Useful Formulas1. IfTis an exponentially distributed random variable with mean1/λ, then the density ofTis given byfT, where:fT(t) =λe-λt,t≥0.2. IfSis a random variable with a gamma distribution of parametersnandλ, wherenis a positiveinteger, then the density ofSis given byfS, where:fS(s) =λe-λs(λs)n-1(n-1)!,s≥0.3. For anM/M/1queue with arrival rateλand service rateμwithλ < μ, the equilibrium distributionis:P(Q=j) = (1-ρ)ρj,j= 0,1,2, . . . ,whereρ=λ/μ.4. For anM/M/∞queue with arrival rateλand service rateμ, the equilibrium distribution is:P(Q=j) =e-ρρjj!,j= 0,1,2, . . . ,whereρ=λ/μ.5. For anM/M/K/Kqueue with arrival rateλand service rateμ, the equilibrium distribution is:P(Q=j) =ρj/j!1 +· · ·+ρK/K!,j= 0,1,2, . . . , K,whereρ=λ/μ.2