Abstract
This paper studies the transient behaviour of a single-channel queueing problem wherein (i) the input, following aPoisson distribution, is in batches of variable size (ii) the queue discipline is first-come-first-served; it being assumed that the batches are pre-ordered for service purposes (iii) the output, following a general distribution, is in batches of variable size. TheLaplace transform of the probability generating function of the waiting line size is obtained and the corresponding results are derived when the service time distribution is (i) hyper-exponential with m branches (ii) phase-type and (iii) exponential. Finally, some particular cases are discussed.
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Murari, K. A queueing problem with arrival and service in batches of variable size. Metrika 19, 27–35 (1972). https://doi.org/10.1007/BF01893274
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DOI: https://doi.org/10.1007/BF01893274