On One Class of Star-Shaped Communication Networks with Packet Switching

A model of a star-shaped network consisting of a central unit and a large number $N$ of corresponding message sources is investigated. It is assumed that each source gives rise to a homogeneous Poisson message stream, whose lengths are mutually independent and exponentially distributed. At the moment it arises, each message is broken down into packets, which are then transmitted through the network as individual messages. The moment of termination of a message transmission is taken to be the moment that the addressee receives the last packet of the message. It is demonstrated that in the limit as $N\to\infty$ (and for sufficiently large $N$), the mean message delivery time is less than in an analogous network with message switching in which messages are not broken down into packets.