A random tandem network with queues modeled as Markov birth-death processes (Extended Abstract)

We consider a tandem network consisting of an arbitrary but finite number $R_m$ of queueing systems, where $R_m$ is a discrete random variable that assumes the values $1,2,ldots,m$ according to suitable probability distribution. The component $C_j$ $(j=1,2,ldots,m)$ of the tandem network is modeled via a birth-death process and consists of an infinite buffer space to hold the customers waiting and of a service center with a single server. We are interested to calculate the probability distribution} of the total number of customers in a random tandem network in steady-state regime