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2026-06-25 16:32:41 -03:00
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* MG1
| Utilizacion | $\rho = \lambda * E(S) = \frac{\lambda}{\mu}$ |
| Estabilidad | $\boxed{\rho < 1} o \boxed{\lambda<\mu}$ |
| Segundo Momento | $E(S^2) = \sigma^2_S + \frac{1}{\mu^2}$ |
| Tiempo en cola | $W_q = \frac{\lambda * E(S^2)}{2(1-\rho)}$ |
| Tiempo en sistema | $W = W_q + \frac{1}{\mu}$ |
| Clientes en cola | $L_q = \lambda * W_q$ |
| Clientes en sistema | $L = \lambda * W$ |
* MM2
| Utilizacion | $\rho = \frac{\lambda}{2 * \mu}$ |
| Estabilidad | $\boxed{\rho < 1} o \boxed{\lambda < 2* \mu}$ |
| Probabilidad de sistema vacio | $P_0 = [1 +\frac{\lambda}{\mu} + \frac{(\lambda / \mu)^2}{2(1-\rho)}]^{-1}$ |
| Probabilidad de esperar | $P_w = \frac{(\lambda/\mu)^2}{2(1-\rho)} * P_0$ |
| Clientes en cola | $L_q = \frac{P_0 * (\lambda/\mu)^2 * \rho}{2 * (1 - \rho)^2}$ |
| Tiempo en cola | $W_q = \frac{L_q}{\lambda}$ |
| Tiempo en sistema | $W = W_q + \frac{1}{\mu}$ |
| Clientes en sistema | $L = \lambda * W$ |
| Criticidad | $\lambda_{crit} = c*\mu = 2*\mu |
* MD1
| Utilizacion | $\rho = \frac{\lambda}{\mu}$ |
| Estabilidad | $\boxed{\rho < 1} o \boxed{\lambda<\mu}$ |
| Tiempo medio de servicio | $E(S) = \frac{1}{\mu}$ |
| Tiempo en cola | $W_q = \frac{\lambda}{2*\mu^2*(1-\rho)}$ |
| Tiempo en sistema | $W = W_q + \frac{1}{\mu}$ |
| Clientes en cola | $L_q = \lambda * W_q$ |
| Clientes en sistema | $L = \lambda * W$ |