Stability of adaptive multistage queues

This paper considers the queue that arises when customers arriving at a Poisson stream ask for a random number of service stages. Each service is made up of the sequence of its stages and each stage requires a time with independent exponential distribution. Two distinct mechanisms act on the queue growth. The first one affects the stage requirement distribution. The second one curtails a service at the first stage end to a new arrival, so introducing a dependence between service and interarrival times. Using the imbedded Markov chain approach, the stability conditions and the stationary distribution are found.