A refinement of the Hunt-Kurtz theory of large loss networks, with an application to virtual partitioning. (English) Zbl 1012.60083

Zachary, Stan; Ziedins, Ilze

Ann. Appl. Probab. 12, No. 1, 1-22 (2002).

Summary: This paper gives a refinement of the results of P. J. Hunt and T. G. Kurtz [Stochastic Processes Appl. 53, No. 2, 363-378 (1994; Zbl 0810.60087)] on the dynamical behavior of large loss networks. We introduce a Lyapunov function technique which, under the limiting regime of Kelly, enables the unique identification of limiting dynamics in many applications. This technique considerably simplifies much previous work in this area. We further apply it to the study of the dynamical behavior of large single-resource loss systems under virtual partitioning, or dynamic trunk reservation, controls. We identify limiting dynamics under the above regime, describing the behavior of the number of calls of each type in the system. We show that all trajectories of these dynamics converge to a single fixed point, which we identify. We also identify limiting stationary behavior, including call acceptance probabilities.

MSC:

60K20	Applications of Markov renewal processes (reliability, queueing networks, etc.)
60G17	Sample path properties
68M20	Performance evaluation, queueing, and scheduling in the context of computer systems
90B15	Stochastic network models in operations research

Keywords:

loss network; functional law of large numbers; Lyapunov function; partitioning; trunk reservation

Citations:

Zbl 0810.60087