, to also find the expected delay of the regulator.