Analytic Computation Schemes for the Discrete-Time Bulk Service Queue

Janssen, Ajem Guido; Leeuwaarden, van Jsh Johan

doi:10.1007/s11134-005-0402-z

Cited by 51 publications

(40 citation statements)

References 22 publications

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“…Alfa (1982) and Singh (1971), as well as its computational aspects, e.g. Bruneel (1993) and Janssen and Leeuwaarden (2005), have been investigated. In fact, quoting from , "The work done on the discrete bulk service queue runs to a large extent parallel to the maturing of queueing theory as a branch of mathematics".…”

Section: Literature Reviewmentioning

confidence: 99%

Appointment Capacity Planning in Specialty Clinics: A Queueing Approach

Izady

2015

Operations Research

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Specialty clinics provide specialized care for patients referred by primary care physicians, emergency departments, or other specialists. Urgent patients must often be seen on the referral day, while non-urgent referrals are typically booked an appointment for the future. To deliver a balanced performance, the clinics must know how much 'appointment capacity' is needed for achieving a reasonably quick access for non-urgent patients. To help identify the capacity that leads to the desired performance, we model the dynamics of appointment backlog as novel discrete-time bulk service queues, and develop numerical methods for efficient computation of corresponding performance metrics. Realistic features such as arbitrary referral and clinic appointment cancellation distributions, delay-dependent no-show behaviour and rescheduling of no-shows are explicitly captured in our models. The accuracy of the models in predicting performance as well as their usefulness in appointment capacity planning is demonstrated using real data. We also show the application of our models in capacity planning in clinics where patient panel size, rather than appointment capacity, is the major decision variable. Permanent repository link:

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Section: Literature Reviewmentioning

confidence: 99%

Appointment Capacity Planning in Specialty Clinics: A Queueing Approach

Izady

2015

Operations Research

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“…[1,2]), and larger than 1 in multiserver models (e.g. [3,4]). Furthermore, service capacity is expressed in number of customers that can be served simultaneously.…”

Section: Introductionmentioning

confidence: 99%

The Discrete-Time Queue with Geometrically Distributed Service Capacities Revisited

Walraevens

Bruneel

Claeys

et al. 2013

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. We analyze a discrete-time queue with variable service capacity, such that the total amount of work that can be performed during each time slot is a stochastic variable that is geometrically distributed. We study the buffer occupancy by constructing an analogous model with fixed service capacity. In contrast with classical discrete-time queueing models, however, the service times in the fixed-capacity model can take the value zero with positive probability (service times are non-negative). We study the late arrival models with immediate and delayed access, the first model being the most natural model for a system with fixed capacity and non-negative service times and the second model the more practically relevant model for the variable-capacity model.

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“…However, the focus was mainly put on the number of waiting customers (see e.g. [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]), whereas the waiting time of customers, also called customer delay, has attracted very few attention, especially in the case of batch arrivals. In [17], [18] and [19] we have computed the probability generating function (PGF) of the customer delay in distinct discrete-time queueing models with batch arrivals and batch service.…”

Section: Introductionmentioning

confidence: 99%

Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

Claeys

Steyaert

Walraevens

et al. 2013

Computers & Operations Research

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We deduce approximations for the tail probabilities of the customer delay in a discrete-time queueing model with batch arrivals and batch service. As in telecommunications systems transmission times are dependent on packet sizes, we consider a general dependency between the service time of a batch and the number of customers within it. The model also incorporates a timer mechanism to avoid excessive delays stemming from the requirement that a service can only be initiated when the number of present customers reaches or exceeds a service threshold. The service discipline is first-come, first-served (FCFS). We demonstrate in detail that our approximations are very useful for the purpose of assessing the order of magnitude of the tail probabilities of the customer delay, except in some special cases that we discuss extensively. We also illustrate that neglecting batch-size dependent service times or a timer mechanism can lead to a devastating assessment of the tail probabilities of the customer delay, which highlights the necessity to include these features in the model. The results from this paper can, for instance, be applied to assess the quality of service (QoS) of Voice over IP (VoIP) conversations, which is typically expressed in terms of the order of magnitude of the probability of Computers & Operations Research May 1, 2013 packet loss due to excessive delays. Preprint submitted to

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Analytic Computation Schemes for the Discrete-Time Bulk Service Queue

Cited by 51 publications

References 22 publications

Appointment Capacity Planning in Specialty Clinics: A Queueing Approach

Appointment Capacity Planning in Specialty Clinics: A Queueing Approach

The Discrete-Time Queue with Geometrically Distributed Service Capacities Revisited

Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

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