Stochastic NetworksCommunication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical structure of the arrival streams of packets at routers in the Internet. How can routing, flow control and connection acceptance algorithms be designed to work well in uncertain and random environments? This compact introduction illustrates how stochastic models can be used to shed light on important issues in the design and control of communication networks. It will appeal to readers with a mathematical background wishing to understand this important area of application, and to those with an engineering background who want to grasp the underlying mathematical theory. Each chapter ends with exercises and suggestions for further reading. |
Contents
Markov chains | 13 |
Further reading | 21 |
Open migration processes | 30 |
Littles | 36 |
Generalizations | 44 |
Approximation procedure | 51 |
4 | 85 |
5 | 108 |
6 | 133 |
Internet congestion control | 151 |
8 | 186 |
Appendix A Continuous time Markov processes | 201 |
| 217 | |
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Common terms and phrases
allocation ALOHA ALOHA protocol approximation arrival rate assume attempts backlog behaviour blocking probability buffer capacity Chapter circuits concave function congestion Consider constraints converges convex customers deduce Define delay drift effective bandwidth electrical network equilibrium distribution Erlang example Exercises Exercise exponentially distributed Figure finite first fixed point flow graph incidence matrix increase independent Lagrange multipliers Lagrangian linear loss network Lyapunov function Markov chain Markov process matrix max-min fair maximize mean migration process minimize node non-negative number of packets objective function optimization problem packets arriving pair parameter Poisson process positive recurrent primal algorithm Proof proportionally fair queueing network random access random variable random walk Remark resource retransmission round-trip route schedule Section server Show slot solution solves stability stationary Suppose term Theorem throughput tion traffic trajectories transition rates transmission unique vector