Discrete-time queues with discretionary priorities

Kim, Kilhwan; Chae, Kyung-Chul

doi:10.1016/j.ejor.2008.12.035

Cited by 27 publications

(15 citation statements)

References 19 publications

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“…For potential models and analyses, we refer the reader to Refs. [19,20]. Another interesting model arises when the priority level of a task may depend on its execution time: that is, people are inclined to give higher priority to easy (short) tasks.…”

Section: Discussionmentioning

confidence: 99%

Stochastic queueing-theory approach to human dynamics

et al. 2012

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Recently, numerous studies have shown that human dynamics cannot be described accurately by exponential laws. For instance, Barabási [Nature (London) 435, 207 (2005)] demonstrates that waiting times of tasks to be performed by a human are more suitably modeled by power laws. He presumes that these power laws are caused by a priority selection mechanism among the tasks. Priority models are well-developed in queueing theory (e.g., for telecommunication applications), and this paper demonstrates the (quasi-)immediate applicability of such a stochastic priority model to human dynamics. By calculating generating functions and by studying them in their dominant singularity, we prove that nonexponential tails result naturally. Contrary to popular belief, however, these are not necessarily triggered by the priority selection mechanism.

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Section: Discussionmentioning

confidence: 99%

Stochastic queueing-theory approach to human dynamics

et al. 2012

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“…In some discrete-time multi-class queueing models correlation exists between the numbers of arrivals of different classes in the same slot, but the numbers of arrivals of each class during consecutive slots are independent and identically distributed [15,20,19,24]. Hence, in [15,20,19,24], correlation is defined slotbased, whereas our definition is customer-based, i.e., we let the classes of consecutive customers in the arrival process be dependent, even across slot boundaries.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, in [15,20,19,24], correlation is defined slotbased, whereas our definition is customer-based, i.e., we let the classes of consecutive customers in the arrival process be dependent, even across slot boundaries. As a result, class clustering is not adequately modelled in [15,20,19,24], whereas the opposite holds in this paper. We believe that the arrival process considered in this paper may be more suitable for particular applications, such as in manufacturing systems or in the scheduling of computing jobs.…”

Section: Introductionmentioning

confidence: 99%

Impact of class clustering in a multiclass FCFS queue with order-dependent service times

Réveil

Claeys

Maertens

et al. 2014

Computers & Operations Research

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In multi-class queueing systems, customers of different classes can enter the system. When studying such systems, it is traditionally assumed that the different classes of customers occur randomly and independently in the arrival stream of customers in the system. This is often in contrast to the actual situation. Therefore, we study a multi-class system with so-called class clustering in the customer arrival stream, i.e., (Markovian) correlation occurs in the classes of consecutive customers. The system under investigation consists of one server that is able to serve two classes of customers. In addition, the service-time distribution of a customer depends on the equality or non-equality of its class with the class of the previous customer. This latter feature occurs frequently in practice. For instance, execution of the same task again can lead to both faster or slower processing times. The first case can occur when the execution of a different task entails resetting a machine, or loading new data, et cetera. The opposite situation appears, for instance, when execution of the same task requires postprocessing (such as cooling down or reinitialisation of a machine). We deduce the probability generating function (pgf) of the system content, from which we can extract various performance measures, among which the mean values of the system content and the customer delay. We demonstrate that class clustering has a tremendous impact on the system performance, which highlights the necessity to include it in the performance assessment of any system in which it occurs.

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“…Priority queueing was, for instance, studied in [3,6,13,15,18,19]. Whereas, GPS was analyzed in [7,8,10,11,17,21].…”

Section: Introductionmentioning

confidence: 99%

On the Influence of High Priority Customers on a Generalized Processor Sharing Queue

Vanlerberghe

Walraevens

Maertens

et al. 2015

Analytical and Stochastic Modelling Techniques and Applications

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Abstract. In this paper, we study a hybrid scheduling mechanism in discrete-time. This mechanism combines the well-known Generalized Processor Sharing (GPS) scheduling with strict priority. We assume three customer classes with one class having strict priority over the other classes, whereby each customer requires a single slot of service. The latter share the remaining bandwith according to GPS. This kind of scheduling is used in practice for the scheduling of jobs on a processor and in Quality of Service modules of telecommunication network devices. First, we derive a functional equation of the joint probability generating function of the queue contents. To explicitly solve the functional equation, we introduce a power series in the weight parameter of GPS. Subsequently, an iterative procedure is presented to calculate consecutive coefficients of the power series. Lastly, the approximation resulting from a truncation of the power series is verified with simulation results. We also propose rational approximations. We argue that the approximation performs well and is extremely suited to study these systems and their sensitivity in their parameters (scheduling weights, arrival rates, loads ...). This method provides a fast way to observe the behaviour of such type of systems avoiding time-consuming simulations.

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Discrete-time queues with discretionary priorities

Cited by 27 publications

References 19 publications

Stochastic queueing-theory approach to human dynamics

Stochastic queueing-theory approach to human dynamics

Impact of class clustering in a multiclass FCFS queue with order-dependent service times

On the Influence of High Priority Customers on a Generalized Processor Sharing Queue

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