Question

Consider the M/M/16 queuing system λ=8 μ=14 and p = λ/(sμ)

$L = L_{q}+\frac{\lambda }{\mu }$

$L_{q}=P(J\geq s)(\frac{\rho }{1-\rho })$

$W_{q}=\frac{L_{q}}{\lambda }$

(a) average number of customers in the system

(b) average waiting time of each customer who enters the system

(c) probability that all servers are occupied

PU > s) = (s!)(1-p)

Answer 1

Using the formulas

PU > s) = (s!)(1-p)

$L_{q}=P(J\geq s)(\frac{\rho }{1-\rho })$

$L = L_{q}+\frac{\lambda }{\mu }$

a)Ls = 0.5714
b) Ws = 0.0714
c)
P(J >= 16) = 0