Why do people press elevator call buttons repeatedly? Many people, particularly those in a rush, keep on pressing the elevator call button despite the light clearly indicating that it was previously pressed, and the knowledge that such action will have no effect.

What theory explains such a behaviour?

I could put forth two hypotheses. When people are desperate they:


Prefer action over inaction - If an action does not carry a high price or penalty, by taking action people feel that at least they are doing something. 
Are more likely to change their beliefs. Complete atheists, for instance, may pray to God, or try a supernatural/spiritual healer, if the life of a dear one is on stake.


But I can't find a theory for neither of these.
It's an interesting phenomenon, and I think it can be seen in many other domains beyond lifts. At least where I live, pedestrian crossings have buttons, which I've seen people repeatedly press. You can see it often on computers and other digital devices when the system does not immediately respond to user input.

Basic Bayesian Rational Actor

My starting point for analysing the behaviour would be that of a bayesian rational actor. While you state that the individual "knows that such action will have no effect." This is not actually true. Many states of the world are possible about the consequence of second and subsequent button presses:


Beneficial: 


The first button press may not have been recorded (perhaps you didn't press the button correctly, perhaps the system malfunctioned)
Repeatedly pressing the button might increase the system's awareness of the importance of the request
The first button press may have timed-out and a second button press may resend the request

Makes no difference: 


The first button press has been recorded and the second button press makes no difference.

Detrimental:


The first button press was recorded. Any subsequent button press resets the time required.



So from the perspective of a Bayesian rational actor, the individual does not know the state of the world. Instead, each state has a certain probability of being true. And each state of the world has a certain cost/benefit. Thus, if the individual assigns very low probability to the detrimental option and minimal cost to the physical movement involved in pressing the button, and some small probability of any of the beneficial scenarios being true, then the beneficial scenarios have the greatest expected utility. This is despite the fact that the "makes no difference scenario" having very high probability of being true. 

The important point is that it is the subjective beliefs and subjective utility which drives action and not the objective state of the world. Most models of human action would also incorporate a random component. So even if people generally preferred not to do the repeated press, they might occasionally. Such randomness can be seen as rational behaviour in the broader sense, in that it allows the actor to sample the utilities associated with actions even if they aren't currently deemed to maximise utility.

Presumably many factors would influence the beliefs about truth and utility in this situation:


The clearer the indicator that the button has been pressed, the more likely the individual will believe that the button has been pressed. So for example, on some pedestrian crossings there is no indicator light, or sometimes the indicator light on a lift button stops working. In such cases, people would presumably be much more likely to repeatedly press.
The more experience someone has with the specific lift or even lifts in general, the less likely they are to draw on general experience with other lifts or with other button-based systems.
The longer the time passes between pressing the button and the lift not arriving, the more likely the individual is to believe that something has failed. Now in some cases this is a lift malfunction, but presumably often another button press would also seem like a more reasonable strategy than if little time has passed.
The cost is assigned to the physical press might vary between people and situations. Some might experience  minor social embarrassment of repeatedly pressing a lift button when others are present. Other people who are less energetic or active, may not wish to expend energy repeatedly pressing the lift button.


Further reading

If you're interested more about these ideas, you could check out some of the ACT-R research on strategy selection.