On the GI/M/\(\infty\) queue with batch arrivals of constant size
type: Item
instance of: scholarly article
title: On the GI/M/\(\infty\) queue with batch arrivals of constant size
zbMATH Open document ID: 0656.60098
DOI: 10.1007/BF01158399
published in: Queueing Systems
publication date: 1987-01-01T00:00:00Z
review text: The authors investigate the GI/M/\(\infty\) queue with batch arrivals of constant size. Two main results are presented: (i) the binomial moments of the number of customers found by an arriving batch can be computed recursively; (ii) the stationary probabilities that an arriving batch finds i customers in the system can be computed by means of the binomial moments (Jordan's formula). Moreover, some stationary probabilities are given.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 68M20
zbMATH DE Number: 4072089
zbMATH Keywords: Jordan formula
zbMATH Keywords: queue with batch arrivals
zbMATH Keywords: stationary probabilities
author: Andreas Brandt
author: Hannelore Sulanke
reviewed by: Anatolij Dvurečenskij
MaRDI profile type: Publication
cites work: On stationary queue length distributions for G/M/s/r queues
cites work: Q4733214
cites work: Q4742086
cites work: Q5582087
cites work: Q3678435
cites work: A Queueing Problem with Arrivals in Batches of Variable Size and Service Rate Depending on Queue Length
cites work: Letter to the Editor—Some Results for the Bulk-Arrival Infinite-Server Poisson Queue
cites work: On the generalization of Erlang's formula
description: scientific article; zbMATH DE number 4072089