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

1989 ◽  
Vol 21 (2) ◽  
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.

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.

Rates of convergence for queues in heavy traffic. II: Sequences of queueing systems

1972 ◽  
Vol 4 (2) ◽  
pp. 382-391 ◽  
Author(s):  
Douglas P. Kennedy
Keyword(s):  
Central Limit ◽  
Queue Length ◽  
Limit Theorems ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Rates Of Convergence ◽  
Traffic Intensity ◽  
Multiple Channel ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit

Estimates are given for the rates of convergence in functional central limit theorems for the queue length process in a sequence of general multiple channel queues. The situation is considered where the traffic intensity in the nth. queue, ρn, tends to ρ ≧ 1 as n approaches infinity. This extends previous work by the author, [6], in which the traffic intensity was fixed ≧ 1.

Rates of convergence for queues in heavy traffic. II: Sequences of queueing systems

1972 ◽  
Vol 4 (02) ◽  
pp. 382-391 ◽  
Author(s):  
Douglas P. Kennedy
Keyword(s):  
Central Limit ◽  
Queue Length ◽  
Limit Theorems ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Rates Of Convergence ◽  
Traffic Intensity ◽  
Multiple Channel ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit

Estimates are given for the rates of convergence in functional central limit theorems for the queue length process in a sequence of general multiple channel queues. The situation is considered where the traffic intensity in thenth. queue, ρn, tends to ρ ≧ 1 asnapproaches infinity. This extends previous work by the author, [6], in which the traffic intensity was fixed ≧ 1.

Rates of convergence for queues in heavy traffic. I

1972 ◽  
Vol 4 (2) ◽  
pp. 357-381 ◽  
Author(s):  
Douglas P. Kennedy
Keyword(s):  
Limit Theorems ◽  
Heavy Traffic ◽  
Rates Of Convergence ◽  
Traffic Intensity ◽  
Channel System ◽  
Multiple Channel ◽  
Skorokhod Representation Theorem ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit ◽  
Quantities Of Interest

Estimates are given for the rates of convergence in functional central limit theorems for quantities of interest in the GI/G/1 queue and a general multiple channel system. The traffic intensity is fixed ≧ 1. The method employed involves expressing the underlying stochastic processes in terms of Brownian motion using the Skorokhod representation theorem.

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.

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

1970 ◽  
Vol 2 (2) ◽  
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.

Rates of convergence for queues in heavy traffic. I

1972 ◽  
Vol 4 (02) ◽  
pp. 357-381 ◽  
Author(s):  
Douglas P. Kennedy
Keyword(s):  
Limit Theorems ◽  
Heavy Traffic ◽  
Rates Of Convergence ◽  
Traffic Intensity ◽  
Channel System ◽  
Multiple Channel ◽  
Skorokhod Representation Theorem ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit ◽  
Quantities Of Interest

Estimates are given for the rates of convergence in functional central limit theorems for quantities of interest in theGI/G/1 queue and a general multiple channel system. The traffic intensity is fixed ≧ 1. The method employed involves expressing the underlying stochastic processes in terms of Brownian motion using the Skorokhod representation theorem.

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