Waiting Lines with Heterogeneous Servers

A “multiple-booth” server system with nonhomogeneous servers is analyzed under the assumption of Poisson distributed arrivals and exponential service time with different individual mean service rates for each server. Explicit expressions for the state probabilities are obtained in closed form under “steady-state” conditions and the expected length of the waiting line is derived therefrom. It is shown that an “equivalent” system with homogeneous servers does not exist. The error incurred in assigning each server the arithmetic mean of the service rates of all of them is analyzed and illustrated if expected number in the system is used as a criterion of comparison.