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COMPUTATIONAL APPROACH FOR TRANSIENT BEHAVIOUR OF M /M (a, b) /1 BULK SERVICE QUEUEING SYSTEM WITH MULTIPLE VACATION AND CATASTROPHE

S. Shanthi, A. Muthu Ganapathi Subramanian, Gopal Sekar

Abstract


In this paper, the transient behavior of single server bulk service queueing system with multiple vacation and catastrophe model has been considered. Multiple vacations follow exponential distribution and Catastrophe follows a Poisson process while the returning from inactive state to vacation state follows Poisson distribution. An infinitesimal generator matrix is formed for all transitions. Time dependent solutions and steady state solutions are acquired by using Cayley Hamilton theorem. Numerical studies have been done for time dependent average number of customers in the queue, transient probabilities of server busy, server is in vacation and server is in inactive for several values of t, λ, µ, α, γ, δ, a and b.


Keywords


Bulk Service; Multiple Vacation; Catastrophe; Infinitesimal Matrix; Direct Truncation Method; Cayley Hamilton; Exponential of a Matrix.

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References


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