scholarly journals Networks of infinite-server queues with multiplicative transitions

2018 ◽  
Vol 123-124 ◽  
pp. 35-49 ◽  
Author(s):  
Dieter Fiems ◽  
Michel Mandjes ◽  
Brendan Patch
Keyword(s):  
Infinite Server ◽  
Infinite Server Queues

scholarly journals Time-Scaling Limits for Markov-Modulated Infinite-Server Queues

2013 ◽  
Vol 29 (1) ◽  
pp. 112-127 ◽  
Author(s):  
J. Blom ◽  
M. Mandjes ◽  
H. Thorsdottir
Keyword(s):  
Scaling Limits ◽  
Infinite Server ◽  
Time Scaling ◽  
Infinite Server Queues ◽  
Markov Modulated

A new view of the heavy-traffic limit theorem for infinite-server queues

1991 ◽  
Vol 23 (01) ◽  
pp. 188-209 ◽  
Author(s):  
Peter W. Glynn ◽  
Ward Whitt
Keyword(s):  
Heavy Traffic ◽  
Rates Of Convergence ◽  
Infinite Server ◽  
Open Networks ◽  
Heavy Traffic Limit ◽  
Many Server Queues ◽  
Finite Set ◽  
Deterministic Service ◽  
Infinite Server Queues ◽  
Service Times

This paper presents a new approach for obtaining heavy-traffic limits for infinite-server queues and open networks of infinite-server queues. The key observation is that infinite-server queues having deterministic service times can easily be analyzed in terms of the arrival counting process. A variant of the same idea applies when the service times take values in a finite set, so this is the key assumption. In addition to new proofs of established results, the paper contains several new results, including limits for the work-in-system process, limits for steady-state distributions, limits for open networks with general customer routes, and rates of convergence. The relatively tractable Gaussian limits are promising approximations for many-server queues and open networks of such queues, possibly with finite waiting rooms.

Sign in / Sign up

Export Citation Format

Share Document