Stability of linear EDF networks with resource sharing

Kruk, Łukasz

doi:10.1007/s11134-017-9553-y

Cited by 3 publications

(4 citation statements)

References 39 publications

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“…Recently, Atar and Shadmi [3] extended the scope of this method to generalized Jackson networks working under the EDF protocol with hard or soft deadlines. Our instability results, together with different behavior of linear strictly subcritical resource sharing networks under the SRPT and EDF service disciplines [30,41], suggest that it might be difficult to further extend the approach of [2] to the general multiserver setting. On the other hand, the above-mentioned EDF stability results suggest using the EDF protocols, with the customer initial lead times equal to large multiples of their service times, as stable proxies of SRPT and SJF in multiserver networks.…”

Section: Discussionmentioning

confidence: 96%

“…On the other hand, the above-mentioned EDF stability results suggest using the EDF protocols, with the customer initial lead times equal to large multiples of their service times, as stable proxies of SRPT and SJF in multiserver networks. See [30], Section 8 for more details.…”

Section: Discussionmentioning

confidence: 99%

“…is the time when the service at the buffers 2, 3, 4 of the customers entering the network in the time interval (t i−1 , t i ] ends. In particular, (30) implies that…”

Section: Proof Of Propositionmentioning

confidence: 99%

“…Using the time t 3 given by (55), rather than (27), and proceeding as in the proof of Proposition 1, we get (28). Iterating, for large M we get (30), where i > 0, i = 1, ..., 7, are constants and…”

Section: Proof Of Propositionmentioning

confidence: 99%

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Instability of SRPT, SERPT and SJF multiclass queueing networks

Kruk

Chojecki

2022

Queueing Syst

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We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol. Both of them are reentrant lines with two servers and eight customer classes. The customer service times in our first system are deterministic, yielding an example of an unstable shortest remaining expected processing time (SERPT) network. In the second one, the service times in one customer class are randomized. Both our examples show also system instability under the shortest job first (SJF) discipline. A simulation study of robustness of our results with respect to changes in the customer interarrival and service times is also provided. Our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and in fact cause instability effects. This is in sharp contrast with their satisfactory performance for single-server queues.

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Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

“…is the time when the service at the buffers 2, 3, 4 of the customers entering the network in the time interval (t i−1 , t i ] ends. In particular, (30) implies that…”

Section: Proof Of Propositionmentioning

confidence: 99%

Section: Proof Of Propositionmentioning

confidence: 99%

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Instability of SRPT, SERPT and SJF multiclass queueing networks

Kruk

Chojecki

2022

Queueing Syst

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The Design of Mobile Distance Online Education Resource Sharing from the Perspective of Man-Machine Cooperation

Zhao

Herencsár

et al. 2021

Mobile Netw Appl

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Minimal and Locally Edge Minimal Fluid Models for Resource-Sharing Networks

Kruk

2021

Mathematics of OR

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We investigate minimal and locally edge minimal fluid models for real-time resource-sharing networks, which are natural counterparts of pathwise minimal and locally edge minimal performance processes for the corresponding real-time stochastic systems. The models under study arise as optimizers of appropriate idleness-based criteria within a suitable family of fluid models for a given resource-sharing network. The class of minimal fluid models is fairly general, corresponding to efficient service protocols in which transmission on each route takes place in the earliest deadline first (EDF) order. For such a model, the distribution of the current lead times of the fluid mass on each route coincides with the fluid arrival measure for this route, truncated below on the current frontier level. Locally edge minimal fluid models may be regarded, in some sense, as fluid counterparts of EDF resource-sharing networks. Under mild assumptions, a locally edge minimal fluid model is uniquely determined by its data. We also show stability of such models in the strictly subcritical case. More generally, each such a subcritical model converges to the invariant manifold in finite time.

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Stability of linear EDF networks with resource sharing

Cited by 3 publications

References 39 publications

Instability of SRPT, SERPT and SJF multiclass queueing networks

Instability of SRPT, SERPT and SJF multiclass queueing networks

The Design of Mobile Distance Online Education Resource Sharing from the Perspective of Man-Machine Cooperation

Minimal and Locally Edge Minimal Fluid Models for Resource-Sharing Networks

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