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MCooltA

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## Homework Statement

So for M/M/C queueing systems, I have two types of problems that I have been asked to deal with.

For the first question I am given in my notes, is where the arrival rate is constant λ=10 and service rate is μ=5.122 with 2 servers, i.e. C=2. For this question, I have used the formula to determine the steady state probabilities Pn, which denotes the probability of having n customers in the system.

[tex] p_{n} = (\rho^{n} / n!)(1/S), n ≤ c [/tex]

[tex] p_{n} = (\rho^{c} / c!)(\rho/c)^{n-c} (1/S), n ≥ c+1[/tex]

where [tex] S = \sum_{n=0}^{c} \rho^{n}/n! + (\rho^{c}/c!)((\rho/c)/(1-(\rho/c)) [/tex]

On another question, I am given the arrival rate λ=4/(n+1) where n is the number of customers in the system, and μ(the service rate) =2, C(servers) =3 with the system being full once there are 4 customers in the system.

To calculate the steady state probabilities for this question, we have used the formula;

[tex]

S=1 + λ_{0}/μ_{1} + λ_{1}/μ_{2} + ... = 1/p_{0}[/tex]

[tex] p_{n} = (λ_{0}λ_{1} + λ_{2}... λ_{n-1})/(μ_{1}μ_{2}μ_{3}...μ_{n}) [/tex]

I am having difficulty understanding which formula I should use, depending on the problem. Is the first formula only required when I have an M/M/C queue and the arrival rate is constant.