Large sample Bayesian analysis for ${\rm Geo}/G/1$ discrete-time queueing models

statistical inference for the probability generating function p.g.f. of the equilibrium waiting time distribution is considered. The consistency of the posterior distribution for such a p.g.f., as well as the weak convergence to a Gaussian process of a suitable rescaling, are proved. As by-products, results on statistical inference for queueing characteristics are also ob- tained. Finally, the problem of estimating the probability of a long delay is considered. 1. Introduction and preliminaries. Discrete-time queueing models have recently received considerable attention, mainly because of their appli- cations to telecommunication systems based on asynchronous transfer mode Ž. ATM , which is the standard transport vehicle of the broadband integrated Let T be the r.v. ''number of time slots between i 1 th and ith batches i Ž. Ž ith interarrival time , and let S be the r.v. ith service time i.e., the size of i . the ith batch . The hypotheses on r.v.'s T 's and S 's are: ii