Limit theorems for stochastic processes associated with a boson gas

1988 ◽  
pp. 16-23 ◽  
Author(s):  
M. van den Berg ◽  
J. T. Lewis
Keyword(s):  
Stochastic Processes ◽  
Limit Theorems

Heavy traffic limit theorems for a queueing system in which customers join the shortest line

1989 ◽  
Vol 21 (02) ◽  
pp. 451-469 ◽  
Author(s):  
Zhang Hanqin ◽  
Wang Rongxin
Keyword(s):  
Stochastic Processes ◽  
Central Limit ◽  
Limit Theorems ◽  
Queueing System ◽  
Heavy Traffic ◽  
Traffic Intensity ◽  
Heavy Traffic Limit ◽  
Functional Central Limit Theorems ◽  
Service Channels ◽  
Functional Central Limit

The queueing system considered in this paper consists of r independent arrival channels and s independent service channels, where, as usual, the arrival and service channels are independent. In the queueing system, each server of the system has his own queue and arriving customers join the shortest line in the system. We give functional central limit theorems for the stochastic processes characterizing this system after appropriately scaling and translating the processes in traffic intensity ρ > 1.

Multiple channel queues in heavy traffic. II: sequences, networks, and batches

1970 ◽  
Vol 2 (02) ◽  
pp. 355-369 ◽  
Author(s):  
Donald L. Iglehart ◽  
Ward Whitt
Keyword(s):  
Stochastic Processes ◽  
Limit Theorems ◽  
Heavy Traffic ◽  
General Setting ◽  
Critical Value ◽  
Multiple Channel ◽  
Heavy Traffic Limit ◽  
Service Channels ◽  
Traffic Behavior

This paper is a sequel to [7], in which heavy traffic limit theorems were proved for various stochastic processes arising in a single queueing facility with r arrival channels and s service channels. Here we prove similar theorems for sequences of such queueing facilities. The same heavy traffic behavior prevails in many cases in this more general setting, but new heavy traffic behavior is observed when the sequence of traffic intensities associated with the sequence of queueing facilities approaches the critical value (ρ = 1) at appropriate rates.

Functional limit theorems for stochastic processes based on embedded processes

1975 ◽  
Vol 7 (01) ◽  
pp. 123-139 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Limit Laws ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
Subordinated Processes ◽  
Analogous Functional

The techniques used by Doeblin and Chung to obtain ordinary limit laws (central limit laws, weak and strong laws of large numbers, and laws of the iterated logarithm) for Markov chains, are extended to obtain analogous functional limit laws for stochastic processes which have embedded processes satisfying these laws. More generally, it is shown how functional limit laws of a stochastic process are related to those of a process embedded in it. The results herein unify and extend many existing limit laws for Markov, semi-Markov, queueing, regenerative, semi-stationary, and subordinated processes.

Sign in / Sign up

Export Citation Format

Share Document