摘要
In this paper, we present the conditions under which the traffic processes in a pure jump Markov process with a general state space are Poisson processes, and give a simple proof of PASTA type theorem in Melamed (1982) and Walrand (1988). Furthermore, we consider a generalized network with phase type negative arrivals and show that the network has a product-form invariant distribution and its traffic processes which represent the customers exiting from the network are Poisson processes.
In this paper, we present the conditions under which the traffic processes in a pure jump Markov process with a general state space are Poisson processes, and give a simple proof of PASTA type theorem in Melamed (1982) and Walrand (1988). Furthermore, we consider a generalized network with phase type negative arrivals and show that the network has a product-form invariant distribution and its traffic processes which represent the customers exiting from the network are Poisson processes.
基金
This research is supported by the National Natural Science Foundation of China.
