Stability of an M\(|G|1\) queue with thick tails and excess capacity (Q1585947)

In computer networks queues are encountered which receive mostly jobs with a small required service time and only occasionally a job with a large service time, as compared to the interarrival times of jobs. The authors consider an M/G/1 queue of this type, where the traffic intensity is infinite. Under the first-come-first-served discipline the occasional long job will generate a long queue. In computer systems one therefore prefers something like the foreground-background (FB) discipline: at any given time the jobs with the least amount of service time received are being served, at a rate inversely proportional to the number of such jobs. This will, for one effect, increase the time it takes to build up a long queue, i.e. the queue, which is unstable under both disciplines, will be `more stable' under FB. Such stability aspects of the behaviour of the given M/G/1 queue under FB are the topic of the paper.