An Approximation for the Variance of the UPCO Offered Load Estimate

T h e estimation of loads offered to a trunk group or server group operating in a blocked-calls-cleared mode plays an important role in many network-provisioning processes. The preferred measurement combination for developing such load estimates consists of usage, offered att e m p t s (peg count), and overflow attempts (usually referred to in the Bell System as UPCO measurements). This paper develops a generalization of some available approximations for the variance of the UPCO offered load estimate for a single measurement interval. T h e analysis considers the peakedness of the offered traffic stream, the level of blocking or call congestion for the group, the duration of the measurem e n t interval, and switch count errors due to the sampling of usage at discrete points in time. The resulting approximation is quite accurate 2575 over a wide range of conditions, is easily computable, and clearly displays the role of the basic factors t h a t control the precision of the estimator. Variance approximations are useful in designing measurements and in studying relationships between traffic measurement errors and the performance of the provisioning and administration processes. For example, the relationship of actual traffic measurement accuracies (which can be further corrupted by wiring, data base, and recording errors) to the quality of the trunk provisioning process was studied in Ref. 1. T h e variance approximation developed here was useful in quantifying the background accuracy of the process.