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2 results

  • On the reversible counters system of Lampard

  • R. M. Phatarfod
  • Journal:
    Journal of Applied Probability / Volume 12 / Issue 3 / September 1975
    Published online by Cambridge University Press:
    14 July 2016, pp. 639-646
    Print publication:
    September 1975

  • The paper considers some properties of the reversible counters system of Lampard [1]. Lampard considers the properties of the process imbedded at the epochs when the counter receiving pulses from the ‘down’ process reaches zero. We consider here the time-dependent and stationary distributions of the original process. Their derivation gives rise to some interesting functional equations, besides being useful for studying queues with Markov-dependent inter-arrival or service times.

  • Note on the reversible counters system of Lampard

  • R. M. Phatarfod
  • Journal:
    Journal of Applied Probability / Volume 11 / Issue 3 / September 1974
    Published online by Cambridge University Press:
    14 July 2016, pp. 624-628
    Print publication:
    September 1974

  • The paper considers an extension to the reversible counters system of Lampard [1]. In Lampard's model the input processes are two independent Poisson processes; this results in a gamma Markov sequence for the time-interval between successive output pulses and a negative binomial Markov sequence for the counts at the times of out-put pulses. We consider the input process to be a bivariate Poisson process and show that the first out-put process given above is not affected, while the second out-put-process becomes of a type studied in the theory of branching processes.