Approximations of the Mean Waiting Time in an M/G/s Queueing System

Boxma, OJ Onno; Cohen, J. W.; Huffels, N

doi:10.1287/opre.27.6.1115

Cited by 98 publications

(36 citation statements)

References 11 publications

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“…It is reported in Boxma et al, 1979 that this is a 'much sharper approximation, which is also particularly good in the heavy traffic case', thus making it appropriate for Rookwood hospital. The authors to this paper produce their own approximation which is 'slightly better' than that of Cosmetatos, 1976.…”

Section: Distribution Of Waiting Timementioning

confidence: 89%

Modelling activities at a neurological rehabilitation unit

Griffiths

Williams

Wood

2013

European Journal of Operational Research

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DeclarationThis work has not previously been accepted in substance for any degree and is not concurrently being submitted in candidature for any degree. Signed:Date: Statement 1This thesis is the result of my own investigations, except where otherwise stated. Other sources are acknowledged by giving explicit references. A bibliography is appended. Signed:Date: Statement 2I hereby give consent for my thesis, if accepted, to be available for photocopying and interlibrary loan, and for the title and summary to be made available to outside organisations. SummaryA queuing model is developed for the neurological rehabilitation unit at Rookwood Hospital in Cardiff. Arrivals at the queuing system are represented by patient referrals and service is represented by patient length of stay (typically five months). Since there are often delays to discharge, length of stay is partitioned into two parts: admission until date ready for discharge (modelled by Coxian phase-type distribution) and date ready for discharge until ultimate discharge (modelled by exponential distribution). The attributes of patients (such as age, gender, diagnosis etc) are taken into account since they affect these distributions. A computer program has been developed to solve this multi-server (21 bed) queuing system to produce steady-state probabilities and various performance measures.However, early on in the project it became apparent that the intensity of treatment received by patients has an effect on the time, from admission, until they are ready for discharge. That is, the service rates of the Coxian distribution are dependent on the amount of therapy received over time. This directly relates to the amount of treatment allocated in the weekly timetables. For the physiotherapy department, these take about eight hours to produce each week by hand. In order to ask the valuable what-if questions that relate to treatment intensity, it is therefore necessary to produce an automated scheduling program that replicates the manual assignment of therapy. The quality of timetables produced using this program was, in fact, considerably better than its alternative and so replaced the by-hand approach. Other benefits are more clinical time (since less employee input is required) and a convenient output of data and performance measures that are required for audit purposes.Once the model is constructed a number of relevant hypothetical scenarios are considered.Such as, what if delays to discharge are reduced by 50%? Also, through the scheduling program, the effect of changes to the composition of staff or therapy sessions can be evaluated, for example, what if the number of therapists is increased by one third? The effects of such measures are analysed by studying performance measures (such as throughput and occupancy) and the associated costs.

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Section: Distribution Of Waiting Timementioning

confidence: 89%

Modelling activities at a neurological rehabilitation unit

Griffiths

Williams

Wood

2013

European Journal of Operational Research

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“… Approximations in [17], [18], [19], [20] work well only when the number of servers is small, commonly less than 20. They are not being suitable for the IaaS cloud with more than 100 servers.…”

Section: Related Workmentioning

confidence: 99%

Modeling Active Virtual Machines on IaaS Clouds Using an <italic>M/G/m/m+K</italic> Queue

Chang

Wang

Muppala

et al. 2016

IEEE Trans. Serv. Comput.

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This paper develops a novel approximate analytical model to evaluate the performance of active virtual machines in IaaS clouds using a M/G/m/m+K queue. The proposed model, combined with the transform-based analytical approach, enables the computation of the probability distribution of the number of jobs in the system and subsequently a set of performance measures, including the mean number of jobs in the system, the mean response time, the probability of immediate service, and the blocking probability. Compared to the existing Markov models of cloud data centers, our approach can reflect the system behavior more accurately even when the service-time distribution has a large coefficient of variation (> 1.5) in a medium-sized IaaS cloud. Numerical results obtained from the proposed analytical model are verified through extensive simulations under various system parameter settings, and compared with the results from existing models.

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“…We can slightly modify (RE) to handle the M/G/N s queue. According to [17,23], if we letG be the random service time, we only need to multiply the right-hand side of (RE) by…”

Section: Assumptions and Constraintsmentioning

confidence: 99%

Optimal pricing and scheduling control of product shipping

Deng

Chen

Shen

2015

Naval Research Logistics

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Abstract:In this article, we seek to understand how a capacity-constrained seller optimally prices and schedules product shipping to customers who are heterogeneous on willingness to pay (WTP) and willingness to wait (WTW). The capacity-constrained seller does not observe each customer's WTP and WTW and knows only the aggregate distributions of WTP and WTW. The seller's problem is modeled as an M/M/N s queueing model with multiclass customers and multidimensional information screening. We contribute to the literature by providing an optimal and efficient algorithm. Furthermore, we numerically find that customers with a larger waiting cost enjoys a higher scheduling priority, but customers with higher valuation do not necessarily get a higher scheduling priority.

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Approximations of the Mean Waiting Time in an M/G/s Queueing System

Cited by 98 publications

References 11 publications

Modelling activities at a neurological rehabilitation unit

Modelling activities at a neurological rehabilitation unit

Modeling Active Virtual Machines on IaaS Clouds Using an <italic>M/G/m/m+K</italic> Queue

Optimal pricing and scheduling control of product shipping

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