The mean queue content of discrete-time queues with zero-regenerative arrivals

Fiems, Dieter; Turck, Koen De

doi:10.1016/j.orl.2012.03.001

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…Not unlike train and session arrival models, the Galton-Watson model is in a fixed state when there are no arrivals. It is, in fact, this property which enables closed-form expressions for the moments of the queue content and delay [20]. This also implies that periods without arrivals are geometrically distributed, and that the single-server queue is overloaded whenever there are arrivals.…”

Section: Introductionmentioning

confidence: 96%

Analysis of Discrete-Time Queues with Branching Arrivals

Fiems

Turck

2023

Mathematics

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We consider a discrete-time single server queueing system, where arrivals stem from a multi-type Galton–Watson branching process with migration. This branching-type arrival process exhibits intricate correlation, and the performance of the corresponding queueing process can be assessed analytically. We find closed-form expressions for various moments of both the queue content and packet delay. Close inspection of the arrival process at hand, however, reveals that sample paths consist of large independent bursts of arrivals followed by geometrically distributed periods without arrivals. Allowing for non-geometric periods without arrivals, and correlated bursts, we apply π-thinning on the arrival process. As no closed-form expressions can be obtained for the performance of the corresponding queueing system, we focus on approximations of the main performance measures in the light and heavy traffic regimes.

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Section: Introductionmentioning

confidence: 96%

Analysis of Discrete-Time Queues with Branching Arrivals

Fiems

Turck

2023

Mathematics

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Queueing models for the analysis of communication systems

Bruneel

Fiems

Walraevens

et al. 2014

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Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays

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The mean queue content of discrete-time queues with zero-regenerative arrivals

Cited by 2 publications

References 12 publications

Analysis of Discrete-Time Queues with Branching Arrivals

Analysis of Discrete-Time Queues with Branching Arrivals

Queueing models for the analysis of communication systems

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