A Roots Method in GI/PH/1 Queueing Model and Its Application

Choi, Kyung Hwan; Yoon, Bong K.

doi:10.7232/iems.2013.12.3.281

Cited by 4 publications

(1 citation statement)

References 12 publications

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“…The classical way of finding the unknown constant coefficients is based on the analyticity of the p.g.f. inside the unit disk, see e.g., Choi and Yoon [6], Samanta [26], Oblakova et al [25], and references therein. Also, Zhao and Campbell [31] pointed out that both the inside and outside roots of the unit disk are playing a significant role in the calculation of system state characteristics.…”

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confidence: 99%

Analysis of $ D $-$ BMAP/G/1 $ queueing system under $ N $-policy and its cost optimization

Nandi¹,

Samanta²,

Kim³

2021

JIMO

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This article studies an infinite buffer single server queueing system under N-policy in which customers arrive according to a discrete-time batch Markovian arrival process. The service times of customers are independent and obey a common general discrete distribution. The idle server begins to serve the customers as soon as the queue size becomes at least N and serves the customers until the system becomes empty. We determine the queue length distribution at post-departure epoch with the help of roots of the associated characteristic equation of the vector probability generating function. Using the supplementary variable technique, we develop the system of vector difference equations to derive the queue length distribution at random epoch. An analytically simple and computationally efficient approach is also presented to compute the waiting time distribution in the queue of a randomly selected customer of an arrival batch. We also construct an expected linear cost function to determine the optimal value of N at minimum cost. Some numerical results are demonstrated for different service time distributions through the optimal control parameter to show the key performance measures.

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confidence: 99%

Analysis of $ D $-$ BMAP/G/1 $ queueing system under $ N $-policy and its cost optimization

Nandi¹,

Samanta²,

Kim³

2021

JIMO

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A Survey on the Queueing Inventory Systems with Phase-type Service Distributions

Choi

Yoon

2016

Proceedings of the 11th International Conference on Queueing Theory and Network Applications

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Asymmetric Information Supply Chain Models with Credit Option

Xu¹,

Zeephongsekul²

2013

Industrial Engineering and Management Systems

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Credit option is a policy that has been studied by many researchers in the area of supply chain management. This policy has been applied in practice to improve the profits of supply chain members. Usually, a credit option policy is proposed by the seller, and often under a symmetric information environment where members have complete information on each others' operations. In this paper, we investigate two scenarios: firstly, the seller offers a credit option to the buyer, and secondly, the buyer attempts to stretch the length of the credit period offered by the seller. The proposed model in both scenarios will be investigated under an asymmetric information structure where some information are private and are only known to the individual who has knowledge of this information. The interactions between buyer and seller will be modeled by non-cooperative Stackelberg games where the buyer and seller take turn as leader and follower. Among some of the numerical results obtained, the seller and buyer's profits obtained from symmetric information games are larger than those obtained from an asymmetric information game in both scenarios. Furthermore, both buyer and seller's profit in the second scenario are better than in the first scenario.

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A Roots Method in GI/PH/1 Queueing Model and Its Application

Cited by 4 publications

References 12 publications

Analysis of $ D $-$ BMAP/G/1 $ queueing system under $ N $-policy and its cost optimization

Analysis of $ D $-$ BMAP/G/1 $ queueing system under $ N $-policy and its cost optimization

A Survey on the Queueing Inventory Systems with Phase-type Service Distributions

Asymmetric Information Supply Chain Models with Credit Option

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