The impact of reneging in processor sharing queues

Gromoll, H. Christian; Robert, Ph.; Zwart, Bert; Bakker, R.F.

doi:10.1145/1140277.1140289

Cited by 12 publications

(15 citation statements)

References 23 publications

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“…In order to improve the bounds for the fraction of fully charged EVs, we next develop a fluid approximation for the number of uncharged EVs in the parking lot. The mathematical results here are closely related to results on processor-sharing queues with impatience [21]. However, the model here is more complicated as there is a limited number of spaces in the system and fully charged cars may not leave immediately as they are still parked.…”

Section: Introductionmentioning

confidence: 62%

“…Here, we study a fluid model, which is a deterministic model that can be thought of as a formal law of large numbers approximation under appropriate scaling. We develop a fluid approximation for finite K, following a similar approach as in [21]. The main differences here are the finitely many servers in the system and that the state space consists of two regions:…”

Section: Fluid Approximationmentioning

confidence: 99%

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Bounds and limit theorems for a layered queueing model in electric vehicle charging

2019

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The rise of electric vehicles (EVs) is unstoppable due to factors such as the decreasing cost of batteries and various policy decisions. These vehicles need to be charged and will therefore cause congestion in local distribution grids in the future. Motivated by this, we consider a charging station with finitely many parking spaces, in which electric vehicles arrive in order to get charged. An EV has a random parking time and a random charging time. Both the charging rate per vehicle and the charging rate possible for the station are assumed to be limited. Thus, the charging rate of uncharged EVs depends on the number of cars charging simultaneously. This model leads to a layered queueing network in which parking spaces with EV chargers have a dual role, of a server (to cars) and customers (to the grid). We are interested in the performance of the aforementioned model, focusing on the fraction of vehicles that get fully charged. To do so, we develop several bounds and asymptotic (fluid and diffusion) approximations for the vector process, which describes the total number of EVs and the number of not fully charged EVs in the charging station, and we compare these bounds and approximations with numerical outcomes.

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Section: Introductionmentioning

confidence: 62%

Section: Fluid Approximationmentioning

confidence: 99%

Bounds and limit theorems for a layered queueing model in electric vehicle charging

2019

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“…Unfortunately, the approach is analytically intractable in general. ( Gromoll, Zwart, Robert, and Bakker (2006) manage to get tractable steady state behavior by approximating the system using a fluid model. However, their results are highly complex, which are not suitable for examining the aforementioned tradeoff analytically.)…”

Section: Customer Abandonmentmentioning

confidence: 99%

A queueing model for managing small projects under uncertainties

Bai

Tang

2016

European Journal of Operational Research

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a b s t r a c tWe consider a situation in which a home improvement project contractor has a team of regular crew members who receive compensation even when they are idle. Because both projects arrivals and the completion time of each project are uncertain, the contractor needs to manage the utilization of his crews carefully. One common approach adopted by many home improvement contractors is to accept multiple projects to keep his crew members busy working on projects to generate positive cash flows. However, this approach has a major drawback because it causes "intentional" (or foreseeable) project delays. Intentional project delays can inflict explicit and implicit costs on the contractor when frustrating customers abandon their projects and/or file complaints or lawsuits. In this paper, we present a queueing model to capture uncertain customer (or project) arrivals and departures, along with the possibility of customer abandonment. Also, associated with each admission policy (i.e., the maximum number of projects that the contractor will accept), we model the underlying tradeoff between accepting too many projects (that can increase customer dissatisfaction) and accepting too few projects (that can reduce crew utilization). We examine this tradeoff analytically so as to determine the optimal admission policy and the optimal number of crew members. We further apply our model to analyze other issues including worker productivity and project pricing. Finally, our model can be extended to allow for multiple classes of projects with different types of crew members.

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“…An interpretation of the fixed point equation (3.2) is given and used to analyze the total number of jobs in the system and to estimate the fraction of jobs that renege. The impact of the variability of the service times and of the lead times and other properties of this queue are extensively investigated in Gromoll et al [11].…”

Section: Introductionmentioning

confidence: 99%

Fluid Limits for Processor-Sharing Queues with Impatience

2008

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Abstract. We investigate a processor sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue, or renege, before completing service. The random time representing a job's patience has a general distribution and may be dependent on its initial service time requirement. A scaling procedure that gives rise to a fluid model with nontrivial yet tractable steady state behavior is presented. This fluid model model captures many essential features of the underlying stochastic model, and it is used to analyze the impact of impatience in processor sharing queues.

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The impact of reneging in processor sharing queues

Cited by 12 publications

References 23 publications

Bounds and limit theorems for a layered queueing model in electric vehicle charging

Bounds and limit theorems for a layered queueing model in electric vehicle charging

A queueing model for managing small projects under uncertainties

Fluid Limits for Processor-Sharing Queues with Impatience

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