scholarly journals Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies

2005 ◽  
Vol 15 (1A) ◽  
pp. 331-391 ◽  
Author(s):  
Baris Ata ◽  
Sunil Kumar
Keyword(s):  
Heavy Traffic ◽  
Asymptotic Optimality ◽  
Traffic Analysis ◽  
Resource Pooling ◽  
Heavy Traffic Analysis ◽  
Processing Networks

scholarly journals Transform Methods for Heavy-Traffic Analysis

2020 ◽  
Vol 10 (4) ◽  
pp. 275-309
Author(s):  
Daniela Hurtado-Lange ◽  
Siva Theja Maguluri
Keyword(s):  
Heavy Traffic ◽  
Moment Generating Function ◽  
Traffic Analysis ◽  
Special Focus ◽  
Queuing Systems ◽  
Resource Pooling ◽  
Heavy Traffic Analysis ◽  
Queue Lengths ◽  
New Perspective ◽  
The Moment

The drift method was recently developed to study queuing systems in steady state. It was used successfully to obtain bounds on the moments of the scaled queue lengths that are asymptotically tight in heavy traffic and in a wide variety of systems, including generalized switches, input-queued switches, bandwidth-sharing networks, and so on. In this paper, we develop the use of transform techniques for heavy-traffic analysis, with a special focus on the use of moment-generating functions. This approach simplifies the proofs of the drift method and provides a new perspective on the drift method. We present a general framework and then use the moment-generating function method to obtain the stationary distribution of scaled queue lengths in heavy traffic in queuing systems that satisfy the complete resource pooling condition. In particular, we study load balancing systems and generalized switches under general settings.

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