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- W2313303987 abstract "In this part we extend and particularise results developed by the author in Part I (pp. 349–375) for a class of queueing systems which can be formulated as Markov renewal processes. We examine those models where the basic transition consists of only two types: ‘arrivals' and ‘departures'. The ‘arrival lobby' and ‘departure lobby' queue-length processes are shown, using the results of Part I to be Markov renewal. Whereas the initial study focused attention on the behaviour of the embedded discrete-time Markov chains, in this paper we examine, in detail, the embedded continuous-time semi-Markov processes. The limiting distributions of the queue-length processes in both continuous and discrete time are derived and interrelationships between them are examined in the case of continuous-time birth–death queues including the M/M /1/ M and M/M /1 variants. Results for discrete-time birth–death queues are also derived." @default.
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- W2313303987 date "1983-06-01" @default.
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- W2313303987 title "Filtering of Markov renewal queues, II: Birth-death queues" @default.
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- W2313303987 doi "https://doi.org/10.1017/s0001867800021224" @default.
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