Equation 8.66 and 8.67 are referred as Erlang's second formula, Erlang's delay formula or Erlang's C formula.
For single server systems (N = 1), the probability of delay reduces to p, which is simply the output utilization or traffic carried by the server. Thus the probability of delay for a single server system is also.
The distribution of waiting times for random arrivals, random service times, and a FIFO service discipline is
where P(> 0) = probability of delay (equation 8.67)
h = average service time of negative exponential service time distribution. By integrating equation 8.68, the average waiting time for all arrivals can be determined as
W(t)„„„ is the expected delay for all arrivals. The average delay of only those arrivals that get
delayed is commonly denoted as
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