JPL's Wireless Communication Reference Website

Chapter: Data Networks
Section: Random Access, ALOHA

Throughput of ALOHA Networks

To express the throughput of the ALOHA random access scheme, it is often assumed that message transmission attempts occur according to a Poisson process with rate G attempts per slot. For channels in which a transmission is successful if and and only if in that slot only a single packet transmission is present, the throughput of successful messages is equal to Both arguments yield the well-known result for the throughput of slotted ALOHA:
      S = G  exp{-G}
For unslotted ALOHA without capture, a test packet is destroyed by any overlapping transmission starting in the time window that Hence, packets transmitted over an unslotted ALOHA channel see on average twice as many interfering packets as in slotted ALOHA. In fact
      S = G  exp{-2 G}
Both unslotted and slotted ALOHA exhibit the typical behaviour that

ALOHA in Mobile Radio Nets

In a radio channel, packets may be received successfully despite interference from competing terminals. This is called `receiver capture'. The larger the differences in received signal power, the more likely it is that one signal is sufficiently strong to capture the receiver

The throughput becomes G times the probability that a particular (a priori chosen) packet is sufficiently stronger than the sum of all interfering packets.

Figure: Throughput S of Slotted ALOHA network (in packet per time slot) versus the attempted traffic G.

Note that some capture models do not predict that S reduces to zero for large G.

Figure: Probability that an access attempt is successful versus the distance between terminal and base station.

Computation of Throughput

The throughput S is found as the offered traffic, multiplied by the probability that a particular, a priori chosen test packet captures the receiver. Thus
S = G   sum      Prob(capture |i interferers)    Prob ( i interferers)
       i = 0
where the probability on i interferers is Poissonian with value G.

The capture probability equals one minus the outage probability. In most analyses, the probability of capture is first expressed for a given local mean power of the test signal. In a Rayleigh-fading channel, the probability of receiving a signal with local-mean power _0 can be expressed in terms of Laplace Transforms of the probability density functions of the power p_i of interferer i. That is,

                           ^i         ^i          z
P(capt | i) = Prob(capt|i=1) = Laplace  {p_i  ;   ---}
where z is the capture ratio or receiver threshold. This observation leads to the mathematically convenient definition of the interference-vulnerability weight function.

Throughput for various propagation and traffic distribution models

One can use the above expression to find the throughput for various distributions of terminals over the "service" area. The expressions for capture probabilities can also be used to find the network delay and stability.

JPL's Wireless Communication Reference Website 1993, 1995.