| Автор | Daley, D. J. |
| Дата выпуска | 1972 |
| dc.description | We are using the term ‘bivariate Poisson process’ to describe a bivariate point process (N<sub>1</sub>(.), N<sub>2</sub>(.)) whose components (or, marginal processes) are Poisson processes. In this we are following Milne (2) who amongst his examples cites the case where N<sub>1</sub>(.) and N<sub>2</sub>(.) refer to the input and output processes respectively of the M/G/∈ queueing system. Such a bivariate point process is infinitely divisible. We shall now show that in a stationary M/M/1 queueing system (i.e. Poisson arrivals at rate λ, exponential service at rate µ > λ, single-server) a similar identification of (N<sub>1</sub>(.), N<sub>2</sub>(.)) yields a bivariate Poisson process that is not infinitely divisible. |
| Формат | application.pdf |
| Издатель | Cambridge University Press |
| Копирайт | Copyright © Cambridge Philosophical Society 1972 |
| Название | A bivariate Poisson queueing process that is not infinitely divisible |
| Тип | research-article |
| DOI | 10.1017/S0305004100047289 |
| Electronic ISSN | 1469-8064 |
| Print ISSN | 0305-0041 |
| Журнал | Mathematical Proceedings of the Cambridge Philosophical Society |
| Том | 72 |
| Первая страница | 449 |
| Последняя страница | 450 |
| Аффилиация | Daley D. J.; The Australian National University |
| Выпуск | 3 |
