Waiting Times When Service Times are Stable Laws: Tamed and Wild.
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH
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Modern telecommunication systems must accommodate tasks or messages of extremely variable time duration. Understanding of that variability, and appropriate stochastic models are needed to describe the resulting queues or buffer contents. To this end, consider an MG1 queue with service times having a positive stable law distribution. Such service times are extremely long and short tailed, and thus do not have finite first and second moments classical queue-theoretic results do not apply directly. Here we suggest two procedures for initially taming stable laws, i.e. so that they possess finite mean and variance. We apply the tamed laws to calculate certain familiar queuing properties, such as the transform of the stationary distribution of the long-run virtual waiting time and mean thereof. We show that, by norming or scaling traffic intensity, waiting times, and other measures of congestion, we can obtain bona fide limiting distributions as the underlying service times become untamed, i.e. return to the wild. Simulations support the theory.
- Statistics and Probability
- Operations Research
- Test Facilities, Equipment and Methods
- Radio Communications
- Non-Radio Communications