A Hybrid of Erlang B and C Formulas and Its Applications

This paper attempts to broaden the usefulness of existing Erlang grade of service formulas, especially when faced with the evolving extensive changes in telephone networks. The old Markov traffic arrival and Markov call duration (or service) models are combined with what may be called more realistic user behavior and network scenarios. For the specified service system models, a generalized merger of ideal loss and ideal delay steady-state representations is developed. It is shown that a particular weighted inverse combination of Erlang and formulas, herein called the hybrid, is useful for grade of service estimates under several conditions. In addition to the usual offered load and the number of servers, the hybrid involves a relative Erlang versus weighting parameter θ. This parameter is non-negative and depends on system applications, as illustrated in a number of examples given. When less than or equal to unity, such as for the popular Poisson model, θ has a simple meaning. It is then the conditional probability that a typical customer elects to wait, or a service request is entered into a queue, given that all servers are busy.