Personal tools
You are here: Home → Electrical and Computer Engineering → Information Theory → Bits and Queues

Bits and Queues

Document Actions
  • Send this
  • Print this
  • Content View
  • Bookmarks
  • CourseFeed

Introduction   ::   Codes   ::   Bounds

Achievability of the bound

It can also be shown (with a lot of work!) that for an $\cdot/M/1$ queue, the upper bound can be achieved when the input process is Poisson with rate λ.

Thus

\begin{displaymath} C = e^{-1} \mu \text{ nats/s}. \end{displaymath}

 

Information-bearing channels

We now generalize to the case where each packet actually carries some kind of information (e.g., bits). I will mostly summarize the results. Let the channel have information-bearing capacity C0 in nats/sec.


Observe that if C0 is sufficiently large, then the λ that maximizes capacity is equal to μ, so no information is carried in the timing. Combining some theorem, we find:

\begin{theorem} \begin{displaymath} C_I \geq \begin{cases} \mu e^{-1} \e... ...\\ \mu C_0 & \text{otherwise}. \end{cases} \end{displaymath} \end{theorem} \begin{displaymath} C_I = 2 \mu e^{-1} \text{ nats/sec } = 1.06 \mu \text{ bits/second}. \end{displaymath}

 

Pretty cool!
Copyright 2008, by the Contributing Authors. Cite/attribute Resource. admin. (2006, May 17). Bits and Queues. Retrieved November 24, 2009, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture12_4.htm. This work is licensed under a Creative Commons License. Creative Commons License
Reuse Course
Download this course