$$ B(x) = \sum_{j=1}^m \alpha_j(1-e^{-\mu_j x}),\quad x>0 $$

where $\backslash alpha\_j$ is the probability that the request is served at phase $j$, in which case the average service rate is $\backslash mu\_j$. After completing service at phase $j$, for some $j$, the request exits the system.

INPUTS

lambda

Arrival rate

mu

mu(j) is the phase $j$ service rate. The total number of phases $m$ is length(mu).

alpha

alpha(j) is the probability that a request is served at phase $j$. alpha must have the same size as mu.

OUTPUTS

U

Service center utilization

R

Service center response time

Q

Average number of requests in the system

X

Service center throughput