Tail asymptotics for the fundamental period in the MAP/G/1 queue

Kim, Bara; Lee, Jisu; Wee, In-Suk

doi:10.1007/s11134-007-9042-9

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…Takahashi and Wang [24], Ahn and Jeon [25], Kim [26] [27], Bekker and Boxma [28], [29]. Baykal-Gürsoy and Xiao [2] analyze a M/M/∞ queue with Markov modulated service rates, and its application to traffic modeling is introduced.…”

Section: A Literature Reviewmentioning

confidence: 99%

A Note on Infinite-Server Markov Modulated and Single-Server Retrial Queues

Duan

Baykal‐Gürsoy

2014

Asia Pac. J. Oper. Res.

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We reconsider the M/M/∞ queue with two-state Markov modulated arrival and service processes and the single-server retrial queue analyzed in Keilson and Servi [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471]. Fuhrmann and Cooper type stochastic decomposition holds for the stationary occupancy distributions in both queues [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471; Baykal-Gürsoy, M and W Xiao (2004). Stochastic decomposition in M/M/∞ queues with Markov-modulated service rates. Queueing Systems, 48, 75–88]. The main contribution of the present paper is the derivation of the explicit form of the stationary system size distributions. Numerical examples are presented visually exhibiting the effect of various parameters on the stationary distributions.

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Section: A Literature Reviewmentioning

confidence: 99%

A Note on Infinite-Server Markov Modulated and Single-Server Retrial Queues

Duan

Baykal‐Gürsoy

2014

Asia Pac. J. Oper. Res.

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“…Tails and related properties of the busy period for GI/G/1 and related models have received much attention during the past 15 years. In addition to [21], the busy period has been studied under various conditions in [3,4,6,7,10,14,16,18]. Our contribution to the body of knowledge in the critical case adds to this.…”

Section: Introductionmentioning

confidence: 99%

On busy periods of the critical GI/G/1 queue and BRAVO

Nazarathy

Palmowski

2022

Queueing Syst

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We study critical GI/G/1 queues under finite second-moment assumptions. We show that the busy-period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics as well as a similar derivation for GI/M/1. The busy-period asymptotics determine the growth rate of moments of the renewal process counting busy cycles. We further use this to demonstrate a Balancing Reduces Asymptotic Variance of Outputs (BRAVO) phenomenon for the work-output process (namely the busy time). This yields new insight on the BRAVO effect. A second contribution of the paper is in settling previous conjectured results about GI/G/1 and GI/G/s BRAVO. Previously, infinite buffer BRAVO was generally only settled under fourth-moment assumptions together with an assumption about the tail of the busy period. In the current paper, we strengthen the previous results by reducing to assumptions to existence of $$2+\epsilon $$ 2 + ϵ moments.

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“…Tails and related properties of the busy period for GI/G/1 and related models have received much attention during the past 15 years. In addition to [21], the busy period has been studied under various conditions in [4], [14], [6], [3], [16], [18], [7] and [10]. Our contribution to the body of knowledge in the critical case adds to this.…”

Section: Introductionmentioning

confidence: 99%

Ruin probabilities for risk process in a regime-switching environment

Palmowski

2021

Scandinavian Actuarial Journal

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We study critical GI/G/1 queues under finite second moment assumptions. We show that the busy period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics as well as a similar derivation for GI/M/1. The busy period asymptotics determine the growth rate of moments of the renewal process counting busy cycles. We further use this to demonstrate a BRAVO phenomenon (Balancing Reduces Asymptotic Variance of Outputs) for the work-output process (namely the busy-time). This yields new insight on the BRAVO effect.A second contribution of the paper is in settling previous conjectured results about GI/G/1 and GI/G/s BRAVO. Previously, infinite buffer BRAVO was generally only settled under fourth-moment assumptions together with an assumption about the tail of the busy-period. In the current paper we strengthen the previous results by reducing to assumptions to existence of 2 + ǫ moments.

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Tail asymptotics for the fundamental period in the MAP/G/1 queue

Cited by 5 publications

References 12 publications

A Note on Infinite-Server Markov Modulated and Single-Server Retrial Queues

A Note on Infinite-Server Markov Modulated and Single-Server Retrial Queues

On busy periods of the critical GI/G/1 queue and BRAVO

Ruin probabilities for risk process in a regime-switching environment

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