Heavy traffic analysis for continuous polling models

1997 ◽  
Vol 34 (3) ◽  
pp. 720-732 ◽  
Author(s):  
Dirk P. Kroese
Keyword(s):  
Steady State ◽  
Gamma Distribution ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Traffic Analysis ◽  
Polling System ◽  
Polling Models ◽  
Heavy Traffic Analysis ◽  
Age Dependent ◽  
The Relationship

We consider a continuous polling system in heavy traffic. Using the relationship between such systems and age-dependent branching processes, we show that the steady-state number of waiting customers in heavy traffic has approximately a gamma distribution. Moreover, given their total number, the configuration of these customers is approximately deterministic.

Heavy traffic analysis for continuous polling models

1997 ◽  
Vol 34 (03) ◽  
pp. 720-732 ◽  
Author(s):  
Dirk P. Kroese
Keyword(s):  
Steady State ◽  
Gamma Distribution ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Traffic Analysis ◽  
Polling System ◽  
Polling Models ◽  
Heavy Traffic Analysis ◽  
Age Dependent ◽  
The Relationship

We consider a continuous polling system in heavy traffic. Using the relationship between such systems and age-dependent branching processes, we show that the steady-state number of waiting customers in heavy traffic has approximately a gamma distribution. Moreover, given their total number, the configuration of these customers is approximately deterministic.

scholarly journals HEAVY-TRAFFIC ANALYSIS OF A NON-PREEMPTIVE MULTI-CLASS QUEUE WITH RELATIVE PRIORITIES

2015 ◽  
Vol 29 (2) ◽  
pp. 153-180 ◽  
Author(s):  
A. Izagirre ◽  
I.M. Verloop ◽  
U. Ayesta
Keyword(s):  
Steady State ◽  
State Space ◽  
Waiting Time ◽  
Queue Length ◽  
Heavy Traffic ◽  
Random Variables ◽  
Random Variable ◽  
Traffic Analysis ◽  
Service Requirement ◽  
Heavy Traffic Analysis

We study the steady-state queue-length vector in a multi-class queue with relative priorities. Upon service completion, the probability that the next served customer is from class k is controlled by class-dependent weights. Once a customer has started service, it is served without interruption until completion. We establish a state-space collapse for the scaled queue-length vector in the heavy-traffic regime, that is, in the limit the scaled queue-length vector is distributed as the product of an exponentially distributed random variable and a deterministic vector. We observe that the scaled queue length reduces as classes with smaller mean service requirement obtain relatively larger weights. We finally show that the scaled waiting time of a class-k customer is distributed as the product of two exponentially distributed random variables.

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