The Power-Series Algorithm Applied to the Shortest-Queue Model

Blanc, J.P.C.

doi:10.1287/opre.40.1.157

Cited by 47 publications

(36 citation statements)

References 17 publications

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“…The first term in the RHS of (7a) is larger than the one in (7b), the other three terms are ordered by (3).…”

Section: So V N +L (I +Ii)~vn+l (I +I-li + 1)mentioning

confidence: 97%

“…The first term in the RHS of (lOa) is larger than in (lOb), the second and third term are ordered by (3) and the forth terms are ordered by (4) (and equal if i =0).…”

Section: Proof Of (4)mentioning

confidence: 99%

“…Their method is not restricted to systems with two queues, but applies equally well to systems with more queues. As far as the shortest queue system is concerned, Blanc [3] reports that the power series method is numerically satisfactory for practically all values of the work load for systems with up to 10 parallel queues. However, the theoretical foundation of this method is still incomplete.…”

Section: Introductionmentioning

confidence: 99%

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Upper and lower bounds for the waiting time in the symmetric shortest queue system

1994

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van der, J. (1992). Upper and lower bounds for the waiting time in the symmetric shortest queue system. (Memorandum COSOR; Vol. 9209). Eindhoven: Technische Universiteit Eindhoven. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. ABSTRACTIn this paper we compare the exponential symmetric shortest queue system with two related systems: the shortest queue system with threshold jockeying and the shortest queue system with threshold blocking. The latter two systems are easier to analyse and are shown to give tight lower and upper bounds respectively for the mean waiting time in the shortest queue system. The approach also gives bounds for the distribution of the total number of jobs in the system.

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“…The first term in the RHS of (7a) is larger than the one in (7b), the other three terms are ordered by (3).…”

Section: So V N +L (I +Ii)~vn+l (I +I-li + 1)mentioning

confidence: 97%

“…The first term in the RHS of (lOa) is larger than in (lOb), the second and third term are ordered by (3) and the forth terms are ordered by (4) (and equal if i =0).…”

Section: Proof Of (4)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Upper and lower bounds for the waiting time in the symmetric shortest queue system

1994

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“…As for numerical methods, one can see in Blanc [3] for power-series algorithm, in Rao [13] or Lian [8] for dimension-reduction method, or in Shi [15] for BRI algorithm.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Stationary Queue Length Distribution for Geo/T-IPH/1 Queue

Hou

Shi

2013

J. Oper. Res. Soc. China

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In this paper we study a Geo/T-IPH/1 queue model, where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states. The queue model can be described by a quasi-birth-anddeath (QBD) process with countably phases. Using the operator-geometric solution method, we first give the expression of the operator and the joint stationary distribution. Then we obtain the probability generating function (PGF) for stationary queue length distribution and sojourn time distribution, respectively.

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“…The aim of the present paper is to quantify the probability of bad luck for systems in which customers join one of the shortest queues upon arrival. For the computations reported in this paper we have used the power-series algorithm to compute the stationary queue length distribution as described in Blanc (1987aBlanc ( , 1987bBlanc ( , 1992 for the shortest-queue system. The efficiency of the algorithm is further enhanced in Blanc (1993).…”

Section: Introductionmentioning

confidence: 99%

Bad luck when joining the shortest queue

Blanc

2009

European Journal of Operational Research

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A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in one's own queue. This paper quantifies the probability that one's service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible. Jel codes: C44, C60

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The Power-Series Algorithm Applied to the Shortest-Queue Model

Cited by 47 publications

References 17 publications

Upper and lower bounds for the waiting time in the symmetric shortest queue system

Upper and lower bounds for the waiting time in the symmetric shortest queue system

Analysis of Stationary Queue Length Distribution for Geo/T-IPH/1 Queue

Bad luck when joining the shortest queue

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