Cutoff calls and telephone equipment reliability

It is often difficult or expensive to measure cutoff calls, which are usually caused by failures and malfunctions in some component of the telephone network. Therefore, it is desirable to have an indirect method for estimating the number of cutoff calls caused by equipment failures in a switching system or facility. This paper discusses a mathematical model that can be used to determine the cutoff call rate in a network component as a function of the failure modes and failure rates in the component, and the call holding time distribution. It includes a discussion of a paradigm for developing reliability objectives that directly reflect service as it is seen by end users. The mathematical model, an M/M/c/c queuing system with server failures, is described. A strong law of large numbers and a central limit theorem for the number of cutoff calls — accumulated either according to the number of failures or over time — are developed. An example from a switching system is given to show how these results are applied in specific cases.