A polling model with an autonomous server

Haan, Roland de; Boucherie, Richard J.; Ommeren, Jan-Kees van

doi:10.1007/s11134-009-9131-z

Cited by 24 publications

(26 citation statements)

References 22 publications

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“…Under the k-limited discipline, the server continues servicing a queue until k jobs are served or the queue becomes empty, whichever occurs first. Another discipline, evaluated more recently in the literature and closely related to the time-limited discipline, is the so-called autonomousserver discipline [1,8], where the server stays at a queue for a certain period of time, even if the queue becomes empty. This discipline may also be seen as the non-exhaustive time-limited discipline.…”

Section: Introductionmentioning

confidence: 99%

Time-limited polling systems with batch arrivals and phase-type service times

et al. 2011

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Abstract. In this paper, we will develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling system. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains.

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Section: Introductionmentioning

confidence: 99%

Time-limited polling systems with batch arrivals and phase-type service times

et al. 2011

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“…Their lifetimes are random and independent of the amount of traffic offered to or transmitted over such links. To capture this phenomenon, De Haan [54] proposes the so-called pure time-limited service policy, where the server visits a queue for a random amount of time, independent of anything else in the system; note that this policy is not work conserving. The reader is referred to [53] (Chapter 1) for an overview of applications of polling models in MANETs.…”

Section: Computer-communication Systemsmentioning

confidence: 99%

Applications of polling systems

Boon¹,

Mei

Winands

2011

Surveys in Operations Research and Management Science

106

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Since the first paper on polling systems, written by Mack in 1957, a huge number of papers on this topic has been written. A typical polling system consists of a number of queues, attended by a single server. In several surveys, the most notable ones written by Takagi, detailed and comprehensive descriptions of the mathematical analysis of polling systems are provided. The goal of the present survey paper is to complement these papers by putting the emphasis on \emph{applications} of polling models. We discuss not only the capabilities, but also the limitations of polling models in representing various applications. The present survey is directed at both academicians and practitioners

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“…where G i is an operator representing the mapping between the queue lengths at the end of a visit to a queue and at the beginning of a visit to Q (i) which incorporates the effect of the switchover times and the routing of the server. We refer to [1,6] for the incorporation of Eqs. (1) and (2) into a numerical iterative framework to compute the joint queue length probabilities.…”

Section: Introductionmentioning

confidence: 99%

“…3, we analyze this general model and describe and analyze some more specified systems. Section 4 relates our work to the so-called exponentially time-limited polling models which were studied in [1,5,6,8] and their extensions in [9]. This latter is done in Sect.…”

Section: Introductionmentioning

confidence: 99%

Analysis of polling models with a self-ruling server

2019

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Polling systems are systems consisting of multiple queues served by a single server. In this paper, we analyze polling systems with a server that is self-ruling, i.e., the server can decide to leave a queue, independent of the queue length and the number of served customers, or stay longer at a queue even if there is no customer waiting in the queue. The server decides during a service whether this is the last service of the visit and to leave the queue afterward, or it is a regular service followed, possibly, by other services. The characteristics of the last service may be different from the other services. For these polling systems, we derive a relation between the joint probability generating functions of the number of customers at the start of a server visit and, respectively, at the end of a server visit. We use these key relations to derive the joint probability generating function of the number of customers and the Laplace transform of the workload in the queues at an arbitrary time. Our analysis in this paper is a generalization of several models including the exponential time-limited model with preemptive-repeat-random service, the exponential time-limited model with non-preemptive service, the gated time-limited model, the Bernoulli time-limited model, the 1-limited discipline, the binomial gated discipline, and the binomial exhaustive discipline. Finally, we apply our results on an example of a new polling discipline, called the 1 + 1 self-ruling server, with Poisson batch arrivals. For this example, we compute numerically the expected sojourn time of an arbitrary customer in the queues.

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A polling model with an autonomous server

Cited by 24 publications

References 22 publications

Time-limited polling systems with batch arrivals and phase-type service times

Time-limited polling systems with batch arrivals and phase-type service times

Applications of polling systems

Analysis of polling models with a self-ruling server

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