# Ponzi, Pyramid and Matrix Scheme

When a Ponzi scheme is not stopped by the authorities, it sooner or later falls apart for one of the following reasons:
1. The promoter vanishes, taking all the remaining investment money (which excludes payouts to investors already made).
2. Since the scheme requires a continual stream of investments to fund higher returns, once investment slows down, the scheme collapses as the promoter starts having problems paying the promised returns (the higher the returns, the greater the risk of the Ponzi scheme collapsing). Such liquidity crises often trigger panics, as more people start asking for their money, similar to a bank run.
3. External market forces, such as a sharp decline in the economy (for example, the Madoff investment scandal during the market downturn of 2008), cause many investors to withdraw part or all of their funds.

Similar:
• A pyramid scheme is a form of fraud similar in some ways to a Ponzi scheme, relying as it does on a mistaken belief in a nonexistent financial reality, including the hope of an extremely high rate of return. However, several characteristics distinguish these schemes from Ponzi schemes:
• In a Ponzi scheme, the schemer acts as a "hub" for the victims, interacting with all of them directly. In a pyramid scheme, those who recruit additional participants benefit directly. (In fact, failure to recruit typically means no investment return.)
• A Ponzi scheme claims to rely on some esoteric investment approach and often attracts well-to-do investors; whereas pyramid schemes explicitly claim that new money will be the source of payout for the initial investments.
• A pyramid scheme typically collapses much faster because it requires exponential increases in participants to sustain it. By contrast, Ponzi schemes can survive simply by persuading most existing participants to reinvest their money, with a relatively small number of new participants.

Matrix in queueing theory:
The basic premise of queueing theory is that when arrival rates equal or exceed service rates overall waiting time within the queue moves towards infinity.
The basic formulation includes three formulae. The traffic intensity, ρ, is the average arrival rate (λ) divided by the average service rate (μ):
$\rho = \lambda / \mu$
The mean number of customers in the system (N):
$N = \rho / (1 - \rho)$
And the total waiting time within the queue (T):
$T = 1 / (\mu - \lambda )$
It is possible to see that as arrival rates rise towards service rates the total waiting time (T) and mean number of customers in the system (N) will move towards infinity. Since service time can never exceed the arrival time in the standard matrix, and total waiting time can only be defined if service times exceed arrival times, the only way for the matrix queue to reach stability is for outside income sources to exceed those being entered into the system.

Currently there are no laws specifically naming matrix schemes illegal in the US. However, the US Federal Trade Commission has issued warnings to the public about these. Additionally, the US Federal Trade Commission and the UK Trading Standards have issued warnings to the public regarding the ease with which these models can be manipulated for fraudulent purposes.
Other countries may have different laws regarding these matrix sites, but information is unavailable at this time.