Light-Traffic Analysis for Queues with Spatially Distributed Arrivals

Kroese, Dirk P.; Schmidt, Volker

doi:10.1287/moor.21.1.135

Cited by 26 publications

(25 citation statements)

References 40 publications

(63 reference statements)

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“…The first two (Palm) stationary moments E 0 [C σ n (q)] and E 0 (C σ n (q)) 2 of C σ n defined in (15) are:…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…The cycle time C σ n defined in (15) can be rewritten in the following fashion and via this expression we obtain the convergence of the required second moments (note C σ n (0) = C σ n−1 (|C|) almost surely by continuity arguments):…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Continuous polling were first introduced by Fuhrmann and Cooper [11], further studied, explored by Coffman and Gilbert [7,8] and Kroese and Schmidt [16,[13][14][15] in a series of works. Stability of such polling systems is discussed in [21,12,20,18].…”

Section: Introductionmentioning

confidence: 99%

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Continuous polling models and application to ferry assisted WLAN

Kavitha

Altman

2011

Ann Oper Res

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In this paper we focus on a class of polling systems encountered while modeling the ferry based wireless local area network (FWLAN). A moving ferry, while walking in a predetermined cyclic path, communicates with the static nodes (or users) of the network via a wireless link. The ferry is assumed to stop and communicate with a node that has a packet to send or to receive, when it is closest to that node. The location distribution of the node to which or from which a packet arrives is assumed to have a support of positive Lebesgue measure. These features imply that polling models with finite number of queues cannot be used to model the system. We study in this paper the continuous polling systems with service disciplines that model the use of the FWLAN (and that are more complex than the classical exhaustive or gated services). Our approach is based on discretization of the continuous polling model. We propose a special way of discretizing the continuous system such that: 1) the known Pseudo conservation laws can be applied to obtain the stationary expected workload of the discrete systems; 2) the limit, of these 'discretized' expected workloads, equals the stationary expected workload of the continuous system. Our results rely heavily on fixed point analysis of infinite dimensional operators.

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“…The first two (Palm) stationary moments E 0 [C σ n (q)] and E 0 (C σ n (q)) 2 of C σ n defined in (15) are:…”

Section: Proof Of Theoremmentioning

confidence: 99%

Section: Proof Of Theoremmentioning

confidence: 99%

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Continuous polling models and application to ferry assisted WLAN

Kavitha

Altman

2011

Ann Oper Res

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“…This result will be used in the next subsection. In Palm stationary regime, τ σ n , c σ n are same for all n, the common values are represented by τ σ * , c σ * and hence we get a fixed point operator, F, to represent equation (10).…”

Section: First Momentsmentioning

confidence: 99%

Continuous Polling with Rerouting and Applications to Ferry Assisted Wireless LANs

Kavitha¹

2011

Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools

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In almost all studied continuous polling systems, the user leaves the system after his service is completed. There are interesting applications, in which the users demand a second service (or more). For example, in a ferry assisted wireless network, for every local data transfer the ferry has to collect the data from the source and then deliver the same to the sink. This type of application can be modeled by polling systems with rerouting. In polling systems with arrivals on a continuum (on a circle), a moving server attends the users as and when it encounters one. When rerouting is supported, after the service is completed, the users can reroute to a different point in the same circle to await another service. We obtain the performance of such a system under quite general conditions, via discretization approach. The results are applied to study a ferry assisted wireless local area network. Our results rely heavily on fixed point analysis of infinite dimensional operators.

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“…Other papers where power-series expansions with respect to λ, arrival intensity, have been used in approximating probability characteristics of stochastic models driven by a Poisson process are Hooghiemstra et al (1988), Rieman and Simon (1988), Blanc (1991), Simon (1993) and Kroese and Schmidt (1995).…”

Section: Introductionmentioning

confidence: 99%

Practical approximations for multivariate characteristics of risk processes

Usabel

1999

Insurance: Mathematics and Economics

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The applicability aspects of power series expansions with respect to the arrival intensity, based on recursive algorithms, when approximating multivariate finit time ruin probabilities will be substantially enhanced using double Laplace transforms.We will also prove that power series methodology may be considered as an outstanding complement to diffusion approximations when the time horizon considered is not large.

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Light-Traffic Analysis for Queues with Spatially Distributed Arrivals

Cited by 26 publications

References 40 publications

Continuous polling models and application to ferry assisted WLAN

Continuous polling models and application to ferry assisted WLAN

Continuous Polling with Rerouting and Applications to Ferry Assisted Wireless LANs

Practical approximations for multivariate characteristics of risk processes

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