G/G/1 queue
In queueing theory, a discipline within the mathematical theory of probability, the G/G/1 queue represents the queue length in a system with a single server where interarrival times have a general (meaning arbitrary) distribution and service times have a (different) general distribution.[1] The evolution of the queue can be described by the Lindley equation.[2]
The system is described in Kendall's notation where the G denotes a general distribution for both interarrival times and service times and the 1 that the model has a single server.[3][4] Different interarrival and service times are considered to be independent, and sometimes the model is denoted GI/GI/1 to emphasise this.
Waiting time
Kingman's formula gives an approximation for the mean waiting time in a G/G/1 queue.[5] Lindley's integral equation is a relationship satisfied by the stationary waiting time distribution which can be solved using the Wiener–Hopf method.[6]
Multiple servers
Few results are known for the general G/G/k model as it generalises the M/G/k queue for which few metrics are known. Bounds can be computed using mean value analysis techniques, adapting results from the M/M/s queue model, using heavy traffic approximations, empirical results[7]: 189 or approximating distributions by phase type distributions and then using matrix analytic methods to solve the approximate systems.[7]: 201
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References
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|doi=10.1017/S0305004100036094instead. - ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/978-3-642-80838-8_5, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1007/978-3-642-80838-8_5instead. - ^ a b Gautam, Natarajan (2012). Analysis of Queues: Methods and Applications. CRC Press. ISBN 9781439806586.
| Single queueing nodes | |
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| Arrival processes | |
| Queueing networks | |
| Service policies | |
| Key concepts | |
| Limit theorems | |
| Extensions | |
| Information systems | |
