Processor-sharing queues: Some progress in analysis

1987 ◽  
Vol 2 (1) ◽  
pp. 1-17 ◽  
Author(s):  
S. F. Yashkov
Keyword(s):  
Processor Sharing ◽  
Processor Sharing Queues

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

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.

Generalized processor sharing queues with heterogeneous traffic classes

2003 ◽  
Vol 35 (3) ◽  
pp. 806-845 ◽  
Author(s):  
Sem Borst ◽  
Michel Mandjes ◽  
Miranda van Uitert
Keyword(s):  
Service Differentiation ◽  
Heterogeneous Traffic ◽  
Processor Sharing ◽  
Generalized Processor Sharing ◽  
Integrated Networks ◽  
Fair Queueing ◽  
Constant Rate ◽  
Processor Sharing Queues ◽  
Workload Distribution ◽  
Heavy Tailed

We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic flows are served in accordance with the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behaviour of the light-tailed traffic flow under the assumption that its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed flow served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is, in fact, asymptotically equivalent to that in the isolated system, multiplied by a certain prefactor, which accounts for the interaction with the heavy-tailed flow. Specifically, the prefactor represents the probability that the heavy-tailed flow is backlogged long enough for the light-tailed flow to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario.

Generalized processor sharing queues with heterogeneous traffic classes

2003 ◽  
Vol 35 (03) ◽  
pp. 806-845 ◽  
Author(s):  
Sem Borst ◽  
Michel Mandjes ◽  
Miranda van Uitert
Keyword(s):  
Service Differentiation ◽  
Heterogeneous Traffic ◽  
Processor Sharing ◽  
Generalized Processor Sharing ◽  
Integrated Networks ◽  
Fair Queueing ◽  
Constant Rate ◽  
Processor Sharing Queues ◽  
Workload Distribution ◽  
Heavy Tailed

We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic flows are served in accordance with the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behaviour of the light-tailed traffic flow under the assumption that its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed flow served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is, in fact, asymptotically equivalent to that in the isolated system, multiplied by a certain prefactor, which accounts for the interaction with the heavy-tailed flow. Specifically, the prefactor represents the probability that the heavy-tailed flow is backlogged long enough for the light-tailed flow to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario.

Law of Large Number Limits of Limited Processor-Sharing Queues

2009 ◽  
Vol 34 (4) ◽  
pp. 937-970 ◽  
Author(s):  
Jiheng Zhang ◽  
J. G. Dai ◽  
Bert Zwart
Keyword(s):  
Processor Sharing ◽  
Processor Sharing Queues

A perturbation method for solving some queues with processor sharing discipline

1989 ◽  
Vol 26 (1) ◽  
pp. 209-214 ◽  
Author(s):  
Bhaskar Sengupta
Keyword(s):  
Difference Equation ◽  
Perturbation Method ◽  
Variable Coefficients ◽  
Processor Sharing ◽  
Order Difference ◽  
The Third ◽  
Algorithmic Solution ◽  
Processor Sharing Queues ◽  
Second Order Difference Equation ◽  
Order Difference Equation

In this paper, we present a perturbation method of solving a second-order difference equation with variable coefficients with some additional assumptions. This method can be used to devise an algorithmic solution for the moments of sojourn times in some processor sharing queues. In particular, we examine three queues. The first has exponential service and a fairly general interrupted arrival mechanism. The second is a cyclic queue. The third is a model for a computer system in which finite and infinite sources interact.

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