A successive censoring algorithm for a system of connected LDQBD-processes

Baër, Niek; Hanbali, Ahmad Al; Boucherie, Richard J.; Ommeren, Jan-Kees van

doi:10.1007/s10479-020-03903-2

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…A queue without state dependent service and arrival processes can be modelled as a Quasi-Birth-and-Death process (QBD) for which the stationary distribution is a mixture of geometric terms, see Hajek [38]. The stationary distribution of a queue controlled by a threshold policy can be obtained using the successive censoring algorithm in Baer, Al Hanbali, Boucherie and van Ommeren [7] and Chapter 7.…”

Section: Marginal Distributionmentioning

confidence: 99%

Queueing and traffic

Baër

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Traffic jams are everywhere, some are caused by constructions or accidents but most occur naturally. These "natural" traffic jams may be a result of variable driving speeds combined with a high number of vehicles. To prevent these traffic jams, we have to understand traffic in general, and to understand traffic we have to understand the relations between the three key parameters of highway traffic, speed, the average speed of a vehicle, flow, the number of vehicles passing a reference point, and density, the number of vehicles on the road. These relations are often displayed in the socalled fundamental diagram of traffic, see Figure 2.1 for an example. A well-known relation between these parameters is that flow equals the product of speed and density. This thesis demonstrates that queueing theory can offer new insights in the remaining relations between these three parameters.An important aspect of traffic is congestion. Congestion is a phenomenon that arises when roads become more and more crowded, speeds will decrease and travel times will increase. This phenomenon is well-known in queueing theory. In basic queueing models we observe that the average queue length and average time spent in the queue increases when the density increases. In the past, see Boon [14], queueing theory has shown its usefulness in the analysis of intersections where vehicles must wait before crossing, however, in the analysis of highway traffic, queueing theory has received little attention.Another aspect of highway traffic is its hysteretic behaviour, explained by Helbing in [46]. He describes traffic by two different phases, non-congested and congested, and describes a hysteretic transition between these two phases. On a quiet highway, traffic is non-congested and average speeds are close to the speed limit. However, when density increases, vehicles will interact with one another until, at some critical point, a transition occurs and traffic becomes congested. In this phase, density is high and average speeds are well below the speed limit, i.e., a traffic jam emerges.

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Section: Marginal Distributionmentioning

confidence: 99%

Queueing and traffic

Baër

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Efficient Computation of Optimal Thresholds in Cloud Auto-scaling Systems

Tournaire

Castel-Taleb

Hyon

2023

ACM Trans. Model. Perform. Eval. Comput. Syst.

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We consider a horizontal and dynamic auto-scaling technique in a cloud system where virtual machines hosted on a physical node are turned on and off in order to minimise energy consumption while meeting performance requirements. Finding cloud management policies that adapt the system to the load is not straightforward and we consider here that virtual machines are turned on and off depending on queue load thresholds. We want to compute the optimal threshold values that minimize consumption costs and penalty costs (when performance requirements are not met). To solve this problem, we propose several optimisation methods, based on two different mathematical approaches. The first one is based on queueing theory and uses local search heuristics coupled with the stationary distributions of Markov Chains. The second approach tackles the problem using Markov Decision Process (MDP) in which we assume that the policy is of a special multi-threshold type called hysteresis. We improve the heuristics of the former approach with the aggregation of Markov Chains and queues approximation techniques. We assess the benefit of threshold-aware algorithms for solving MDPs. Then, we carry out theoretical analyzes of the two approaches. We also compare them numerically and we show that all of the presented MDP algorithms strongly outperform the local search heuristics. Finally, we propose a cost model for a real scenario of a cloud system to apply our optimisation algorithms and to show their practical relevance. The major scientific contribution of the paper is a set of fast (almost in real time) load-based threshold computation methods that can be used by a cloud provider to optimize its financial costs.

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A successive censoring algorithm for a system of connected LDQBD-processes

Cited by 2 publications

References 21 publications

Queueing and traffic

Queueing and traffic

Efficient Computation of Optimal Thresholds in Cloud Auto-scaling Systems

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