Parameter estimation using partial information with applications to queueing and related models

Parameter estimation based on the differences of two positive exponential family random variables is studied. Waiting time data, adjusted for idle times when necessary, are used for estimating the parameters in GI/G/1 queues. The sampling plan presented uses incomplete information on the differences between service and inter-arrival times rather than full information on service and inter-arrival times. A variation of the EM algorithm is proposed to derive parameter estimates. Specific examples are discussed, and the performances of the maximum likelihood and the corresponding estimates obtained by the EM algorithm are compared via simulations. Related applications to inventory, insurance and life-testing models are briefly considered.