English

On Erlang Queue with Multiple Arrivals and its Time-changed Variant

Probability 2025-01-16 v1

Abstract

We introduce and study a queue with the Erlang service system and whose arrivals are governed by a counting process in which there is a possibility of finitely many arrivals in an infinitesimal time interval. We call it the Erlang queue with multiple arrivals. Some of its distributional properties are obtained that includes the state-phase probabilities, the mean queue length and the distribution of busy period etc. Also, we study a time-changed variant of it by subordinating it with an independent inverse stable subordinator where we obtain its state probabilities and the mean queue length.

Keywords

Cite

@article{arxiv.2501.08789,
  title  = {On Erlang Queue with Multiple Arrivals and its Time-changed Variant},
  author = {R. B. Pote and K. K. Kataria},
  journal= {arXiv preprint arXiv:2501.08789},
  year   = {2025}
}