Reference no: EM131920894
Question: 1. Determine the probability that an arriving customer is refused entry in a M/M/1/K system if
a) the previous customer was accepted in the system;
b) the previous customer was also rejected entry to the system.
2. Consider an M/M/1/K system with arrival rate λ > 0 and service rate µ > 0, such that ρ = λ/µ < 1. Determine the minimum value of the system storage capacity k to have at most p percent of lost customers, with p>∈ {10-1, 10-2, 10-3} and ρ ∈ {0.7, 0.9}.
3. Consider an M/M/m/m system with m ≥ 1, arrival rate λ and G = 5.
a) Evaluate B(m, G) for m ∈ {1, 2, 3,..., 20}
b) How many servers do we need to have B(m, G) ≤ 10-6.
c) What's the value of λ for which we have B(m, G) = 10-6 with m = 9 and µ = 12 [customer/s]?
d) How many customers do we have in the system in the previous case?
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