On the “Output” process of a state dependent queue
- 1 July 1972
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1972 (2) , 182-186
- https://doi.org/10.1080/03461238.1972.10404649
Abstract
It is well known that if in a queueing situation the arrivals occur in a Poisson stream with intensity λ, and probability differential of a service completion is μd t+o(dt), then in the steady state the successive epochs of service completion also occur in a Poisson stream with intensity λ, that of arrivals. Here, we shall show that this criteria could be proved in the more general case in which the probability differential of a service completion is directly proportional to the number of customers momentarily present in the system.Keywords
This publication has 5 references indexed in Scilit:
- On the service time distribution and the waiting time process of a potentially infinite capacity queueing systemJournal of Applied Probability, 1969
- On the Improvement of the Operational Characteristics of Single-Server Queues by the Use of a Queue-Length-Dependent Service MechanismJournal of the Royal Statistical Society Series C: Applied Statistics, 1969
- The Output of a Queuing SystemOperations Research, 1956
- Stochastic Properties of Waiting LinesJournal of the Operations Research Society of America, 1955
- Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov ChainThe Annals of Mathematical Statistics, 1953