Deterministic fluid approximation — single server

Abstract

To analyze the behavior of some existing service facility which serves a single category of customers, imagine that one were to record the arrival and departure times of all customers over some very long period of time, possibly several years. Such data do exist for some real systems. For example, any computer controlled traffic signal system is connected with many permanently installed vehicle detectors. At any particular traffic signal (server) there is likely to be one or more detectors upstream of the signal and also detectors downstream (perhaps near the next downstream signal). These detectors transmit an electrical pulse to the computer every time a vehicle passes. Most of these data are discarded after use, but they could be kept on a magnetic tape. Any airport also maintains a record of all aircraft movements including arrivals and departures from the runway and gate positions.