## On Certain Priority Queues |

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alternating priority model Appendix arrivals in unit Avi-Itzhak becomes empty convergence customer arriving customers in unit cycle of tasks distribution function distribution of busy Distribution of Queue Distribution of Virtual equation expected value given HELLY-BRAY THEOREM Hence joint distribution Kronecker delta Laplace transform Laplace-Stieltjes transform lemma length and virtual limiting distribution m|g|1 queue Math n-th task non-sero switching rule non-zero switching obtained by assuming Opns performing a 2-task Poisson input Poisson process PRIORITY QUEUES Proof q.xun ux queue length random variables respectively Semi-Markov Process Semi-Markov sequence sequence of random server is performing server is serving service completion service in unit service started service time distribution service units single server started in unit Stat Stochastic Processes Substitution Takacs tandem queue term is obtained Theorem 1.3 Theorem Theorem TL(t total service Transition Probabilities units alternately virtual waiting waiting in unit