Optimization of polling systems with Bernoulli schedules

Blanc, J.P.C.; Mei, R.D. van der

doi:10.1016/0166-5316(93)e0045-7

Cited by 27 publications

(22 citation statements)

References 28 publications

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“…Both properties have also been found in [5] for the unconstrained optimization problem with Bernoulli schedules as service disciplines.…”

Section: Smentioning

confidence: 72%

“…Note the resemblance of the behaviour of the optimal time limits as function of the load with that of the optimal Bernoulli schedules in [5]. In particular, the optimal set of time limits is, for each set of cost factors, such that at least one time-limit is infinite (i.e., the corresponding station is served exhaustively), and the stations for which the time limits are infinite are the stations for which the ratio c j µ j is maximal over j = 1, .…”

Section: Smentioning

confidence: 99%

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The Power-Series Algorithm for Polling Systems with Time Limits

Blanc

1998

Prob. Eng. Inf. Sci.

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“…Both properties have also been found in [5] for the unconstrained optimization problem with Bernoulli schedules as service disciplines.…”

Section: Smentioning

confidence: 72%

Section: Smentioning

confidence: 99%

The Power-Series Algorithm for Polling Systems with Time Limits

Blanc

1998

Prob. Eng. Inf. Sci.

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“…If a system is stable for all positive values of the arrival rate, then the bilinear mapping discussed in [12] for obtaining convergence of the series This maps λ = ∞ to θ = 1/G. Table 5 but their presence close to the origin influences good choices for G and H. Unfortunately, this makes the PSA in its present forms unsuitable for optimization of the current system whereby the performance has to be evaluated for a variety of parameter settings, in contrast to the successful optimization in, e.g., Blanc and Van der Mei [14].…”

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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“…This discipline can be viewed as the stochastic counterpart of the k-limited discipline. Analogous to UkL, Blanc and Van der Mei [3] try to find those q; that minimize the objective function (3.5). Their main approach is a numerical one, based on the use of the so-called power series algorithm.…”

Section: Remark 36mentioning

confidence: 99%

Static Optimization of Queueing Systems

Boxma

1995

Recent Trends in Optimization Theory and Applications

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This paper discusses some recent developments in the static: optimization of queueing systems. Special attention is given to three problem classes: (i) the optimal allocation of servers, or service capacity, to queues in a network; (ii) the optimal allocation of the visits of a single server to several queues (a polling system); (iii) the optimal allocation of a single arrival stream to several single server queues. l. INTRODUCTIONWhen several users compete for the use of a common resource, the limited capacity of the resource can give rise to congestion. This situation occurs in a plethora of everyday situations: people queue at a counter in a bank or supermarket, congestion occurs in road traffic, products encounter delays at machines during their production process, messages wait for access to a common transmission channel and computer jobs for the use of a set of processors. Queueing occurs even when the service capacity of the resource strongly exceeds the demand. This is due to the fact that the interarrival times of the users, and their required service times, are generally not fixed. A mathematical model of congestion phenomena therefore usually represents interarrival and service times of users by random variables. The resources are called service facilities, with a single server or multiple servers, and the users are called customers. Customers often visit a number of service facilities, encountering several queues during their stay in the system. Queueing theory is devoted to the description, analysis and optimization of such queueing systems. It concentrates on a few key performance measures, like queue lengths and waiting times. Due to the stochastic nature of the arrival and service processes, and of the routing process of customers through a network of queues, the main performance measures are also random variables (or moments thereof). Generally, costs are in a natural way associated with these performance measures. The ultimate goal of performance analysis is optimization -and that is the subject of this paper. While an enormous amount of literature has been devoted to the probabilistic analysis of queueing systems, their optimization is somewhat lagging behind. This is partly due

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Optimization of polling systems with Bernoulli schedules

Cited by 27 publications

References 28 publications

The Power-Series Algorithm for Polling Systems with Time Limits

The Power-Series Algorithm for Polling Systems with Time Limits

Tandem Queues with Impatient Customers for Blood Screening Procedures

Static Optimization of Queueing Systems

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