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Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates. (English) Zbl 1117.60083
For a processor sharing queueing system with time varying arrival and service rate the transient sojourn time distribution of a virtual customer is approximated by fluid limits and diffusion limits. A virtual customer observes the system over the time which can be termed a virtual processing time for him under the observed state of the other customers present (contrary to the concept of tagged customers who influences the other customers as well). The asymptotics are derived by accelerating the arrival and service rates in parallel. The asymptotic results for the sojourn times (their distributional approximations) are compared with simulations, especially concerning first and second moments.

##### MSC:
 60K25 Queueing theory 68M20 Performance evaluation of computer systems; queueing; scheduling 90B22 Queues and service (optimization)
##### References:
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