stability of retrial queues with versatile retrial policy - European ...
stability of retrial queues with versatile retrial policy - European ...
stability of retrial queues with versatile retrial policy - European ...
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14 Stability <strong>of</strong> <strong>retrial</strong> <strong>queues</strong> <strong>with</strong> <strong>versatile</strong> <strong>retrial</strong> <strong>policy</strong>7. Stability <strong>of</strong> the <strong>retrial</strong> queue <strong>with</strong> batch arrivalsConsider a single server <strong>retrial</strong> queue <strong>with</strong> the <strong>versatile</strong> <strong>retrial</strong> <strong>policy</strong>. Let us now considerthat at every arrival epoch t k , k = 1,2,...,arandombatch<strong>of</strong>a k customers enters the system.If the server is busy at the arrival epoch, then the whole batch <strong>of</strong> customers joins theorbit, whereas if the server is free, then one <strong>of</strong> the arriving customers starts his serviceand the others join the orbit. We assume that the input flow <strong>of</strong> customers occurs accordingto a Poisson process <strong>with</strong> rate λ, the sequence <strong>of</strong> batch sizes {a k } is independent andidentically distributed <strong>with</strong> general distribution and mean a, where0< a0andμ = 0, so the driving sequence (7.2) will have thefollowing form:ξ n =∏ (λσn,u 1 n)∑k=1a (n)k + ( a 1 − 1 ) (I u 2 n ≤λ ) ( )λ− Iλ + θ λ + θ
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