The author considers, in this paper, a class of stochastic open networks with multiple service classes. These networks have the following properties. Individuals arrive from outside at various service classes at rates which may depend on the state of the system, bringing workloads which are independent and identically distributed within classes and which have finite means. As an individual enters a service class his workload begins to be reduced at a service rate which is state dependent. On completion of his workload an individual moves to a different class or leaves the system, with probability that may again be state dependent. Moreover the author assumes that the arrival flows to different service classes in the system from outside form independent Poisson processes with state-dependent rates. Under these hypotheses the network behaviour is represented as a Markov process and some specific results about the insensitivity property for the system is proved. Leonardo Pasini
Recensione dell'articolo: (Zachary, Stan - " A note on insensitivity in stochastic network " - J.Appl.Probab. 44 (2007), no.1, 238–248.)
PASINI, Leonardo
2008-01-01
Abstract
The author considers, in this paper, a class of stochastic open networks with multiple service classes. These networks have the following properties. Individuals arrive from outside at various service classes at rates which may depend on the state of the system, bringing workloads which are independent and identically distributed within classes and which have finite means. As an individual enters a service class his workload begins to be reduced at a service rate which is state dependent. On completion of his workload an individual moves to a different class or leaves the system, with probability that may again be state dependent. Moreover the author assumes that the arrival flows to different service classes in the system from outside form independent Poisson processes with state-dependent rates. Under these hypotheses the network behaviour is represented as a Markov process and some specific results about the insensitivity property for the system is proved. Leonardo PasiniI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.