JPL's Wireless Communication Reference Website

Chapter: Data Networks
Section: Random Access

Throughput of Random Access Schemes

An important measure of performance is the throughput. In slotted systems, the slot length is taken as the unit of time.

In virtually all protocols (including ALOHA, CSMA, ISMA), S is approximately equal to G for small G, i.e., if the channel is lightly loaded. At larger traffic loads (larger G), conflicts, called "collisions" occurs, so S < G

 
Figure: Throughput S [in packets per unit of time] versus attempted traffic G for slotted ALOHA, unslotted ALOHA, non-persistent CSMA and 1-persistent CSMA

Throughput Analysis

  Algorithm Throughput S
S for G =
Average number
of attempts G/S
 
  Slotted ALOHA S = G exp[-G] S = G/S=
Unslotted ALOHA S = G exp[-2G] S = G/S=
Nonpersistent CSMA and ISMA S = G /(1+G) S = G/S=
1-persistent CSMA and ISMA S = (G + G2) / (1 + G * exp[G]) S = G/S=

Non-persistent CSMA / ISMA is the only curve for which S does not reduce to zero for large G. If terminals can indeed infinitely fast sense the channel, as is assumed here, collisions can be avoided completely.

Note that the average number of (re-) transmission attemps only equals G/S in a stable system. Stability is problematic is retransmission waiting times are short in a network with many terminals.

Mathematica Source Code

Plot[{G Exp[-G], G Exp[-2 G], G /(1+G),
 (G + G*G) / (1 + G * Exp[G])}, {G, 0, 5 },
  Frame -> True]

Performance over wireless channels

In a wireless channel performance differs substantially from the performance over cable Local area Network. The following figures compare various random access methods for the following set of parameters and assumptions:

 
Figure: Probability that an access attempt is successful versus the distance between terminal and base station.
  • orange: slotted ALOHA
  • blue: non-persistent ISMA, with signalling delay d. The attempt may fail if the terminal is inhibited.
  • green 1-persistent ISMA
 
 
  Figure: Throughput (in packet per unit of time) versus attempted traffic.  

The above curves suggest that the mobile channel gives a better performance than the (wired) channel with capture. This is due to the capture effect.


JPL's Wireless Communication Reference Website Jean-Paul M.G. Linnartz, 1993, 1996.