A Generalized Queueing Discipline for Product Form Network Solutions

Noetzel, Andrew S.

doi:10.1145/322154.322166

Cited by 38 publications

(14 citation statements)

References 7 publications

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“…The operation of the network was presented as a sequence of discrete time intervals (clock cycles). The specific features of the model were different from those of models known to obey the Jackson's theorem [3][4][5][6][7][8][9][10][11][12][13][14][15]. However, our analysis proved that Jackson's theorem remains valid for networks with discrete time, deterministic service time and various queueing disciplines.…”

mentioning

confidence: 77%

Interconnection networks with heterogeneous activity or finite buffers

Rykalova

Levitin

Brower

2008

Proceedings of the 11th Communications and Networking Simulation Symposium

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We present theoretical models and numerical results for performance of a multiprocessor network modeled as a ring and as a 2-dim wraparound square lattice of nodes with local processors that generate messages with rate λ per clock cycle and two or, respectively, four output ports/buffers. Two different models are considered. One assumes that the generation rate of a node depends on the intensity of the flow of arriving messages. The other model considers networks with limited buffers. The average queue lengths and average latency are obtained. The results show that the model of independent queues, which is valid for networks with homogeneous activity and infinite buffers, is not applicable, which violates the Jackson theorem. INTRODUCTIONIn our previous papers [1,2] we presented a model of a multiprocessor network in the form of a ring and a 2-dimensional toroidal (wraparound) square lattice. The operation of the network was presented as a sequence of discrete time intervals (clock cycles). The specific features of the model were different from those of models known to obey the Jackson's theorem [3][4][5][6][7][8][9][10][11][12][13][14][15]. However, our analysis proved that Jackson's theorem remains valid for networks with discrete time, deterministic service time and various queueing disciplines. We obtain theoretical and numerical (simulation) results for the performance of the model. We showed that for the ring topology the average number of messages in queue could be derived from closed form expression (1) and (2), for ring and torus topology, accordingly.

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confidence: 77%

Interconnection networks with heterogeneous activity or finite buffers

Rykalova

Levitin

Brower

2008

Proceedings of the 11th Communications and Networking Simulation Symposium

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“…An example of these models could be the generalization of the BCMP server types in the last-batchprocessor-sharing (LBPS) [19]. Also the relationship of local balance or Markov implies Markov to inter-server control flows could be investigated.…”

Section: Discussionmentioning

confidence: 99%

“…Noetzel [19] abstracts from the four BCMP server types [7] and introduces a generalized queueing discipline called last-batch-processor-sharing (LBPS).…”

Section: A Product Form Queueing Network (Pfqn)mentioning

confidence: 99%

Discussion on the Zorn-Hypothesis on Inter-server Control Flow and Product Form Queueing Networks

Kluth

2012

2012 IEEE 19th International Conference and Workshops on Engineering of Computer-Based Systems

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The hypothesis: "If a system can be represented by a model without any inter-server control flow, the underlying problem is of type Product Form Queueing Network (PFQN), otherwise of type Non Product Form Queueing Network (NPFQN)" was raised by W. Zorn. This launches a new distinction criterion between Product Form and Non Product Form Queueing Networks on a structural level. In this paper a validation of this hypothesis is discussed with the help of different representative examples.

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“…, N, k = 1, * * -, K ; (27) Substituting (27) in (23) the following formula for conditional throughputs U , ( k ) for load-independent networks is obtained, which is also given by Marie [24]. (28) blMk)PlI + P l l P l 2…”

Section: A State Of a Station Is Denoted By A Pairmentioning

confidence: 99%

Approximate analysis of load dependent general queueing networks

Akyildiz

Sieber

1988

IIEEE Trans. Software Eng.

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Abstracf-A method for approximate solutions to load dependent closed queueing networks containing general service time distributions and FCFS scheduling disciplines is presented. The technique demonstrated is an extension of the well-known method of Marie. A new formula for the conditional throughputs is derived. After each iteration a check is performed to guarantee that the results obtained are within a tolerance level E . These iterations are repeated whenever invalid results are detected. On the average, the solutions obtained vary by less than 5 percent from their respective exact and simulation results.

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A Generalized Queueing Discipline for Product Form Network Solutions

Cited by 38 publications

References 7 publications

Interconnection networks with heterogeneous activity or finite buffers

Interconnection networks with heterogeneous activity or finite buffers

Discussion on the Zorn-Hypothesis on Inter-server Control Flow and Product Form Queueing Networks

Approximate analysis of load dependent general queueing networks

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