On ross's conjectures about queues with non-stationary poisson arrivals
- 1 March 1982
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 19 (1) , 245-249
- https://doi.org/10.2307/3213936
Abstract
Ross (1978) conjectured that the average delay in a single-server queue is larger when the arrival process is a non-stationary Poisson process than when it is a stationary Poisson process with the same rate. We present an example where equality obtains. When the number of waiting-positions is finite, Ross conjectured that the proportion of lost customers is greater in the nonstationary case. We present a counterexample to this conjecture.Keywords
This publication has 6 references indexed in Scilit:
- Queues with non-stationary input stream: Ross's conjectureAdvances in Applied Probability, 1981
- The Relation between Customer and Time Averages in QueuesOperations Research, 1980
- A Single Server Queueing Loss Model with Heterogeneous Arrival and ServiceOperations Research, 1980
- A heterogeneous arrival and service queueing loss modelNaval Research Logistics Quarterly, 1978
- Average delay in queues with non-stationary Poisson arrivalsJournal of Applied Probability, 1978
- On Erlang's FormulaThe Annals of Mathematical Statistics, 1969