Exact Results for the Distribution of the Partial Busy Period for a Multi-Server Queue

Autor:	Zuk, Josef, Kirszenblat, David
Rok vydání:	2023
Předmět:	Mathematics - Probability 90B22 (Primary) 60K25 60J74 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Exact explicit results are derived for the distribution of the partial busy period of the M/M/c multi-server queue for a general number of servers. A rudimentary spectral method leads to a representation that is amenable to efficient numerical computation across the entire ergodic region. An alternative algebraic approach yields a representation as a finite sum of Marcum Q-functions depending on the roots of certain polynomials that are explicitly determined for an arbitrary number of servers. Asymptotic forms are derived in the limit of a large number of servers under two scaling regimes, and also for the large-time limit. Connections are made with previous work. The present work is the first to offer tangible exact results for the distribution when the number of servers is greater than two.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.01874 Zobrazit plný text záznamu View this record from Arxiv