Estimating customer delay and tardiness sensitivity from periodic queue length observations

A single server commences its service at time zero every day. random number of customers decide when to arrive the system so as minimize waiting and tardiness costs. The costs are proportional with rates $$\alpha $$ $$\beta , respectively. Each customer’s optimal arrival depends on others’ decisions; thus, resulting strategy is a Nash equilibrium. This work considers estimation ratio $$\displaystyle \theta \equiv \beta /(\alpha +\beta )$$ from queue length data observed daily discrete points, given that use equilibrium strategy. method moments estimator constructed conditions. Remarkably, does not require itself, or even an accurate estimate support. strongly consistent, error asymptotically normal. Moreover, asymptotic variance function covariance matrix (at sampling times) derived. performance demonstrated through simulations shown be robust instants each