Performance analysis and optimization with the power-series algorithm

Blanc, J.P.C.

doi:10.1007/bfb0013849

Cited by 39 publications

(28 citation statements)

References 12 publications

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“…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). Other approaches to shortest-queue systems can be found, among others, in Haight (1958), Flatto and McKean (1977), Halfin (1985), Rao and Posner (1987), Hanqin and Rongxin (1989), Adan, Wessels and Zijm (1990), Adan, Van Houtum and Van der Wal (1994) and Wu and Posner (1997).…”

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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Section: Introductionmentioning

confidence: 99%

Bad luck when joining the shortest queue

Blanc

2009

European Journal of Operational Research

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“…[3] reviews the PSA in its generality. The applicability and complexity of the PSA for polling systems with various visit and service rules have been discussed in [2].…”

Section: Introductionmentioning

confidence: 99%

“…The coefficients of the power-series expansions of the moments are obtained from those of the state probabilities in a straightforward manner, cf. [3]. The moments of the waiting time distributions for jobs at the various stations, assuming service in order of arrival, follow from the moments of the marginal queue-length distribution through a general relationship between the generating function of the queue-length distribution and the Laplace-Stieltjes transform of the waiting time in M/G/1-type systems, cf.…”

Section: Introductionmentioning

confidence: 99%

The Power-Series Algorithm for Polling Systems with Time Limits

Blanc

1998

Prob. Eng. Inf. Sci.

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“…which are not included in the above scheme because the factor in front of this coefficient vanishes, are determined by the requirement that the probabilities sum to one. The efficiency of the algorithm is further enhanced in [13]. A peculiarity of the current system with reneging customers is that it is stable for all λ > 0.…”

Section: B Power-series Expansionsmentioning

confidence: 99%

“…An option for numerical analysis of the M/M/S queue with batch services and deadlines that we have considered is the power-series algorithm (PSA) as summarized in Blanc [13]. The PSA has proven to be a very useful analytic-numerical method for the analysis of multi-dimensional Markov chains.…”

Section: B Power-series Expansionsmentioning

confidence: 99%

Tandem Queues with Impatient Customers for Blood Screening Procedures

Bar‐Lev

Blanc

Boxma

et al. 2011

Methodol Comput Appl Probab

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We study a blood testing procedure for detecting viruses like HIV, HBV and HCV. In this procedure, blood samples go through two screening steps. The first test is ELISA (antibody Enzyme Linked Immuno-Sorbent Assay). The portions of blood which are found not contaminated in this first phase are tested in groups through PCR (Polymerase Chain Reaction). The ELISA test is less sensitive than the PCR test and the PCR tests are considerably more expensive. We model the two test phases of blood samples as services in two queues in series; service in the second queue is in batches, as PCR tests are done in groups. The fact that blood can only be used for transfusions until a certain expiration date leads, in the tandem queue, to the feature of customer impatience. Since the first queue basically is an infinite server queue, we mainly focus on the second queue, which in its most general form is an S-server M/G [k,K] /S + G queue, with batches of sizes which are bounded by k and K.Our objective is to maximize the expected profit of the system, which is composed of the amount earned for items which pass the test (and before their patience runs out), minus costs. This is done by an appropriate choice of the decision variables, namely, the batch sizes and the number of servers at the second service station. As will be seen, even the simplest version of the batch queue, the M/M [k,K] /1 + M queue, already gives rise to serious analytical complications for any batch size larger than 1. These complications are discussed in detail. In view of the fact that we aim to solve realistic optimization problems for blood screening procedures, these analytical complications force us to take recourse to either a numerical approach or approximations. We present a numerical solution for the queue length distribution in the M/M [k,K] /S +M queue and then formulate and solve several optimization problems. The power-series algorithm, which is a numerical-analytic method, is also discussed.

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Performance analysis and optimization with the power-series algorithm

Cited by 39 publications

References 12 publications

Bad luck when joining the shortest queue

Bad luck when joining the shortest queue

The Power-Series Algorithm for Polling Systems with Time Limits

Tandem Queues with Impatient Customers for Blood Screening Procedures

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