Analysis of a simple Markovian re-entrant line with infinite supply of work under the LBFS policy

Adan, I.J.B.F.; Weiss, Gideon

doi:10.1007/s11134-006-0065-4

Cited by 55 publications

(28 citation statements)

References 10 publications

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“…In summary: For this example, each queue undergoes fluctuations in service rate around the average service rate of ν, where for alternating periods of expected duration 2T (2,2) , the service rates alternate between ν 1+r 1+2r and ν 1+3r 1+2r .…”

Section: Examplementioning

confidence: 96%

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A Push–Pull Network with Infinite Supply of Work

2009

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We consider a two-node multiclass queueing network with two types of jobs moving through two servers in opposite directions, and there is infinite supply of work of both types. We assume exponential processing times and preemptive resume service. We identify a family of policies which keep both servers busy at all times and keep the queues between the servers positive recurrent. We analyze two specific policies in detail, obtaining steady state distributions. We perform extensive calculations of expected queue lengths under these policies. We compare this network with the Kumar-Seidman-Rybko-Stolyar network, in which there are two random streams of arriving jobs rather than infinite supply of work.

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Section: Examplementioning

confidence: 96%

“…We split the time spent in the state (2, 2) equally between the two strips. Hence the network spends an expected time 2T (2,2) = (1+r)(1+2r) μ (1−r) in each strip before moving to the other strip. Consider the horizontal strip.…”

Section: Examplementioning

confidence: 99%

A Push–Pull Network with Infinite Supply of Work

2009

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“…To illustrate MaxFTP, we describe its implementation for a simple re-entrant line with 2 servers and 3 classes (this network has been recently studied in Adan and Weiss (2006)). We demonstrate the effectiveness of our results by means of simulations in which the asymptotic attributes of MaxFTP are empirically tested (Section 6).…”

Section: Introductionmentioning

confidence: 99%

Near optimal control of queueing networks over a finite time horizon

Nazarathy

Weiss

2008

Ann Oper Res

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We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line.

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“…Example 2 is a simple reentrant line. This example resembles the continuous-time reentrant line in [1]. Example 3 is the acquisition queue presented in Section II.…”

Section: Description As a Linear System With Noisementioning

confidence: 99%

“…In [1] (see also [20]) the authors have shown that a continuous-time reentrant line is stable when using the Last Buffer First Serve (LBFS) control that prioritizes step 3 over step 1, and a non-idling policy in server 2. This policy ensures that server 1 is maximally utilized.…”

Section: Example 2: Simple Reentrant Linementioning

confidence: 99%

Model predictive control for the acquisition queue and related queueing networks

Leeuwaarden

Lefeber

Nazarathy

et al. 2010

Proceedings of the 5th International Conference on Queueing Theory and Network Applications

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Model Predictive Control (MPC) is a well established method in control theory and engineering practice. It is often the method of choice for systems that need to be controlled in view of constraints. The main idea of MPC is to solve an optimization problem over a given time horizon at each control epoch, and to use the obtained solution for controlling the system until the next control epoch. In many cases this optimization problem can be formulated as a tractable quadratic programming problem. In this paper we apply MPC to discrete-time queueing networks that incorporate multiple product routes, delays, self-generated arrivals and multi-job processing. We compare our MPC-based controller to simple threshold policies and show improved performance. We also mention some open theoretical problems related to this control method.

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Analysis of a simple Markovian re-entrant line with infinite supply of work under the LBFS policy

Cited by 55 publications

References 10 publications

A Push–Pull Network with Infinite Supply of Work

A Push–Pull Network with Infinite Supply of Work

Near optimal control of queueing networks over a finite time horizon

Model predictive control for the acquisition queue and related queueing networks

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