ESTIMATING CUSTOMER LOSS RATES FROM TRANSACTIONAL DATA

Research Report SRR97-012

ESTIMATING CUSTOMER LOSS RATES FROM TRANSACTIONAL DATA

D.J. Daley and L.D. Servi

Abstract: Suppose that in a stationary M/M/c queueing system with arrival rate $\lambda$ and service rate $\mu$ , customers may be lost via either balking with probability $\varpi$ or reneging at rate $\eta$ . All of $\lambda$ , $\mu$ and the loss parameter $\varpi$ or $\eta$ as applicable are unknown and are to be estimated from transactional data (i.e. the set of service initiation and service completion epochs) observed on a (long) time interval of length T. The number of arrivals during idle periods and the total duration of these periods yield an unbiased estimator of $\lambda$ , and the total service provided together with the number of service completions yields an unbiased estimator of $\mu$ . The number of service completions during the busy periods and their lengths yields a consistent estimator for the customer loss rate; its asymptotic ( $T\to\infty$ ) bias is found. The asymptotic variances of all estimators are derived.

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