Journal Article10.1007/BF02411477
On inference concerning time-dependent queue performance: the M/G/1 example
D. P. Gaver,P. A. Jacobs +1 more
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TL;DR: This paper proposes easily-computed approximations to the finite-time expected waiting time for anM/G/1 system starting from an empty state and can be applied to the variety of queueing models that are close siblings of M/g/1.
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Abstract: This paper proposes easily-computed approximations to the finite-time expected waiting time for anM/G/1 system starting from an empty state. Both unsaturated (ρ 1) conditions are considered. Numerical evidence is presented to indicate that the quality of the approximations is usefully good, especially when ease of computation is an issue. Further, the methodology is adapted to assess expected waiting time when inference must be made from a random sample of service times, and the decision is made to do so nonparametrically, i.e., without fitting a specific function. The results appear reasonable and potentially useful, and are not burdensome to obtain. The methodology investigated can also be applied to the variety of queueing models that are close siblings ofM/G/1: priority and breakdowns and “vacations” being examples. Of course other approximating and inferential options remain to be investigated.
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Citations
Fundamentals of Queueing Theory
Rodney Coleman
- 01 May 1975
TL;DR: The Fundamentals of Queueing Theory, Fourth Edition as discussed by the authors provides a comprehensive overview of simple and more advanced queuing models, with a self-contained presentation of key concepts and formulae.
2.6K
Bayesian inference in Markovian queues
TL;DR: Joint posterior distribution of the arrival rate and the individual service rate is obtained from a sample consisting of observations of the interarrival process and complete service times.
55
Parameter estimation for partially observed queues
TL;DR: In this paper, the authors considered a FIFO queue with deterministic service times and two independent arrival streams of observed and unobserved packets, and formulated a maximum likelihood estimation of /spl lambda/ based on the arrival times and waiting times of k observed packets.
The average virtual waiting time as a measure of performance
TL;DR: The M/G/1 queue is considered and the estimation and limiting behaviour of the index of exponential decay of the average virtual waiting time is provided.
3
•Posted Content
Parameter and State Estimation in Queues and Related Stochastic Models: A Bibliography.
TL;DR: This is an annotated bibliography on estimation and inference results for queues and related stochastic models, allowing for researchers and practitioners to explore the various types of results that exist.
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Bradley Efron,Robert Tibshirani +1 more
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