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}
}