Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
A new formula for the transient behaviour of a non-empty M/M/1/∞ queue
Applied Mathematics and Computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Analysis of random walks with an absorbing barrier and chemical rule
Journal of Computational and Applied Mathematics
Time dependent analysis of M/M/1 queue with server vacations and a waiting server
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
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It has been shown by Sharma and Tarabia [1] that a power series technique can be successfully applied to derive the transient solution for an empty M/M/1/N queueing system. In this paper, we further illustrate how this technique can be used to extend [1] solution to allow for an arbitrary number of initial customers in the system. Moreover, from this, other more commonly sought results such as the transient solution of a nonempty M/M/1/~ queue can be computed easily. The emphasis in this paper is theoretical but numerical assessment of operational consequences is also given.