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The paper considers a queueing system with limited processor sharing. No morethan n jobs may be served simultaneously. This system may be used for modelingbandwidth sharing in wireless communication systems and processes of service incomputer networks. If there are n jobs in the considered queueing system and anew job arrives, then the arriving job is lost or the service of a job isinterrupted and this job is lost. We study two rules to choose the job to belost. In accordance with one of these rules, the job with the shortestremaining length is lost. Relations are obtained between the stateprobabilities of considered system and the state probabilities of thecorresponding unlimited processor sharing system. These relations allow tocompute the state probabilities for considered system if the stateprobabilities for the unlimited processor sharing system are known. In the caseof Poisson arrival process, the probability that the server capacity isexhausted is equal to the probability that a job is lost. We have obtained anexplicit formulas for the stationary state probabilities and the lossprobability for this case. These probabilities are invariant under the joblength distribution under the condition that the average value of the length isfixed.

Queueing Systems with Some Versions of Limited Processor Sharing Discipline