On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes

1992 ◽  
Vol 24 (03) ◽  
pp. 653-698
Author(s):  
Sergei Grishechkin
Keyword(s):  
Processing Time ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Batch Arrivals ◽  
Processor Sharing Queues ◽  
Residual Processing

The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for the M/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerning M/G/1 queues with shortest residual processing time discipline.

On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes

1992 ◽  
Vol 24 (3) ◽  
pp. 653-698 ◽  
Author(s):  
Sergei Grishechkin
Keyword(s):  
Processing Time ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Batch Arrivals ◽  
Processor Sharing Queues ◽  
Residual Processing

The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for the M/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerning M/G/1 queues with shortest residual processing time discipline.

GI/G/1 processor sharing queue in heavy traffic

1994 ◽  
Vol 26 (2) ◽  
pp. 539-555 ◽  
Author(s):  
Sergei Grishechkin
Keyword(s):  
Queue Length ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Traffic Intensity ◽  
Random Measures ◽  
Processing Times ◽  
Processor Sharing Queues ◽  
Limiting Behaviour ◽  
Residual Processing

Consider GI/G/1 processor sharing queues with traffic intensity tending to 1. Using the theory of random measures and the theory of branching processes we investigate the limiting behaviour of the queue length, sojourn time and random measures describing attained and residual processing times of customers present.

GI/G/1 processor sharing queue in heavy traffic

1994 ◽  
Vol 26 (02) ◽  
pp. 539-555 ◽  
Author(s):  
Sergei Grishechkin
Keyword(s):  
Queue Length ◽  
Branching Processes ◽  
Heavy Traffic ◽  
Processor Sharing ◽  
Traffic Intensity ◽  
Random Measures ◽  
Processing Times ◽  
Processor Sharing Queues ◽  
Limiting Behaviour ◽  
Residual Processing

Consider GI/G/1 processor sharing queues with traffic intensity tending to 1. Using the theory of random measures and the theory of branching processes we investigate the limiting behaviour of the queue length, sojourn time and random measures describing attained and residual processing times of customers present.

Stationary increments in the accumulated work process in processor-sharing queues

1989 ◽  
Vol 26 (3) ◽  
pp. 671-677 ◽  
Author(s):  
R. D. Foley ◽  
Georgia-Ann Klutke
Keyword(s):  
Processing Time ◽  
Response Times ◽  
Processor Sharing ◽  
Work Process ◽  
Conditional Response ◽  
New Approach ◽  
Stationary Increments ◽  
Processor Sharing Queues

We present a new approach to the processor-sharing queue that allows us to study the accumulated work process of a job that requires an amount of processing time x. Our approach simplifies the proofs of some earlier results on expected conditional response times and extends them to the M/G/φ (·) class. The approach illuminates some of the paradoxical features of these systems.

PERFORMANCE ESTIMATION OFM/DK/1 QUEUE UNDER FAIR SOJOURN PROTOCOL IN HEAVY TRAFFIC

2008 ◽  
Vol 23 (1) ◽  
pp. 61-74
Author(s):  
Yingdong Lu
Keyword(s):  
Markov Process ◽  
Waiting Time ◽  
Service Time ◽  
Infinitesimal Generator ◽  
Heavy Traffic ◽  
Queuing System ◽  
Performance Estimation ◽  
Processor Sharing ◽  
Average Waiting Time ◽  
Processor Sharing Queues

We study the performance of aM/DK/1 queue under Fair Sojourn Protocol (FSP). We use a Markov process with mixed real- and measure-valued states to characterize the queuing process of system and its related processor sharing queue. The infinitesimal generator of the Markov process is derived. Classifying customers according to their service time, using techniques in multiclass queuing system, and borrowing recently developed heavy traffic results for processor-sharing queues, we are able to derive approximations for average waiting time for the jobs.

scholarly journals Heavy-traffic limits for Discriminatory Processor Sharing models with joint batch arrivals

2020 ◽  
Vol 48 (2) ◽  
pp. 136-141
Author(s):  
P. Vis ◽  
R. Bekker ◽  
R.D. van der Mei ◽  
R. Núñez-Queija
Keyword(s):  
Heavy Traffic ◽  
Processor Sharing ◽  
Batch Arrivals

Stationary increments in the accumulated work process in processor-sharing queues

1989 ◽  
Vol 26 (03) ◽  
pp. 671-677 ◽  
Author(s):  
R. D. Foley ◽  
Georgia-Ann Klutke
Keyword(s):  
Processing Time ◽  
Response Times ◽  
Processor Sharing ◽  
Work Process ◽  
Conditional Response ◽  
New Approach ◽  
Stationary Increments ◽  
Processor Sharing Queues

We present a new approach to the processor-sharing queue that allows us to study the accumulated work process of a job that requires an amount of processing time x. Our approach simplifies the proofs of some earlier results on expected conditional response times and extends them to the M/G/φ (·) class. The approach illuminates some of the paradoxical features of these systems.

scholarly journals The impact of reneging in processor sharing queues

2006 ◽  
Vol 34 (1) ◽  
pp. 87-96 ◽  
Author(s):  
H. Christian Gromoll ◽  
Philippe Robert ◽  
Bert Zwart ◽  
Richard Bakker
Keyword(s):  
Processor Sharing ◽  
Processor Sharing Queues ◽  
The Impact
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