We consider an Erlang loss system (modem bank) with two streams of arriving customers, where arrival rates vary by time-of-day. We can observe one of the traffic streams (our customers), but we do not know how many servers the system has, or the characteristics of the other stream. Using detailed sample-path data, we construct a maximum likelihood estimator that makes good use of the data, but is slow to evaluate. As an alternative, we present an estimation system based on traffic data summarized by hour. This estimation system is much faster, and tends to produce good lower bounds on the size of the system and competing traffic.