
#+title:     Otra Presentacion más
#+author:    Fede
#+email:     federico.nicolas.polidoro@gmail.com

* M/M/2
banco con dos cajeros. arribos $\lambda$ = 20 cli/h, servicio: $\mu$ = 30. Encontrar E(n) y E(t)

** RTA
*** encontrar L o E(n)
$\rho = \frac{\lambda}{2*\mu}$

$\rho = \frac{20}{2*30} = \frac{20}{60} = 0,33$

$P_0 = (1-\rho) /(1+\rho) = \frac{2/3}{4/3} = \frac{1}{2}$

$L_q = \frac{P_0 * (\lambda / \mu)^c * \rho}{c!(1-\rho)^2}$

$L_q = \frac{\frac{1}{2} * \frac{20}{30}^2 * \frac{1}{3}}{2 * \frac{2}{3}^2}$

$L_q = \frac{\frac{1}{2} * \frac{4}{9} * \frac{1}{3}}{\frac{8}{9}} = \frac{1}{12}$

$L = L_q + \frac{\lambda}{\mu}$

$L = \frac{1}{12} + \frac{2}{3}$

$L = \frac{9}{12} = 0.75$

*** E(t) sin usar little

$W_q = \frac{L_q}{\lambda} = \frac{\frac{1}{12}}{20} = \frac{1}{240}$

$W = W_q + \frac{1}{ \mu }$

* MD1
\lambda = 6000
\mu = 8000
\c = 1

** RTA
*** Encontrar  E(n)


*** Encontrar  E(T)


* Colas con prioridades
en servicio hay clase 2(2min) y hay

\left {
\begin{array}{ccc}
Clase 1 -> 2 personas \\
Clase 2 -> 3 personas

\end{array}

** RTA
b. T_q = 2 min + (2*8 min) = 18 min.

a. T = T_q + 8min = 26min.
