We consider a variation of the processor-sharing (PS) queue, inspired by freelance job websites where multiple freelancers compete for a single job. We develop fluid limit approximations for the overloaded PS-model with multiple (possibly infinitely many) service stages. Based on this approximation, we estimate what proportion of freelancers get the job they apply for. In addition, the PS model studied here is an instance of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions.
|Number of pages||27|
|Journal||Probability in the Engineering and Informational Sciences|
|Early online date||20 Dec 2017|
|Publication status||Published - Jan 2019|
- fluid limits
- freelance job websites
- Lyapunov functions