An initiative for a classified bibliography on G-networks

Do, Tien Van

doi:10.1016/j.peva.2010.10.001

Cited by 27 publications

(9 citation statements)

References 231 publications

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“…Since their introduction, G-networks have been extensively studied covering several extensions such as triggered movement, which redirect customers among the queues [15]; catastrophes or batch service [18], adders [19]; multiple classes of positive customers and signals [20], state-dependent service disciplines [21,22,23], tandem networks [24,25], deletion of a random amount of work [26,27], retrials [28,29] (not exhaustive list). For a complete bibliography see [30,31,32]. G-networks have been shown to be a diverse application tool to analyse and optimise the effects of dynamic load balancing in large scale networks [33] as well as in Gene Regulatory Networks [34,35].…”

Section: Related Workmentioning

confidence: 99%

A Random Access G-Network: Stability, Stable Throughput, and Queueing Analysis

Dimitriou¹,

Παππάς²

2019

Prob. Eng. Inf. Sci.

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The effect of signals on stability, throughput region, and delay in a two-user slotted ALOHA based random-access system with collisions is considered. This work gives rise to the development of random access G-networks, which can model virus attacks or other malfunctions and introduce load balancing in highly interacting networks. The users are equipped with infinite capacity buffers accepting external bursty arrivals. We consider both negative and triggering signals. Negative signals delete a packet from a user queue, while triggering signals cause the instantaneous transfer of packets among user queues. We obtain the exact stability region, and show that the stable throughput region is a subset of it. Moreover, we perform a compact mathematical analysis to obtain exact expressions for the queueing delay by solving a Riemann boundary value problem. A computationally efficient way to obtain explicit bounds for the queueing delay is also presented. The theoretical findings are numerically evaluated and insights regarding the system performance are derived.

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Section: Related Workmentioning

confidence: 99%

A Random Access G-Network: Stability, Stable Throughput, and Queueing Analysis

Dimitriou¹,

Παππάς²

2019

Prob. Eng. Inf. Sci.

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“…Since the works of Gelenbe (see [1,2] and [4][5][6][7]), Gqueue has drawn great attention from researchers to apply the concept in diverse fields, such as manufacturing system, industrial engineering, computer and communication networks. Survey on the analysis and applications of G-queue can be referred to [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

An alternative approach in finding the stationary queue length distribution of a queueing system with negative customers

et al. 2021

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A single-server queueing system with negative customers is considered in this paper. One positive customer will be removed from the head of the queue if any negative customer is present. The distribution of the interarrival time for the positive customer is assumed to have a rate that tends to a constant as time t tends to infinity. An alternative approach will be proposed to derive a set of equations to find the stationary probabilities. The stationary probabilities will then be used to find the stationary queue length distribution. Numerical examples will be presented and compared to the results found using the analytical method and simulation procedure. The advantage of using the proposed alternative approach will be discussed in this paper.

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“…Since the introduction by Gelenbe, these types of queues have drawn great attention and studied extensively. The application is then widen to other areas such as communication systems, industrial engineering and manufacturing systems [3][4][5]. In practical applications, the term of negative customers is used to resemble viruses, inhibitory signals and orders of demand.…”

Section: Introductionmentioning

confidence: 99%

Stationary queue length of a single-server queue with negative arrivals and nonexponential service time distributions

et al. 2018

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Abstract. In this paper, a single-server queue with negative customers is considered. The arrival of a negative customer will remove one positive customer that is being served, if any is present. An alternative approach will be introduced to derive a set of equations which will be solved to obtain the stationary queue length distribution. We assume that the service time distribution tends to a constant asymptotic rate when time t goes to infinity. This assumption will allow for finding the stationary queue length of queueing systems with non-exponential service time distributions. Numerical examples for gamma distributed service time with fractional value of shape parameter will be presented in which the steady-state distribution of queue length with such service time distributions may not be easily computed by most of the existing analytical methods.

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An initiative for a classified bibliography on G-networks

Cited by 27 publications

References 231 publications

A Random Access G-Network: Stability, Stable Throughput, and Queueing Analysis

A Random Access G-Network: Stability, Stable Throughput, and Queueing Analysis

An alternative approach in finding the stationary queue length distribution of a queueing system with negative customers

Stationary queue length of a single-server queue with negative arrivals and nonexponential service time distributions

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