Sojourn times in polling systems with various service disciplines

Boxma, Onno; Bruin, J Josine; Fralix, Brian

doi:10.1016/j.peva.2009.05.004

Cited by 39 publications

(55 citation statements)

References 16 publications

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“…Let pgg, pg = 1 − pgg respectively represent the probability that an arrival is a globally gated user and a gated user. Let bg(q), b (2) g (q) represent the conditional first and second moments of the service time given that the arrival is at point q and further given that the arrival is a gated user. Let bgg(q), b (2) gg (q) represent same quantities for a globally gated user.…”

Section: Continuous Polling Systemsmentioning

confidence: 99%

“…Let bg(q), b (2) g (q) represent the conditional first and second moments of the service time given that the arrival is at point q and further given that the arrival is a gated user. Let bgg(q), b (2) gg (q) represent same quantities for a globally gated user. Letb := E[b(Q)], bgg := E[bgg(Q)] andbg := E[bg(Q)] (expectations are with respect to 1 P Q ) represent the unconditional moments.…”

Section: Continuous Polling Systemsmentioning

confidence: 99%

“…Note thatb =bgpg +bggpgg. Similarly define the second moments,b (2) g The bar of the same variable, likebg represent the average w.r.t. to the position distribution P Q , i.e.,bg = E[bg(Q)].…”

Section: Continuous Polling Systemsmentioning

confidence: 99%

“…Similarly variables like τ (2) ,τ (2) etc. are functions on [0, |C|] × [0, |C|] while τ (2) (q, q ′ ) represents the function value at (q, q ′ ). Let q ∧ |C| represent the minimum value, min{q, |C|}.…”

Section: Continuous Polling Systemsmentioning

confidence: 99%

See 3 more Smart Citations

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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Section: Continuous Polling Systemsmentioning

confidence: 99%

Section: Continuous Polling Systemsmentioning

confidence: 99%

Section: Continuous Polling Systemsmentioning

confidence: 99%

Section: Continuous Polling Systemsmentioning

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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“…H. Takagi (1986), O. Boxma et al (2009)). Also, in a loop system, in the sense explained in Konheim et al (1972) (see Fig.1.1) where the server takes a tour of N stations each slot and its capacity is unbounded, then the main station behaves as described in our proposed slot-bound priority discipline; Konheim analyzed the N input stations instead of the main station.…”

Section: Introductionmentioning

confidence: 99%

Delay analysis of a discrete-time multiclass slot-bound priority system

2011

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This paper introduces a new priority mechanism in discretetime queueing systems that compromises between first-come-first-served (FCFS) and head-of-line (HoL) priority. In this scheduling discipline -which we dubbed slot-bound priority -customers of different priority classes entering the system during the same time-slot are served in order of their respective priority class. Customers entering during different slots are served on a FCFS basis. In this paper we study the delay in an N -class discretetime queueing system under slot-bound priority. General independent arrivals and class-specific general service time distributions are assumed. Expressions for the probability generating function of the delay of a random type-j customer are derived, from which the respective moments are easily obtained. The tail behaviour of these distributions is analyzed as well, and some numerical examples show the effect slot-bound priority can have on the performance measures.

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An analytic model for enhancing IEEE 802.11 point coordination function media access control protocol

Liu

Zhao

Zhou

2011

Eur. Trans. Telecomms.

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The design of media access control (MAC) protocol that can efficiently support the real-time applications in Wireless Local Area Networks (WLANs) is a challenging task, it requires that the MAC layer provide strict delay guarantees for sensitive traffic, the Point Coordination Function (PCF) with Round Robin (RR) polling scheme has been included in IEEE 802.11 MAC protocol to achieve this objective. However, the RR scheme seems difficult to guarantee QoS and satisfy the low delay of the sensitive traffic, yet it can hardly differentiate from priority service for the key station. Thus we utilize an analytic model with two-level-polling mechanism to enhance the RR scheme, and the comparison results show us that the efficiency as well as impartiality of proposed scheme is better than that of the RR scheme.

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Sojourn times in polling systems with various service disciplines

Cited by 39 publications

References 16 publications

Continuous polling models and application to ferry assisted WLAN

Continuous polling models and application to ferry assisted WLAN

Delay analysis of a discrete-time multiclass slot-bound priority system

An analytic model for enhancing IEEE 802.11 point coordination function media access control protocol

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