Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Taylor series solution of the M/M/1 queueing system
Journal of Computational and Applied Mathematics
A new formula for the busy period of a non-empty multiserver queueing system
Applied Mathematics and Computation
Exact Transient Solutions of Nonempty Markovian Queues
Computers & Mathematics with Applications
The transient solution to M/Ek/1 queue
Operations Research Letters
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This paper studies the most general model of the Markovian queues namely M/M/1/∞ queue with any arbitrary number "i" of customers being present in the system initially. For this model, a new and simple series form is obtained for the transient state probabilities whence all particular cases concerning the system being empty and steady-state situations can be derived straightaway. The coefficients in this series satisfy iterative recurrence relations which would allow for the rapid and efficient numerical evaluations of the state probabilities. Moreover, a simple algebraic proof to show the equivalence between different formulae of a non-empty M/M/1/∞ and the new formula is established.