Estimating Customer Loss Ratesfrom Transactional Data
نویسندگان
چکیده
Suppose that in a stationary M/M/c queueing system with arrival rate and service rate , customers may be lost via either balking with probability $ or reneging at rate. All of , and the loss parameter $ or 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 , and the total service provided together with the number of service completions yields an unbiased estimator of. The number of service completions during the busy periods and their lengths yields a consistent estimator for the customer loss rate; its asymptotic (T ! 1) bias is found. The asymptotic variances of all estimators are derived. Abstract Suppose that in a stationary M/M/c queueing system with arrival rate and service rate , customers may be lost via either balking with probability $ or reneging at rate. All of , and the loss parameter $ or 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 , and the total service provided together with the number of service completions yields an unbiased estimator of. The number of service completions during the busy periods and their lengths yields a consistent estimator for the customer loss rate; its asymptotic (T ! 1) bias is found. The asymptotic variances of all estimators are derived.
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