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Predicting Response Times in Processor-Sharing Queues
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ward, Amy R. Whitt, Ward |
| Copyright Year | 2000 |
| Abstract | We investigate the possibility of reliably predicting response times in real time (e.g., at the time a job arrives) in the M/G/1 processor-sharing queue. The proposed prediction is the conditional mean given current state information. We consider several forms of state information, always including the remaining service requirement of the job of interest and the number of other jobs in the system. We consider three cases for the other jobs’ service requirements: First, we assume that all the remaining service requirements are known; second, we assume that the amount of completed work of each customer in service is known; and third, we assume that nothing more is known. We thus are able to study the value of different kinds of information. We calculate the conditional mean and variance of the response time, given the state information, by numerically inverting Laplace transforms. We evaluate the reliability by looking at the ratio of the standard deviation to the mean. This ratio tends to decrease as the remaining service requirements or the number of jobs in service increase. We establish this property theoretically by proving laws of large numbers and central limit theorem refinements. |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/fic/028/01 |
| Alternate Webpage(s) | http://www.columbia.edu/~ww2040/response.pdf |
| Alternate Webpage(s) | http://www.ieor.columbia.edu/~ww2040/response.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/fic%2F028%2F01 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
