Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals

In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distributi...

Full description

Saved in:
Bibliographic Details
Published in:Queueing systems 2023-12, Vol.105 (3-4), p.171-187
Main Authors: Mehra, Somya, Taylor, Peter G.
Format: Article
Language:English
Subjects:
Arrivals
Business and Management
Computer Communication Networks
Control
Customer services
Markov analysis
Multivariate analysis
Operations Research/Decision Theory
Poisson density functions
Probability Theory and Stochastic Processes
Queues
Random variables
Servers
Statistical analysis
Supply Chain Management
Systems Theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution.
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-023-09891-x