An analytic solution of the waiting time distribution for the discrete-time GI/G/1 queue

Murata, Masayuki; Miyahara, Hideo

doi:10.1016/0166-5316(91)90042-2

Cited by 11 publications

(5 citation statements)

References 10 publications

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“…To prove Theorem 2 we must apply the result (14) of Theorem 1 to the system of integral equations (35).…”

Section: Proofs Of Resultsmentioning

confidence: 99%

Some Results for the Actual Waiting Time in Batch Arrival Queueing Systems

Kempa

2010

Stochastic Models

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The article deals with the queueing system of GI /G /1 type with individual service and batch arrival of customers. The method of integral equations on a half-axis [0, ∞) is applied to obtain new results for the actual waiting time w n of nth arriving customer. The transient and steady state as n tends to infinity are considered. Some simplifications and numerical results for M /M /1, M /E 2 /1, and M 2 /M /1 queueing systems are derived as well.

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“…To prove Theorem 2 we must apply the result (14) of Theorem 1 to the system of integral equations (35).…”

Section: Proofs Of Resultsmentioning

confidence: 99%

Some Results for the Actual Waiting Time in Batch Arrival Queueing Systems

Kempa

2010

Stochastic Models

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“…Konheim [102], Murata and Miyahara [128], and Stadje [157], have suggested to approximate the G/G/1 queue by its discrete counterpart. For determining the coefficients C z j in (6.40), the following property can be used: Proof The proof consists of computing the k j 's successively by equating coefficients in K (z) = M (z)K(z).…”

Section: ) Andmentioning

confidence: 99%

Multiaccess, Reservations & Queues

Denteneer¹,

Leeuwaarden²

2008

Philips Research Book Series

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Scope to the 'Philips Research Book Series'As one of the largest private sector research establishments in the world, Philips Research is shaping the future with technology inventions that meet peoples' needs and desires in the digital age. While the ultimate user benefits of these inventions end up on the high-street shelves, the often pioneering scientific and technological basis usually remains less visible.This 'Philips Research Book Series' has been set up as a way for Philips researchers to contribute to the scientific community by publishing their comprehensive results and theories in book form.

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“…A multiserver queueing system with geometric service times and a general independent arrival process is analyzed in [8]. Geometric service times are also considered in [9,10,11], while [12] and [13] deal with general service times, but only for the single-server case.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Discrete-Time G(G)/Geom/c Queueing Model

Wittevrongel

Bruneel

Vinck

2002

NETWORKING 2002: Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile A

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Abstract. This paper presents the steady-state analysis of a discretetime infinite-capacity multiserver queue with c servers and independent geometrically distributed service times. The arrival process is a batch renewal process, characterized by general independent batch interarrival times and general independent batch sizes. The analysis has been carried out by means of an analytical technique based on generating functions, complex analysis and contour integration. Expressions for the generating functions of the system contents during an arrival slot as well as during an arbitrary slot have been obtained. Also, the delay in case of a firstcome-first-served queueing discipline has been analyzed.

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An analytic solution of the waiting time distribution for the discrete-time GI/G/1 queue

Cited by 11 publications

References 10 publications

Some Results for the Actual Waiting Time in Batch Arrival Queueing Systems

Some Results for the Actual Waiting Time in Batch Arrival Queueing Systems

Multiaccess, Reservations & Queues

Analysis of the Discrete-Time G(G)/Geom/c Queueing Model

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