A STATE-DEPENDENT POLLING MODEL WITH <i>k</i>-LIMITED SERVICE

Winands, E.M.M.; Adan, I.J.B.F.; Houtum, Geert‐Jan van; Down, Douglas G.

doi:10.1017/s0269964809000217

Cited by 25 publications

(18 citation statements)

References 31 publications

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“…For two-queue systems where both queues are served according to the 1-limited discipline, the problem of finding the queue length distribution can be shown to translate into a boundary value problem [6,7,11,13]. For general k, an exact evaluation for the queue-length distribution is known in two-queue exhaustive/k-limited systems (see [21,24,25,28]). The situation where both queues follow the k-limited discipline has not been solved yet.…”

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confidence: 99%

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Boon¹,

Winands²

2014

Prob. Eng. Inf. Sci.

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In this paper, we study a two-queue polling model with zero switchover times and klimited service (serve at most k i customers during one visit period to queue i, i = 1, 2) in each queue. The arrival processes at the two queues are Poisson, and the service times are exponentially distributed. By increasing the arrival intensities until one of the queues becomes critically loaded, we derive exact heavy-traffic limits for the joint queue-length distribution using a singular-perturbation technique. It turns out that the number of customers in the stable queue has the same distribution as the number of customers in a vacation system with Erlang-k 2 distributed vacations. The queue-length distribution of the critically loaded queue, after applying an appropriate scaling, is exponentially distributed. Finally, we show that the two queue-length processes are independent in heavy traffic.

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confidence: 99%

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Boon¹,

Winands²

2014

Prob. Eng. Inf. Sci.

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“…Nearly all of the existing literature on polling systems makes the assumption of state-independent switch-overs, i.e., switch-overs are assumed to be independent of the current state of the system. Notable exceptions are the recent studies of Altman et al [3], Günalay and Gupta [86], Gupta and Srinivasan [87], Singh and Srinivasan [144] and Winands et al [177]. The choice of modeling state-independent setups is generally not motivated by an application but by the tractability of the resulting analysis.…”

Section: Typical Featuresmentioning

confidence: 99%

Applications of polling systems

Boon¹,

Mei

Winands

2011

Surveys in Operations Research and Management Science

102

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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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“…The upstream transmission process of each ONU can be described by a vacation queuing system, in which each TW of the ONU is considered as a busy period while the time between two successive TWs of the ONU is treated as a vacation period. In general, the modeling of a vacation queuing system with limited service discipline is quite difficult [17]. In the gatedlimited service EPON, the number of packets that an ONU can transmit in a TW is limited by the maximum TW size.…”

Section: Introductionmentioning

confidence: 99%

Optimum Transmission Window for EPONs With Limited Service

Huang

Lee

2019

IEEE Access

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This paper studies the Ethernet Passive Optical Network (EPON) with gated-limited service. The transmission window (TW) is limited in this system to guaranteeing a bounded delay experienced by disciplined users, and to constrain malicious users from monopolizing the transmission channel. Thus, selecting an appropriate TW size is critical to the performance of EPON with gated-limited service discipline. To investigate the impact of TW size on packet delay, we derive a generalized mean waiting time formula for M/G/1 queue with vacation times and gated-limited service discipline. A distinguished feature of this model is that there are two queues in the buffer of each optical network unit (ONU): one queue is inside the gate and the other one is outside the gate. Furthermore, based on the Chernoff bound of queue length, we provide a simple rule to determine an optimum TW size for gated-limited service EPONs. Analytic results reported in this paper are all verified by simulations.Index Terms-Ethernet Passive Optical Network (EPON), Gated-Limited Service, M/G/1.

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A STATE-DEPENDENT POLLING MODEL WITH k-LIMITED SERVICE

Cited by 25 publications

References 31 publications

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Applications of polling systems

Optimum Transmission Window for EPONs With Limited Service

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