References & Further Reading

References

S. M. Ross, Introduction to Probability Models, Academic Press, 11th ed., 2014
The primary reference for this chapter. Chapters 5 (Poisson process), 6 (CTMCs), and 8 (queueing theory) cover all the material in the same order. Ross's style is rigorous but example-driven.
J. R. Norris, Markov Chains, Cambridge University Press, 1998
The standard graduate-level treatment of both discrete-time and continuous-time Markov chains. Chapter 2 gives the most careful treatment of the generator matrix, Kolmogorov equations, and the matrix exponential solution.
P. Brémaud, Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, Springer, 1999
An excellent reference for the interplay between Markov chains, simulation, and queueing theory. Chapters on reversibility and product-form networks complement this chapter.
G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Oxford University Press, 3rd ed., 2001
A comprehensive probability text with excellent chapters on Poisson processes (Ch. 6), continuous-time Markov chains (Ch. 6), and queues (Ch. 11). Good for a second reading at a slightly higher level.
R. G. Gallager, Stochastic Processes: Theory for Applications, Cambridge University Press, 2013
Gallager's treatment of Poisson processes (Ch. 2) and CTMCs (Ch. 6) is notable for its clarity and careful attention to the relationship between the defining axioms and the derived properties. Excellent for telecommunications engineers.
L. Kleinrock, Queueing Systems, Volume 1: Theory, Wiley, 1975
The classic reference for queueing theory in computer and communications networks. Chapters 3–4 cover M/M/1, M/M/c, Erlang formulas, and Little's law with many worked examples from networking.
A. K. Erlang, Solution of Some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges, 1917
The foundational paper of queueing theory. Erlang derives the blocking formula (Erlang-B) for a telephone exchange with Poisson arrivals and a finite number of trunks. The unit of traffic intensity (Erlang) is named after him.
S.-D. Poisson, Recherches sur la probabilité des jugements en matière criminelle et en matière civile, Bachelier, Paris, 1837
The treatise where the Poisson distribution first appeared, derived as the limit of the binomial distribution. Historically important as the origin of the 'law of small numbers.'
A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, 4th ed., 2002
A widely used engineering probability text. Chapter 16 covers Poisson processes and CTMCs with an engineering perspective. Good for supplementary examples.
F. P. Kelly, Reversibility and Stochastic Networks, Wiley, 1979
The definitive reference on reversibility, quasi-reversibility, and product-form queueing networks. The insensitivity of Erlang-B (Exercise 17) is a special case of Kelly's general theory.
M. Haenggi, Stochastic Geometry for Wireless Networks, Cambridge University Press, 2013
The standard reference for stochastic geometry models of wireless networks. Chapters 2–3 develop the spatial Poisson point process, building directly on the Poisson properties of this chapter.
F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks, NOW Publishers, 2009
A two-volume monograph on spatial stochastic models for wireless networks. Volume I develops the theory; Volume II covers applications to MAC protocols and interference management.