Necessary conditions for global stability of multiclass queueing networks

Hasenbein, John J.

doi:10.1016/s0167-6377(97)00022-9

Cited by 46 publications

(20 citation statements)

References 13 publications

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“…Hasenbein (1998) extended these results to the uid models of certain two-station queueing networks with probabilistic routing.…”

Section: Discussionmentioning

confidence: 90%

“…In these unstable examples, the total number of jobs in the system goes to inÿnity with time. Other recent work on the stability of queueing networks and uid networks includes Harrison and Nguyen (1995), Bramson (1997Bramson ( , 1999, Bertsimas et al (1996), Dumas (1996Dumas ( , 1997, Dai and Weiss (1996), Foss and Rybko (1995), Winograd and Kumar (1996), , Chen andZhang (1997, 1998), Morrison and Kumar (1998), and Hasenbein (1997).…”

Section: Introductionmentioning

confidence: 99%

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The Stability of Two-Station Multitype Fluid Networks

Dai

Vate

2000

Operations Research

118

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This paper studies the uid models of two-station multiclass queueing networks with deterministic routing. A uid model is globally stable if the uid network eventually empties under each nonidling dispatch policy. We explicitly characterize the global stability region in terms of the arrival and service rates. We show that the global stability region is deÿned by the nominal workload conditions and the "virtual workload conditions," and we introduce two intuitively appealing phenomena-virtual stations and push starts-that explain the virtual workload conditions. When any of the workload conditions is violated, we construct a uid solution that cycles to inÿnity, showing that the uid network is unstable. When all the workload conditions are satisÿed, we solve a network ow problem to ÿnd the coe cients of a piecewise linear Lyapunov function. The Lyapunov function decreases to zero, proving that the uid level eventually reaches zero under any nonidling dispatch policy. Under certain assumptions on the interarrival and service time distributions, a queueing network is stable or positive Harris recurrent if the corresponding uid network is stable. Thus, the workload conditions are su cient to ensure the global stability of two-station multiclass queueing networks with deterministic routing.

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“…Hasenbein (1998) extended these results to the uid models of certain two-station queueing networks with probabilistic routing.…”

Section: Discussionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

The Stability of Two-Station Multitype Fluid Networks

Dai

Vate

2000

Operations Research

118

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“…Therefore, some scholars use the queuing network method to solve the problem of cell scheduling. Hasenbein [7]and Harrison [8] treat each batch part as a work piece, and use an ordinary single-server queuing network to find the approximate solution. The queuing network method shortens the waiting time of parts.…”

Section: Introductionmentioning

confidence: 99%

Inter Cell Scheduling Based on Queuing Networks

Lv¹,

Zhang²,

Han³

2017

Proceedings of the 3rd Annual International Conference on Management, Economics and Social Development (ICMESD 17)

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Abstract. In virtual cellular manufacturing, the processing lines are more complex, products are multi-varieties and small quantities, jobs spend 90% of the time waiting for the machine to be processed is common. In order to reduce the waiting time, this paper study the inter cell scheduling based on queuing network. The virtual cellular manufacturing system is seen as a queuing network, and the input parameters of each node within the network are calculated by the external arrival rate. Under the strategy of batch service. Scheduling target is minimize the total processing time, maximize the minimum of equipment load. Batch service queuing network model is established. The model is solved by the immune optimization algorithm, which achieves the shortest processing time, and avoids the parts waiting. Finally, taking the actual production process of ship enterprises as an example, it is proved that the batch service queuing network method is feasible and efficient.

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“…We note that our terminology is somewhat different than that in [DaV00], and in related work [Ha97] and [DaHV99]. There, the authors employ the term "fluid networks" rather than "fluid models", and employ the term "global stability" for when the fluid networks are stable.…”

Section: Global Stabilitymentioning

confidence: 99%

“…This argument heavily uses the structure of V (S), which was defined with appropriate "gaps" between its classes so that service at V 1 (S) will prevent service at V 2 (S) and vice versa, because of the presence of low priority classes in between. More detail is given in [DaV00] and in [Ha97], which looks at a related problem. (The reference [DaV96] cited in [DaV00] never appeared due to an unrelated flaw in extending push starts to the queueing network setting.…”

Section: Systematic Presentation Of Virtual Stations and Push Startsmentioning

confidence: 99%

Stability of Queueing Networks

Down¹

Lecture Notes in Mathematics

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Necessary conditions for global stability of multiclass queueing networks

Cited by 46 publications

References 13 publications

The Stability of Two-Station Multitype Fluid Networks

The Stability of Two-Station Multitype Fluid Networks

Inter Cell Scheduling Based on Queuing Networks

Stability of Queueing Networks

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