STABILITY OF A SIMPLE RE-ENTRANT LINE WITH INFINITE SUPPLY OF WORK : THE CASE OF EXPONENTIAL PROCESSING TIMES(&lt;Special Issue&gt;Network Design, Control and Optimization)

Weiss, Gideon

doi:10.15807/jorsj.47.304

Cited by 13 publications

(21 citation statements)

References 8 publications

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“…in [3] and [6]. Jackson networks with an infinite supply of work are a special case of multiclass queueing networks with virtual infinite buffers, introduced in [2], [8], [9], and [10].Recall that all service and interarrival times in a Jackson network are independent and exponentially distributed. Also, assume that the routing matrix P has spectral radius less than 1,…”

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confidence: 99%

Jackson networks with unlimited supply of work

Weiss¹

2005

J. Appl. Probab.

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We consider a Jackson network in which some of the nodes have an infinite supply of work: when all the customers queued at such a node have departed, the node will process a customer from this supply. Such nodes will be processing jobs all the time, so they will be fully utilized and experience a traffic intensity of 1. We calculate flow rates for such networks, obtain conditions for stability, and investigate the stationary distributions. Standard nodes in this network continue to have product-form distributions, while nodes with an infinite supply of work have geometric marginal distributions and Poisson inflows and outflows, but their joint distribution is not of product form.

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confidence: 99%

Jackson networks with unlimited supply of work

Weiss¹

2005

J. Appl. Probab.

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“…It is straightforward to verify that (20) agrees with the QP in (14)- (18). Formulation (20) is in the form that is required by most commercial QP solvers.…”

Section: Detailed Description Of the Qpmentioning

confidence: 95%

“…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%

“…The latter is motivated by both the acquisition queue [5] and multi-class queueing networks with infinite virtual queues [16], [20]. In these types of queueing models, a server in the network can generate arrivals and is often faced with the control choice of either letting new jobs enter the system or serving jobs that are presently waiting for service.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Infinite GJN is an extension of Jackson network with an infinite supply of work in [13], and is a special case of multiclass queueing networks with virtual infinite buffers, which were introduced in [13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%