Some Results for Bulk-Arrival Queues with State-Dependent Service Times - Harris, Carl M. (Management Science, 1970)
The Poisson bulk-arrival single-channel first-come-first-served queuing system is generalized so that the service times are conditioned on the length of the queue at the moment service is begun. Some general theory is developed for the model, and three specific cases are explored. For each of the examples, results are obtained that characterize queue behavior using the imbedded-Markov-chain approach. Included in these results are tables of steady-state probabilities and expected queue sizes for numerous combinations of the parameters.