Scheduling in polling systems

Wierman, Adam; Winands, E.M.M.; Boxma, Onno

doi:10.1016/j.peva.2007.06.015

Cited by 45 publications

(37 citation statements)

References 31 publications

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“…With respect to mean sojourn times, it follows from [30] that SJF is optimal. For non-anticipating scheduling disciplines, the results in [1] suggest that the optimal discipline for minimizing mean sojourn times belongs to the family of multilevel PS disciplines.…”

Section: Discussionmentioning

confidence: 99%

The impact of scheduling policies on the waiting-time distributions in polling systems

Bekker¹,

Vis²,

Dorsman

et al. 2014

Queueing Syst

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We consider polling models consisting of a single server that visits the queues in a cyclic order. In the vast majority of papers that have appeared on polling models, it is assumed that at each of the individual queues the customers are served on a First-Come-First-Served (FCFS) basis. In this paper we study polling models where the local scheduling policy is not FCFS, but instead, is varied as Last-ComeFirst-Served (LCFS), Random Order of Service (ROS), Processor Sharing (PS) and Shortest-Job-First (SJF). The service policies are assumed to be either gated or globally gated. The main result of the paper is the derivation of asymptotic closed-form expressions for the Laplace-Stieltjes transform (LST) of the scaled waiting-time and sojourn-time distributions under heavy-traffic assumptions. For FCFS service the asymptotic sojourn-time distribution is known to be of the form U Γ, where U and Γ are uniformly and gamma distributed with known parameters. In this paper we show that the asymptotic sojourntime distribution (1) for LCFS is also of the form U Γ, (2) for ROS is of the formŨ Γ whereŨ has a trapezoidal distribution, and (3) for PS and SJF is of the formŨ * Γ whereŨ * has a generalized trapezoidal distribution. These results are rather intriguing and lead to new fundamental insight in the impact of the local scheduling policy on the performance of polling models. As a by-product the heavy-traffic results suggest simple closed-form approximations for the complete waiting-time and sojourn-time distributions for stable systems with arbitrary load values. The accuracy of the approximations is evaluated by simulations.

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Section: Discussionmentioning

confidence: 99%

The impact of scheduling policies on the waiting-time distributions in polling systems

Bekker¹,

Vis²,

Dorsman

et al. 2014

Queueing Syst

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“…Moments can be obtained by differentiation or Taylor series expansion, and are also discussed in [21]. In this subsection we will only mention some results that will be used later.…”

Section: Momentsmentioning

confidence: 99%

“…Figures 1 and 2 show the mean waiting time for type 1 customers in the system without priorities, the mean waiting time for type H and type L customers, and the weighted average of these two, as a function of the threshold t. The figures show that a unique optimal threshold exists that minimises the mean weighted waiting time for customers in Q1. This value depends on the service discipline used and is discussed in [21]. In this example the optimal threshold is 1 for gated, and 1.38 for exhaustive.…”

Section: Examplementioning

confidence: 99%

“…In production environments, e.g., one could give highest priority to jobs with a service requirement below a certain threshold level. This might decrease the overall mean waiting time without having to purchase additional resources [21]. Priority polling models also can be used to study traffic intersections where conflicting traffic flows face a green light simultaneously; e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Most of these papers only provide approximations or focus on pseudo-conservation laws. In [21] exact mean waiting time results are obtained using the Mean Value Analysis (MVA) framework for polling systems, developed in [22]. The MVA framework can only be used to find the first moment of the waiting time distribution for each customer type, and the mean residual cycle time.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Two-Queue Polling Model with Two Priority Levels in the First Queue

Boon¹,

Adan²,

Boxma³

2008

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools

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In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and low priority customers. For this situation the following service disciplines are considered: gated, globally gated, and exhaustive. We study the cycle time distribution, the waiting times for each customer type, the joint queue length distribution at polling epochs, and the steady-state marginal queue length distributions for each customer type.

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On competitive analysis for polling systems

Gautam

2020

Naval Research Logistics

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Polling systems have been widely studied, however most of these studies focus on polling systems with renewal processes for arrivals and random variables for service times. There is a need driven by practical applications to study polling systems with arbitrary arrivals (not restricted to time‐varying or in batches) and revealed service time upon a job's arrival. To address that need, our work considers a polling system with generic setting and for the first time provides the worst‐case analysis for online scheduling policies in this system. We provide conditions for the existence of constant competitive ratios, and competitive lower bounds for general scheduling policies in polling systems. Our work also bridges the queueing and scheduling communities by proving the competitive ratios for several well‐studied policies in the queueing literature, such as cyclic policies with exhaustive, gated or l‐limited service disciplines for polling systems.

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Scheduling in polling systems

Cited by 45 publications

References 31 publications

The impact of scheduling policies on the waiting-time distributions in polling systems

The impact of scheduling policies on the waiting-time distributions in polling systems

A Two-Queue Polling Model with Two Priority Levels in the First Queue

On competitive analysis for polling systems

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