In this paper we deduced explicitly expressions for the transient state distribution for a queueing problem having chemical" rules with arbitrary number of customers present initially in the system, in addition to having the possibility of catastrophe and hence system repair. Our calculations based on using generating function and Laplace transformation techniques, the obtained solution of the probabilities distribution enables us to recover the well known formula and other cases such as the transient solution of the standard M/M/1/∞ queue with λ = μ. Finally, the theory is underpinned by numerical results."
Alshreef, G. and Tarabia, A.
"Transient Analysis of Chemical Queue with Catastrophes and Server Repair,"
Information Sciences Letters: Vol. 12
, PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol12/iss2/2