FLUID LIMIT OF A PS-QUEUE WITH MULTISTAGE SERVICE. Issue 1 (20th December 2017)

• Record Type: Journal Article
• Authors: Frolkova, Maria; Zwart, Bert
• Is Part Of: Probability in the engineering and informational sciences. Volume 33:Issue 1(2019)
• Page Start: 1
• Page End: 27
• Publication Date: 2017-12-20
• Subjects: fluid limits, -- freelance job websites, -- Lyapunov functions, -- processor-sharing, -- routing; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964817000456
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract : 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.