Queues with Negative Arrivals

Gelenbe, Erol; Sigman, Karl

doi:10.21236/ada213860

Cited by 38 publications

(48 citation statements)

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“…If we reduce to the single arrival case (i.e., g 1 = 1, g k = 0 for k ≥ 2), then it is possible to check that the stability Condition (40) agrees with appropriate particularizations of the stability results given by Gelenbe and Schassberger [12] in the context of G-networks and by Gelenbe et al [11] for single node queues with more general descriptions of arrival and service processes.…”

Section: Model Stability and Stationary Distributionmentioning

confidence: 83%

Optimal control and performance analysis of anM^X/M/1queue with batches of negative customers

Artalejo

Economou

2004

RAIRO-Oper. Res.

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We consider a Markov decision process for an M X /M/1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different thresholds. Exact and asymptotic results concerning the computation of the stationary distribution of the model are also derived.

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Section: Model Stability and Stationary Distributionmentioning

confidence: 83%

Optimal control and performance analysis of anM^X/M/1queue with batches of negative customers

Artalejo

Economou

2004

RAIRO-Oper. Res.

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“…If the queue is empty, the negative customer disappears at which it arrives because negative customers cannot accumulate at queues. A single server system with negative and positive customers was studied in [43]. Stability conditions for G-networks were given in [58].…”

Section: G-networkmentioning

confidence: 99%

G-Networks and the Performance of ICT with Renewable Energy

Zhang

2020

SN COMPUT. SCI.

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As a consequence of developing information and communication technology that is playing a significant role in our society and has changed our life dramatically, we witnessed a significant increase in energy consumption in computer systems and networks. Subsequently, energy harvesting technologies with renewable energy are of great interest in the field of computer systems and networks, and thus lead to abundant research which has been carried out to address energy harvesting from different aspects. However, the majority of them focuses on wireless or small-scale networks, which left wired networks with a general structure neglected. We first present a comprehensive systemic review of the trends of overall energy consumption, and energy and quality of service optimization in computer systems and networks. Then, this paper reviews the recent research progress in G-networks and energy packet networks with renewable and intermittent energy from both the system paradigms and the performance optimization and energy reduction algorithms for the wired networks.

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“…Those studied models have been used to simulate computer communication system and the manufacturing system et al The appropriate killing strategy must be determined in the queueing system with negative arrivals. Gelenbe et al [1] investigated a single-sever G-queue system with the RCE and RCH killing strategies. Jain and Sigman [2] considered the effect of disaster on M/G/1 queueing system.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, by numerical examples, we analyze the effect of the parameters on the average queue length and the average waiting time of customer in Section 6. (1) We assume that interarrival times of positive and negative customers follow the geometrically distributed with probabilities (0 < < 1) and (0 < < 1). That is,…”

Section: Introductionmentioning

confidence: 99%

The Geo/Geo/1+1 Queueing System with Negative Customers

Guo

Wang

et al. 2013

Mathematical Problems in Engineering

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We study a Geo/Geo/1+1 queueing system with geometrical arrivals of both positive and negative customers in which killing strategies considered are removal of customers at the head (RCH) and removal of customers at the end (RCE). Using quasi-birthdeath (QBD) process and matrix-geometric solution method, we obtain the stationary distribution of the queue length, the average waiting time of a new arrival customer, and the probabilities of servers in busy or idle period, respectively. Finally, we analyze the effect of some related parameters on the system performance measures.

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Queues with Negative Arrivals

Cited by 38 publications

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Optimal control and performance analysis of anM^X/M/1queue with batches of negative customers

Optimal control and performance analysis of anM^X/M/1queue with batches of negative customers

G-Networks and the Performance of ICT with Renewable Energy

The Geo/Geo/1+1 Queueing System with Negative Customers

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Queues with Negative Arrivals

Cited by 38 publications

References 0 publications

Optimal control and performance analysis of anMX/M/1queue with batches of negative customers

Optimal control and performance analysis of anMX/M/1queue with batches of negative customers

G-Networks and the Performance of ICT with Renewable Energy

The Geo/Geo/1+1 Queueing System with Negative Customers

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Product

Resources

About

Optimal control and performance analysis of anM^X/M/1queue with batches of negative customers

Optimal control and performance analysis of anM^X/M/1queue with batches of negative customers