Estimating characteristics of queueing networks using transactional data

We are motivated by queueing networks in which queues are difficult to observe but services are easy to record. Our goal is to estimate the queues from service data. More specifically, we consider an open queueing network with Poisson external arrivals, multiserver stations, general service times and Markovian switches of customers between stations. Customers' transitions between stations may be either immediate or of exponentially distributed durations. Each customer is supplied with an Identification Number (ID) upon entering the network. Operational data are collected which include transaction times (starts and terminations of services) and IDs of served customers. Our objective is to estimate the evolution of the queues in the network, given the collected data. We cover estimation at both end of busy periods and in real time. The applicability of the theory is demonstrated by analyzing a service operation.