On the stability of queueing systems under precedence restrictions for the service of customers

The paper considers queueing systems under precedence-based queueing disciplines and derives conditions for the stability of the system. The precedence restrictions are posed on customers’ service in a way that a service can start only if some previous customers are served completely and some later customers arrived already. The stability depends on the interarrival times only through their means and the stability condition splits into two terms: with respect to a typical customer, one is representing the influences of future arrivals and one is representing the influences of past arrivals.