Expected Units In Queue - Erlang Service Times

In a queuing model the fundamental relationship defining the expected number of units in the queue, `L_q`, dependent on the mean arrival rate and the expected waiting time in the queue.

Thus the fundamental relationship is:  `L_q` = `lamda * W_q`

When the inputs are define by a Poisson distribution and service times are defined by an Elang distrbution, `sigma^2` = 1/(k`mu^2'), in this case the expected number of units in the queue,`L_q`, is computed by this equation.

Inputs are:

• `lambda' (mean arrival rate)
• k
• `mu` (mean service rate)
• `rho` service utilization factor