论文信息 - Transient analysis of the M/M/1 queue

Transient analysis of the M/M/1 queue

A new approach is used to obtain the transient probabilities of the M/M/1 queueing system. The first step of this approach deals with the generating function of the transient probabilities of the uniformized Markov chain associated with this queue. The second step consists of the inversion of this generating function. A new analytical expression of the transient probabilities of the M/M/1 queue is then obtained.

[1] Sheldon M. Ross,et al. Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2] J. Kingman. THE SINGLE SERVER QUEUE , 1970 .

[3] John Riordan,et al. Inverse Relations and Combinatorial Identities , 1964 .

[4] P. R. Parthasarathy. A transient solution to an M/M/1 queue: a simple approach , 1987, Advances in Applied Probability.

[5] Harshinder Singh,et al. On the probability that the kth customer finds an M/M/1 queue empty , 1992, Advances in Applied Probability.

[6] Ward Whitt,et al. Calculating time-dependent performance measures for the M/M/1 queue , 1989, IEEE Trans. Commun..

[7] Jean Pellaumail. Systèmes markoviens discrets stationnaires et applications , 1991 .

[8] R. R. P. Jackson,et al. Elements of Queueing Theory with Applications , 1962 .

[9] Ward Whitt,et al. Decompositions of theM/M/1 transition function , 1991, Queueing Syst. Theory Appl..

[10] G. M. Jenkins,et al. Stochastic Service Systems. , 1964 .

[11] R. A. Acton. Introduction to Congestion Theory in Telephone Systems , 1961 .

[12] D. V. Lindley,et al. Stochastic Service Systems. , 1963 .