# And variance var s s 8 e s e s s 8 2 s 8 15 recall

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and variance Var( S | S > 8) = E [( S - E [ S | S > 8]) 2 | S > 8] = 15 . Recall that for ρ = P ( S > 8) λ/μ , Pollaczek-Khintchine formula shows that expected length of the call is given by W = 1 λ ρ 2 (1 + c 2 ) 2(1 - ρ ) + ρ 156 Note: it is okay if you use heavy tail approximation, but you will have a slightly different value. (d) Similarly as in part ( b ) , heavy traffic approximation yields P ( W q > 10) P E V ρc 2 χ + c 2 V 2(1 - ρ ) Exp (1) > 10 ! = P ( Exp (1) > 0 . 069) = e - 0 . 069 = 0 . 93 . Here, we noted that W q W when the system is in heavy traffic and used the approximation developed in class.
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