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Large deviations of sojourn times in processor sharing queues. (English) Zbl 1094.60062
The paper considers a GI/G/1 queue operating under the processor sharing (PS) service discipline. The GI/G/1 PS queue is positive recurrent when the load $$\rho < 1$$, which is assumed throughout the paper. Some specific assumptions are imposed on the distribution of the service times. The paper considers a customer entering the system in steady state. Let $$V$$ be the sojourn time of this tagged customer. The main focus is on the asymptotic behavior of $$P\{ V > x\}$$ as $$x \to \infty$$, under light-tailed service times. Proposition 1 says that $$\limsup_{x \to \infty } \frac{1} {x}\log P\{ V > x\} \leqslant - \gamma$$, where $$\gamma$$ is a constant given in terms of the main characteristics of the system. Under additional assumption, Theorem 3.1 shows that $$\lim_{x \to \infty } \frac{1} {x}\log P\{ V > x\} = - \gamma$$. The results are compared to a number of other service disciplines.

##### MSC:
 60K25 Queueing theory (aspects of probability theory)
##### Keywords:
logarithmic estimates
Full Text:
##### References:
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