Optimization of Number of Servers

The total system cost

$$C(c,m)=c_m m + c_t T(m,r,\mu,\lambda) + c_p P_{m+r}(\mu,\lambda)$$ (78)

. The optimization of number of servers $m$ is performed by simple comparison of different $m$ within some reasonable bounds $m_{min} \le m \le m_{max},\ m_{min} > \lambda / \mu$

$$m(c,r)=arg \min_{m_{min} \le m \le m_{max}} C(c,m,r)$$ (79)

.