Transience of multiclass queueing networks via fluid limit models. (English) Zbl 0865.60079
J. G. Dai [ibid. 5, No. 1, 49-77 (1995; Zbl 0822.60083)] and J. G. Dai and the author [IEEE Trans. Autom. Control 40, No. 11, 1889-1904 (1995; Zbl 0836.90074)] have demonstrated the stability of the stochastic system via the stability of a fluid approximation. The author establishes a converse result to obtain criteria for transience for stochastic queueing networks based on a fluid limit model. In particular, he shows that if the fluid limit model explodes at a linear rate, then the associated queueing network with independent and identically distributed service times and a renewal arrival process explode faster than any fractional power.
Reviewer: P.R.Parthasarathy (Madras)
MSC:
60K25 | Queueing theory (aspects of probability theory) |
90B25 | Reliability, availability, maintenance, inspection in operations research |
60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |
90B35 | Deterministic scheduling theory in operations research |