An approach to reduce the Erlang C probability of the M/M/2 system

In this paper we describe an approach to improve the performance of the M/M/2 system by replacing its homogeneous servers with heterogeneous servers. Denoting by β the ratio of the slow service rate to the fast service rate, we show that there exists an interval of β within which the Erlang C probability is reduced and there exists an optimal load ratio at which the Erlang C probability reaches its minimum. Based on these results, we develop a strategy that controls the Erlang C probability. The principles presented in this paper are also applicable to reduce the Erlang B probability.