Analysis of Queue Size for N-Strategy and Multiple-vacation M/G/1 Queue with Bernoulli Interruption Vacation and Random Start-time
This article studies a N-strategy and multiple-vacation M/G/1 queuing model with Bernoulli interruption vacation and random start-time,in which Bernoulli interruption vacation means that if a customer arrives during the vacation,the waiter interrupts the vacation with probability p(0≤p≤l)and immediately starts the service facility,otherwise,he/she does not interrupt the vacation with probability(1-p)until the end of the vacation.After the system startup is completed,if the number of customers in the system is greater than or equal to the given threshold N,the server starts serving the customers until the system becomes empty again.We apply the total probability decomposition technology,the renewal process theory and the Laplace transform tool to discuss the transient queue-length distribution of the system at time t,and obtain the Laplace transform expressions of the transient queue-length distribution.On the basis of transient analysis,the recursive expressions of the steady queue-length distribution are derived by employing the L'Hospital's rule.Also,some other queueing indicators,such as the probability generating function of the steady queue-length distribution,the average queue size and the probability distribution of the additional queue-length,are presented by using some algebraic operations.Finally,some special cases are discussed.
Bernoulli interruption vacationRandom start-timeN-strategyTotal probability decompositionQueue-length distribution
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