Performance analysis of automatic call distributors with call waiting lamps

In various businesses there is often a need to match incoming calls with agents-for example, airline reservation systems, operator services, and catalog sales. This need is met through use of automatic call distributors (ACD). The simplest and most usual way for an ACD to match calls and agents is first in first out, i.e. the call that has waited the longest in queue is matched to the agent who has been idle the longest. For this simple call matching, the M/M/m and M/G/m queueing models have been used to understand the performance of an ACD. These models do not address ACDs that have call waiting lamps. Call waiting lamps are used to inform agents to handle calls more quickly when the call distribution system is busy, and to resume a normal pace when the system becomes less busy. A queueing model is developed for an ACD system that accounts for call waiting lamps. Formulas are developed for expected durations of the call waiting lamp on and off times, and a method is given to find the distribution for a queuing system with lamps. The modeling is used to yield numerical results for an ACD application-operator services-that is related historically to call waiting lamps. The results include call waiting lamp on and off durations, and show when call waiting lamps are useful, and when they are not