The M/M/C queueing system in a random environment

Liu, Zaiming; Yu, Senlin

doi:10.1016/j.jmaa.2015.11.074

Cited by 21 publications

(8 citation statements)

References 10 publications

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“…Attention has been devoted in the literature also to queues with more complex random switching mechanisms, that arise naturally in the study of packet arrivals to a local switch (see, for instance, Burman and Smith [8]). Similar mechanisms have been studied recently also by Arunachalam et al [2], Pang and Zhou [36], Liu and Yu [30] and Perel and Yechiali [38].…”

Section: Introductionsupporting

confidence: 73%

M/M/1 queue in two alternating environments and its heavy traffic approximation

Crescenzo

Giorno

Kumar

et al. 2018

Journal of Mathematical Analysis and Applications

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We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of the process in terms of a generalized mixture of two geometric distributions. In the special case when only one kind of switch is allowed, we analyze the transient distribution, and investigate the busy period problem. The analysis is also performed by means of a suitable heavy-traffic approximation which leads to a continuous random process. Its distribution satisfies a partial differential equation with randomly alternating infinitesimal moments. For the approximating process we determine the steady-state distribution, the transient distribution and a first-passage-time density.

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Section: Introductionsupporting

confidence: 73%

M/M/1 queue in two alternating environments and its heavy traffic approximation

Crescenzo

Giorno

Kumar

et al. 2018

Journal of Mathematical Analysis and Applications

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“…This assertion can be verified by the stability condition given in Liu and Yu (2016). We assume that a customer receives a reward of R units for completing service.…”

Section: Model Descriptionmentioning

confidence: 88%

Optimal balking strategies in the M/M/1 queue with multi-phase failures and repairs

Liu

2017

Oper Res Int J

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In this paper, we study the equilibrium strategies in the M/M/1 queue with partial and total failures. The state of the server is modulated by a random environment. Based on different precision levels of system information, we study separately the threshold strategies for the fully observable case and mixed strategies for the fully unobservable case. In addition, we illustrate the effect of several parameters on equilibrium behavior via numerical examples. Some possible generalizations are also discussed.

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“…The servers may be identical with similar processing power or heterogeneous with varying speeds and efficiency [26]. While the request arrival rate λ maintains Poisson's distribution, the processing rate µ increases by a factor c [29] such that the traffic intensity ρ = λ/cµ. In the event any of the queues are empty, some servers may be rendered idle.…”

Section: F Slice Request Queuingmentioning

confidence: 99%

A Survey on Slice Admission Control Strategies and Optimization Schemes in 5G Network

Ojijo

Falowo

2020

IEEE Access

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The Fifth Generation(5G) communication network is envisioned to provide heterogeneous services tailored to specific user demands. These services are diverse and can be generally categorized based on latency, bandwidth, reliability, and connection density requirements. The 5G infrastructure providers are expected to employ network function virtualization, software-defined networking, and network slicing for cost-effective and efficient network resource allocation. In the 5G network, when an infrastructure provider receives a slice request, a slice admission control scheme is applied and an optimization algorithm is used to achieve predefined objectives. To this end, a number of slice admission control objectives, strategies and algorithms have been proposed. However, there is a need to present a coherent review and bridge the gap between many aspects of slice admission control. In this paper, we present the latest developments in this research area. Thus, we begin by introducing slice admission control and discuss background concepts associated with slicing. We then extend our discussion to slice admission objectives followed by the strategies and optimization algorithms. Finally, we conclude with a summary of analysis containing the optimization algorithms.

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The M/M/C queueing system in a random environment

Cited by 21 publications

References 10 publications

M/M/1 queue in two alternating environments and its heavy traffic approximation

M/M/1 queue in two alternating environments and its heavy traffic approximation

Optimal balking strategies in the M/M/1 queue with multi-phase failures and repairs

A Survey on Slice Admission Control Strategies and Optimization Schemes in 5G Network

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