Generalized folding-algorithm for sojourn time analysis of finite qbd processes and its queueing applications

San-qi, L. I.; Sheng, Hong-Dah

doi:10.1080/15326349608807397

Cited by 27 publications

(2 citation statements)

References 8 publications

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“…Our work extends the work of Gaver et al (1984) to determine the stationary distribution of a LDQBD with a finite number of levels to more general transitions, see Remark 1. The censoring algorithm Kemeny and Snell (1960) also forms the basis for the folding algorithm in Ye and Li (1994) and Li and Sheng (1996), where the stationary distribution of a finite QBD was obtained by sequentially splitting (and renumbering) the state space in odd and even numbered sets, followed by application of the censoring algorithm to the two resulting subsets. In the literature, the censoring algorithm is also called exact aggregation/disaggregation algorithm in which the state space is aggregated to obtain a smaller (and easier to solve) Markov chain.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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We consider a Markov Chain in which the state space is partitioned into sets where both transitions within sets and between sets have a special structure. Transitions within each set constitute a finite level dependent quasi-birth-and-death-process (LDQBD), and transitions between sets are restricted to six types of transitions. These latter types are needed to preserve the sets structure in the reduction step of our algorithm. Specifically, we present a successive censoring algorithm, based on matrix analytic methods, to obtain the stationary distribution of this system of connected LDQBD-processes.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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“…Our work extends the work of Gaver, Jacobs and Latouche [34] to more general transitions, see Remark 7.1. The censoring algorithm [54] also forms the base for the folding algorithm in Ye and Li [106] and Li and Sheng [66], where the stationary distribution of a finite QBD was obtained by sequentially splitting (and renumbering) the state space in odd and even numbered sets, followed by application of the censoring algorithm to the two resulting subsets.…”

Section: Introductionmentioning

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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An auxiliary server threshold queueing model and its application to the operational characteristics of web server system

Lee

Cho

2007

Applied Mathematical Modelling

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This paper analyzes an auxiliary server queueing model in which secondary servers are added to the main server(s) when the queue length exceeds some predetermined threshold value at the main queue. We model this system by the level-dependent quasi-birth-death (QBD) process and develop computation algorithms. We apply this model to the web-server system to explore some specific operational characteristics and draw some useful conclusions.

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Generalized folding-algorithm for sojourn time analysis of finite qbd processes and its queueing applications

Cited by 27 publications

References 8 publications

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

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

Queueing and traffic

An auxiliary server threshold queueing model and its application to the operational characteristics of web server system

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